MSC/PATRAN TUTORIAL # 1 MODELING A BAR PROBLEM
I. THE PHYSICAL PROBLEM
In the simple bar problem below, there are three separate sections of the bar. bar. Each section has different properties. The following properties apply, Al Aluminum, St Steel, E for Steel = 200 E !a, E for Al = "0 E !a All #ars ha$e s%uare cross section and the right and left ends of the bar are built in. The force &'& = 000 (ewtons
'
St
The 2)d model of the problem is shown below.
Al
F
St
Al 2 cm
1 cm
5cm F
5 cm
5 cm
10cm
2
II. THINKING ABOUT THE MECHANICS The analytic solution for stresses stresses and displacements for this problem problem is readily a$ailable. Any *echanics of *aterials te+t will pro$ide e%uations for the displacements and stresses throughout the bar. The problem is indeterminant because there there are two reactions reactions one at each wallwall- and
only one rele$ant e%uilibrium e%uation
necessary to use the ∑ F = 0 -. Therefore, itit is necessary x
*echanics of materials stress and or displacement- e%uations as well as the force e%uilibrium e%uations to sol$e the p roblem. The normal stress due to a+ial loading is gi$en by
σ xx = P
A , where ! is the internal force in the a+ial direction and A is the cross sectional area PL of the bar. The displacements displacements are computed from from u = here / is the bars length and E is AE the Elastic 1oungs- modulus. Some basic %uestions to consider before creating the computational model are . 3here will will the the stresses stresses be tensil tensile e and where where will they they be compress compressi$e4 i$e4 2. 3hat will will be the magnit magnitude ude and direc direction tion of of the reacti reaction on forces4 forces4 5. 3here 3here will will the the displa displacem cement ents s be greate greatest4 st4 6. 7ow do the the displacem displacements ents $ary $ary along the the length length linear, linear, %uadrati %uadratic c etc.-4 etc.-4 8. 3hat will will the the local effect effect of the concent concentrated rated load load be on the the stresses4 stresses4 9. Is the model model fully fully constrai constrained ned from from rigid rigid body rotatio rotations ns and displac displacement ements4 s4 Answering these questions qualitatively, along with the quantitative analytical solutions for the stresses and displacements, will provide reinforcement that your computational model is correctly constructed.
III. GEOMETRIC AND FINITE ELEMENT MODEL Some general notes on !AT:A( !AT:A( A general finite finite element analysis can be bro;en down into into 5 principle tas;s< tas;s< preprocessing, analysis and post processing. The p reprocessing tas; includes building the geometric model, building the finite element model, gi$ing these elements the correct properties, setting the boundary conditions and loading conditions and finally, assembling these elements into a connected structure for analysis. The analysis stage simply sol$es for the un;nown degrees of freedom, as well as reactions and stresses. In the postprocessing stage, the results are e$aluated and displayed. The accuracy of these results is postulated during this postprocessing tas;.
The !atran and (astran software together perform all 5 of the principle tas;s of a finite element analysis. The pre and post processors are uni%ue to !AT:A( itself. itself. 7owe$er, this pac;age allows the user to do the actual solution analysis on a $ariety of different pac;ages. At many sites you ha$e the option of using the *S>(astran pac;age, which is probably the most widely used sol$er in industry. *any of the other pac;ages commonly used in in industrial settings settings A#A?@AS, A#A?@AS, A(S1S, *A:*A:- are also compatible with with !AT:A(. !AT:A(.
IV. FINITE ELEMENT THEORY THEORY The exact details of the formulation of the rod elements in MSC/Nastran is given in the MSC/Nastran manuals and is somewhat lengthy. However, the basic formulation of an isoparametric 2 node rod element is not difficult and will provide us with sufficient background information to begin to understand the convergence and other accuracy studies. studies. This basic form can be found in any standard standard text of finite
5
element analysis. For Example see Finite Element Modeling for Stress Analysis, by R.D. Cook, John Wiley & Sons, 1995.
V. STEP BY STEP INSTRUCTIONS FOR MODELING THE BAR PROBLEM USING MSC/PATRAN @nless you ha$e used the !AT:A( software numerous times in the past, the steps shown below should be followed e+actly. 7owe$er, in order to prepare you to do independent finite element wor; using !AT:A( in the future, you are encouraged to go bac; after you ha$e completed the assignment and in$estigate modeling options using different !AT:A( selections. Also, I encourage you to ta;e notes as you go through this e+ercise in order to prepare for the time when you will be as;ed &build a certain geometric structure& or &apply a certain type of boundary condition& with out being gi$en the specific steps for carrying out this tas;.
The *S>!atran program is menu dri$en much in the same way that most 3indows programs are dri$en. Selecting a category from a menu may result in a pull down set of options or in a subordinate menu. Selections in menus may be in the form of buttons to turn on or off, or in the form of bo+es which re%uire te+t. Te+t entered into bo+es may be changed by positioning the cursor at the point of te+t insertion and either typing the new te+t or erasing the incorrect te+t. A standard finite element analysis normally proceeds across the top menus starting with eometry and ending with :esults. Selecting one of these top menus results in a set of menus which allow you to complete that tas; in the analysis process. enerally, it is best to attempt to proceed from the top of these menus toward the bottom, answering %uestions as you go. !reliminaries for using *S !atran and (astran normally include - /og in to the machine. 2- hange to the directory that you wish to contain your results. 5- To start the program *S>!atran, clic; on Start>!rograms>*Scommon- and choose *S !atran 0.
In the instructions below, the following abbre$iations and terms will be used TM = Top Men. This refers to the horiBontal menu options residing at the top of the screen after !AT:A( has been initiated. RM = R!"t Men. This refers to the menus that pop up after an option has been chosen from the top menu. These menus reside on the far right side of the !AT:A( des;top. SM = S$o%&!n'te Men. This referees to the menus that pop up from options selected in the right menu. C(!)* = @nless otherwise stated, this indicates a clic; with the left mouse button. Bo(&+')e will indicate te+t that occurs in the !AT:A( menus. Italics te+t will indicate te+t that you must enter into te+t bo+es in the !AT:A( menus or te+t that you choose in a menu scroll bo+.
Cur first step is to create a new database 'rom the T* choose F!(e In the resulting pull down menu choose Ne, A S* called Ne, D't'$'-e pops up Turn off no chec;- Mo&!+ P%e+e%en)e-
6
If the new database for has come up showing a directory on a remote computer as opposed to a directory on the local machine-, then switch the directory to the local directory cD*S @nder Ne, D't'$'-e N'e enter bar.db lic; O0 The geometry of the structure will be determined ne+t 'rom the T* choose Geoet% A :* called Geoet% will result Set A)t!on = Create O$e)t = Point Meto& = XYZ Set the Po!nt ID list to 1 Set Re+e%en)e Coo%&!n'te F%'e to Coord 0 Turn off the Ato E2e)te button Enter the following into the point coordinates list [0,0,0] [.05,0,0] [.10,0,0] [.20,0,0] note that !AT:A( will accept either commas or blan;s as separators between coordinateslic; App( At this point 6 points should appear on your &bar.db ) default$iewport ) defaultgroup ) entity& main $iewportThe ne+t Fob is to connect these points to form 5 lines 3hile still in the Geoet% :*, Set A)t!on = Create O$e)t = Curve Meto& = Point Turn off the Ato E2e)te button if it is on for the following, it is assumed that you ha$e created points ,2,5,6 numbered from left to right in the main $iewport. If the numbers are not in that order, follow the procedure below from left to right regardless of point numberslic; in the St'%t!n" Po!nt L!-t bo+ lic; on node in the main $iewport. lic; in the En&!n" Po!nt L!-t bo+ lic; on the point 2 in the main $iewport lic; on App( A line will be drawn from point to point 2. This line should be named line lic; in the St'%t!n" Po!nt L!-t bo+ lic; on point 2 in the main $iewport. lic; in the En&!n" Po!nt L!-t bo+ lic; on the point 5 in the main $iewport lic; on App( A line will be drawn from point 2 to point 5. This line should be named line 2lic; in the St'%t!n" Po!nt L!-t bo+ lic; on node 5 in the main $iewport lic; in the En&!n" Po!nt L!-t bo+ lic; on the point 6 in the main $iewport lic; on App( A line will be drawn from point 5 to point 6. This line should be named line 5-
8
The finite element mesh is specified ne+t 'rom the T* choose E(eent A :* appears called F!n!te E(eentSet A)t!on = Create O$e)t = Mesh eed Tpe = !ni"or# Select N$e% o+ E(eent- button downN$e% = Turn off the Ato E2e)te button uplic; in C%3e- L!-t bo+ lic; on the left most cur$e in the main $iewport The words &ur$e & will be added to the C%3e L!-tlic; App( circles which represent finite element nodes will appear on ends of the cur$elic; C%3e L!-t bo+ lic; on the center cur$e in the main $iewport the words &ur$e 2& will be added to the C%3e L!-tlic; App( circles which represent finite element nodes will appear on ends of the cur$elic; C%3e L!-t bo+ lic; on right most cur$e in the main $iewport the words &ur$e 5& will be added to the C%3e L!-tlic; App( circles which represent finite element nodes will appear on ends of the cur$eThe nodes created abo$e must now be tied together with elementsup at the top of the :*Set A)t!on = Create O$e)t = Mesh Tpe = Curve lic; on #ar2 under E(eent Topo(o" lic; C%3e L!-t #o+ lic; the left most cur$e in the main $iewport should be cur$e lic; App( lic; C%3e L!-t #o+ lic; the middle cur$e in the main $iewport should be cur$e 2lic; App( lic; C%3e L!-t #o+ lic; the right most cur$e in the main $iewport should be cur$e 5lic; App( numbers for the nodes will appear o$er the geometry pointsup at the top of the :*Set A)t!on = $%uivalence O$e)t = &ll Tpe = 'olerance Cube The purpose here is to tie the nodes together that lie on top of one anotherSet the E4!3'(en)!n" To(e%'n)e to .005 lic; App( at the bottom of the :*(The command window at the bottom of the PATRA des!top will tell you that " nodes were deleted. #n addition circles will appear over the ends of the middle curve to indicate the equivalencing of the $overlapping$ nodes%
9
The boundary conditions are specified ne+t 'rom the T* choose Lo'&/BC5 A :* called Lo'&/Bon&'% Con&!t!on- will appear Set A)t!on = Create O$e)t = (is)lace#ent Tpe = *odal Set C%%ent Lo'& C'-e = (e"ault Enter Ne, Set N'e as +Cla#) This is for the right and left clamping of the bar structurelic; Inpt D't'... a S* appears Set Inpt T%'n-('t!on- to -0,0,0 #e sure An'(-!- Coo%&!n'te F%'e is Coord0 lic; CG bac; in the Lo'&/Bon&'% Con&!t!on- :*lic; Se(e)t App(!)'t!on Re"!on Turn on the Geoet% button downlic; in bo+ under Se(e)t Geoet%!) Ent!t!e A !atran item menu appears Fust to the left of the :*lic; on the picture with a point in this menu In the main $iew port, clic; on the left most point on the line A S* called Se(e)t!on Co!)e- appears hoose Po!nt 1 This will cause the words &!oint & assuming point is the leftmost point on the line- to appear in the Se(e)t Geoet%!) Ent!t!e- bo+ in the :*lic; on A&& Fust below this bo+ This will remo$e the words &!oint & from the Se(e)t Geoet%!) Ent!t!e- bo+ and add them to the App(!)'t!on Re"!on bo+lic; in the Se(e)t Geoet%!) Ent!t!e- bo+ again. e&t 'lic! point " in the main view port (assuming point " is the right most point in the bar structure% A S* called Se(e)t!on Co!)e- appears hoose Po!nt 6 lic; A&& The App(!)'t!on Re"!on bo+ should now ha$e the words &!oint 2& in it and the Se(e)t Geoet%!) Ent!t!e- bo+ should be emptylic; CG The Lo'& / Bon&'% Con&!t!on :* appears againlic; App( 5 displacement constraint arrows should now appear in the main $iewport window on the e+treme right and on the e+treme left points in the bar structure-
The loads are specified ne+t ontinuing on in the Lo'&/BC5- :*change A)t!on = Create O$e)t = /orce Tpe = *odal hange the Ne, Set N'e to aial lic; Inpt D't'... a S* appears Enter the force $ector -1.$3,0,0
"
lea$e the moments lic; O0
i.e. blan;-
ontinuing on in the Lo'&/BC5- :*lic; Se(e)t App(!)'t!on Re"!on a Se(e)t App(!)'t!on menu appears as well as a small P't%'n item menu In the Se(e)t App(!)'t!on- menu, turn on the Geoet% F!(te% (e+t, clic; in the bo+ labeled Se(e)t Geoet%!) Ent!t!elic; in the P't%'n item menu Fust to the left of the :*- on the point icon In the main $iewport, clic; on the 5rd point from the left its number should be !oint 6- will be added to the Se(e)t Geoet%!) Ent!t!e- listlic; A&& the points number will be added to the App(!)'t!on Re"!on listlic; O0 Lo'&/BC5- menu now reappearslic; App( bottom of the :*7 A $ector with the load should appear on the 5rd point from the left in the main $iewport-
The materials are specified ne+t Cn the T* select M'te%!'(a :* will appear called M'te%!'(Set A)t!on = Create O$e)t = Isotro)ic Meto& = Manual In)ut lic; M'te%!'( N'e bo+ Input the name teel lic; Inpt P%ope%t!e S* called Inpt Opt!on- appears Input E('-t!) Mo&(- = 2.0$11 Input Po!--on = 0. lic; O0 #ac; in the *aterials :*, clic; App( lic; M'te%!'( N'e bo+ Input the name to be &lu#inu# lic; Inpt P%ope%t!e- bo+ S* called Inpt Opt!on- appears Input E('-t!) Mo&(- = 4.0$10 Input Po!--on = 0. lic; O0 #ac; in the *aterials :*, clic; App( The E2!-t!n" M'te%!'(- bo+ should ha$e teel and &lu#inu# in it-
The properties for each element are assigned ne+t Cn the T* select P%ope%t!ea :* will appear called E(eent P%ope%t!eSet A)t!on = Create D!en-!on = 1d
H
synta+
Tpe = rod lic; P%ope%t Set N'e bo+ Enter bar1 lic; Inpt P%ope%t!ea S* appears called Inpt P%ope%t!elic; in the M'te%!'( N'e bo+ lic; on the word &Steel& in the M'te%!'(- P%ope%t Set bo+ the words mSteel will appear in the M'te%!'( N'e bo+lic; in the A%e' bo+ Enter 0.0003 lic; O0 note If you Fust input the word Steel in the M'te%!'( N'e bo+, the element will not ha$e the correct properties. The e+act mSteel is necessary#ac; in the E(eent P%ope%t!e- :*lic; Se(e)t Me$e%- bo+ a !atran item menu will appear to the left of the :* In the item menu, clic; in the bo+ which contains the element with end nodes as opposed to the cur$e in the left bo+This allows you to pic; finite element entities as opposed to the geometric entities in the other bo+lic; on element in the main $iewport element is the left most element in the bar structureThe words Elm will appear in the Se(e)t Me$e%- bo+lic; A&& The words Element appear in the App(!)'t!on Re"!on bo+lic; App( in the E(eent P%ope%t!e- menu #ar will be added to the E2!-t!n" P%ope%t Set- bo+hange P%ope%t Set N'e to bar2 lic; Inpt P%ope%t!e-... a S* called Inpt P%ope%t!e- will appear lic; the M'te%!'( N'e bo+ lic; A(!n in the M'te%!'(- P%ope%t Set- bo+ The words mAluminum will appear in the M'te%!'(- N'e bo+hange the A%e' to 0.0028 lic; O0
#ac; on the E(eent P%ope%t!e- *enulic; the Se(e)t Me$e%- bo+ A !atran item menu appears Fust to the left of the :* In this item menu, clic; in the bo+ which contains the element with end nodes as opposed to the cur$e in the other bo+lic; on element 2 in the main $iewport Element 2 is the middle element in the bar structureThe words Elm 2 appears in the Se(e)t Me$e%- bo+lic; A&& The words Element 2 appear in the App(!)'t!on Re"!on bo+ (ote If anything other than Element 2 is in the App(!)'t!on Re"!on bo+, it must be deleted.lic; App( The words bar2 will be added to the E2!-t!n" P%ope%t!e- Setbo+hange P%ope%t Set N'e to bar5
lic; Inpt P%ope%t!e-... a S* called Inpt P%ope%t!e- will appear lic; the M'te%!'( N'e bo+ lic; A(!n in the M'te%!'(- P%ope%t Set- bo+ The words mAluminum will appear in the M'te%!'(- N'e bo+hange the A%e' to 0.0001 lic; O0 lic; the Se(e)t Me$e%- bo+ A !atran item menu appears Fust to the left of the :* In this item menu, clic; in the right bo+ which contains the element with end nodes as opposed to the cur$e in the other bo+lic; on element 5 in the main $iewport Element 5 is the right most element in the bar structureThe words Elm 5 appears in the Se(e)t Me$e%- bo+lic; A&& The words Element 5 appear in the App(!)'t!on Re"!on bo+ (ote If anything other than Element 5 is in the App(!)'t!on Re"!on bo+, it must be deleted.lic; App( The words bar5 will be added to the E2!-t!n" P%ope%t!e- Setbo+-
The analysis is to be done is specified ne+t Cn the T* select An'(-!a :* will appear called An'(-!Set A)t!on = &nal6e O$e)t = $ntire Model Meto& = /ull +un lic; on T%'n-('t!on P'%'ete%a S* will appear hange the D't' Otpt to OP6 'n& P%!nt lic; O0 lic; on So(t!on Tpe a S* will appear Set So(t!on Tpe = L!ne'% St't!) button downlic; O0 bac; in the analysis menulic; App( The analysis will ta;e a few seconds maybe 0J to runIn the :* analysis Set A)t!on = +ead 7ut)ut 2 O$e)t = +esult $ntities Meto& = 'ranslate lic; on Se(e)t Re-(t- F!(e a S* will appear 'ind and select the file $'%.op6 1ou may need to use the KfindL tools in 3indows to locate the file. Cccasionally (astran will put the M.op2 file in a weird place. Cccasionally it e$en puts the file on the hard dri$e of the license file ser$er. If you cannot find the file on your local
0
hard dri$e then loo; on the file ser$ers hard dri$e. The file ser$er for the (/ is N'E/A#0. The file ser$er for the library is 7C!!E:. 1ou should be able to access either of these from your local machine o$er the networ;lic; O0 #ac; in the An'(-!- :* lic; App( (e+t you will post process the results by $iewing and e+porting them Cn the T* select Re-(ta :* will appear called Re-(tSet A)t!on = Create O$e)t = 8uic9 Plot A S* appears @nder Se(e)t Re-(t C'-e highlight the option (e"ault, tatic ubcase @nder Se(e)t F%!n"e Re-(t 7ighlight (is)lace#ents, 'ranslational @nder Se(e)t De+o%'t!on Re-(t 7ighlight (is)lace#ents, 'ranslational lic; App( A olored picture displaying the displacement results will appear. It includes numeric results for ma+ and min displacement as well as color)coded results for the entire beam. To sa$e this plot use the Kcopy to lipboardL icon usually Fust to the right of the print icon- to copy the $iewport to the clipboard. Then paste the picture into a word processing document. If you want to print the $iewport directly, you can Fust use the normal 3indows commands 'ile>!rint(e+t, to see the stresses @nder Se(e)t Re-(t C'-e 7ighlight the option (e"ault, tatic ubcase @nder Se(e)t F%!n"e Re-(t 7ighlight tress, tensor hange the 8'nt!t to X Co#)onent @nder Se(e)t De+o%'t!on Re-(t 7ighlight (is)lace#ents, 'ranslational lic; App( A olored picture displaying the stresses results will appear. It includes numeric results for ma+ and min Stresses as well as color)coded results for the entire beam. To sa$e this plot use the Kcopy to lipboardL icon usually Fust to the right of the print icon- to copy the $iewport to the clipboard. Then paste the picture into a word document. If you want to print the $iewport directly, you can Fust use the normal 3indows commands 'ile>!rint-
(e+t you will end your !AT:A( session by sa$ing your database and e+iting Cn the T* select F!(e
'rom the pull down menu select S'3e Cn the T* select F!(e 'rom the pull down menu select 8!t
VI. E9ERCISES:
. 7and in the output file bar.f09. In this file, highlight the reaction forces, stresses and the displacements. 2. 7and in the two picture files which ha$e the pictures of your finite element model and the displacement and stress results. 5. Are any of the members in or close to the plastic range of the material4 6. hec; the problem against some analytic answer to see if your displacement and stress results are the correct order of magnitude. It might be easiest to sol$e the statically determinant problem and use that as a bound for the displacements and stresses as opposed to sol$ing the statically indeterminant problem. If you decide to use this approach, e+plain how the statically determinant problem gi$es bounds for the displacements and stresses. Are these upper or lower bounds4 Are your 'EA based answers consistent with this analytic chec;4 8. 3ill it increase the accuracy of the results to use a greater number of elements4 3hy or why not4 9. Are there any physical phenomena that this bar might e+perience that we ha$e not ta;en into account4 ". 3ill this type of element correctly capture the physics of the problem if the lower force is set to Bero and the upper force is maintained at 000 (4 3hy or 3hy not4
2
MSC Patran Tutorial # 2 Modeling of a Truss I. THE PHYSICAL PROBLEM: The truss structure shown below has nine members. Each of the members is made of aluminum and each has the same cross sectional area. The lower left corner of the structure is constrained in all three directions. The lower right hand corner is constrained in the 1 and O directions, but is free to roll in the P direction. A $ertical load of 00 (ewtons is applied at the midpoint of the top of the truss. The loading is directed downward. The truss geometry is symmetric about the $ertical line through the point at which the force is applied. *aterial properties, as well as physical dimensions, are gi$en below. 'or the truss below * " 1oungQs modulus = 0 x )0 N + ( m % Aluminum!oissonQs ratio = 0.5 Truss members are 5 cm P 5 cm- s%uare Y
P = 1;; Ne,ton-
1
X
1 6
II. THIN0ING ABOUT THE MECHANICS #efore you begin the computational model of the structure, study the structure for a few minutes to determine if it has any peculiarities. As; a few introductory %uestions I. Is the truss constrained from any rigid body displacements or rotations4 II. 3hat direction do you e+pect the reactions to be in4 III. 3hat magnitudes should the directions ha$e4 IR. Are there any KBero)forceL members in the truss4 R. @se the method of sections or another method if you prefer- to analytically determine the stresses in a few of the members.
III. THE GEOMETRIC AND FINITE ELEMENT MODEL In the modeling instructions below, the geometry is specified by creating the *S>!atran geometric entity called a &cur$e& between each of the trusss Foints. In this manner, each truss member becomes a separate cur$e in the geometric portion of the database. The lengths and directions of the cur$es correspond to those of the members in the physical truss structure. Each of the truss members is modeled using a single 2)node rod element. Each element is originally created with two uni%ue nodes which n o other element shares. The procedure called
5
&e%ui$alencing& in *S>!AT:A( creates a single node from two or more nodes which ha$e the same physical location. Therefore, after e%ui$alencing, there are nine elements and si+ nodes in this structure. These elements ha$e three displacement degrees of freedom per node. The elements can only model a+ial membrane- deformations. #ending type deformations, which are e$idenced by rotation of the element cross section, are not accounted for by this particular element. Torsion of the members is also neglected. The neglect of torsion and bending are $ery common assumptions in truss problems, as these are higher order effects in a great number of truss type structures. !hysically, this non)bending assumption is representati$e of pinned Foints for 2)N- or spherical Foints for 5)N-. It should be noted, howe$er, that there are some situations where these assumptions would not allow your model to correctly capture the physics of the problem. This type of modeling assumption should be carefully considered. The loading is modeled with a single concentrated force of magnitude 00 on the center node of the top of the structure. It is also possible to position loads on geometric entities li;e points and surfaces instead of on finite element entities li;e nodes. This is demonstrated in other tutorials. The boundary conditions are established by constraining the displacements at the lower left node to be Bero in all 5 directions and the lower right node to be Bero in the 1 and O directions. *aterial properties and lengths are input corresponding to the figure of the truss abo$e. (ote that it is not necessary to carefully number the nodes of the structure for minimiBation of the bandwidth of the stiffness matri+. The code automatically renumbers the nodes for bandwidth minimiBation before sol$ing the system of e%uations.
IV. THE FINITE ELEMENT THEORY The finite elements used to model two and three dimensional truss structures are actually Fust the simple 2)node bar elements spatially e+trapolated to function in two or three dimensional space. This spatial e+trapolation is in the form of a transformation of the a+ial d irection of the arbitrarily oriented bar into the global fi+ed- coordinate system. The results of the transformation is found in the following stiffness matri+ for the two dimensional case.
c" cs − c " − cs s " − cs − s " A E cs K = " L − c " − cs c cs " cs s " − cs − s where the order of the degrees of freedom is { u) , v) , u " , v " } . The A, E, and / are the cross sectional area, 1oungQs elastic- modulus and a+ial length respecti$ely. The c and s in the matri+ stand for os θ - and Sin θ - respecti$ely. The orientation of the bar and the angle θ are shown below.
V2 U2
V1
Y O X U1
6
This element does not ha$e any stiffness associated with rotational degrees of freedom. Therefore, bending and torsion effects are not included in this model nor is it possible to load the structure with moments. Also, the element, in the manner it is used in this analysis, does not ha$e the ability to model large deformations and will not warn the user in case of buc;ling type failures i.e. geometric nonlinearities-. Similarly, this type of analysis does not ha$e the ability to correctly model stresses which are not in the elastic range of the material i.e. material nonlinearities-.
V. STEP BY STEP INSTRUCTIONS FOR BUILDING THE TRUSS MODEL USING PATRAN !reliminaries for using *S>!AT:A( include - /og on to the computer 2- hange to the directory that you wish to contain your analysis results 5- /eft clic; STA:T lower left corner of the (T des;top-, go to !:C:A*S, then top *S common-, then to *S !atran 0. This will bring up the *S>!atran !rogram.
In the instructions below, the following abbre$iations and terms will be used TM = Top Men. This refers to the horiBontal menu options residing at the top of the screen after !AT:A( has been initiated. RM = R!"t Men. This refers to the menus that pop up after an option has been chosen from the top menu. These menus reside on the far right side of the !AT:A( des;top. SM = S$o%&!n'te Men. This referees to the menus that pop up from options selected in the right menu. C(!)* = @nless otherwise stated, this indicates a clic; with the left mouse button. Bo(&+')e will indicate te+t that occurs in the !AT:A( menus. Italics te+t will indicate te+t that you must enter into te+t bo+es in the !AT:A( menus or te+t that you choose in a menu scroll bo+.
. Cur first step is to create a new database 'rom the T* choose F!(e In the resulting pull down menu choose Ne, D't'$'-e A S* called Ne, D't'$'-e pops up Turn off button up- Mo&!+ P%e+e%en)e@nder Ne, D't'$'-e N'e enter truss.db lic; O0 A menu called Ne, Mo&e( P%e+e%en)e- will appear Select To(e%'n)e to be $'-e& on te o&e( Set Mo&e( D!en-!on = 2.0 An'(-!- )o&e = MSC/N'-t%'n An'(-!- Tpe = -t%)t%'( lic; O0
2. The geometry of the truss will be determined ne+t 'rom the T* choose Geoet%
8
A :* called Geoet% will result Set A)t!on = Create O$e)t = Curve Meto& = XYZ Set the C%3e ID list to 1 Set Re+e%en)e Coo%&!n'te F%'e to Coord 0 Turn off the Ato E2e)te button unchec;Enter the following into the Ve)to% Coo%&!n'te- list -1,0,0 Enter the following into the O%!"!n Coo%&!n'te- list -0,0,0 note that !AT:A( will accept either commas or blan;s as separators between coordinateslic; App( #uild the rest of the truss using the following table /ine (umber 2 5 6 8 9 " H
Rector oordinates ,0,0 0,,0 0,,0 ,0,0 ,,0 ,0,0 ,),0 ,0,0 0,,0
Crigin oordinates 0,0,0 0,0,0 ,0,0 0,,0 0,0,0 ,0,0 ,,0 ,,0 2,0,0
(ote that the commands onstruct, /ine, P1O do (CT wor; based on the coordinates of the 2 end points of the truss member. These commands generate lines based on the origin and the $ector for that particular truss member. (ote that if you ma;e a mista;e you can erase by clic;ing on the undo button on the top of the !AT:A( des;top. This will erase the /AST C(ST:@TIC( C**A(N C(/1. In other words, it will ta;e the process bac; to before you hit the App( button the last time. 5. The boundary conditions are specified ne+t 'rom the T* choose Lo'&/BC5 A :* called Lo'&/Bon&'% Con&!t!on- will appear Set A)t!on = Create O$e)t = (is)lace#ent Tpe = *odal Set C%%ent Lo'& C'-e = (e"ault Enter Ne, Set N'e as le"t"i This is for the clamping of the left most bottom nodeslic; Inpt D't'... a S* appears Set Lo'&/BC S)'(e F')to% = 1. Set T%'n-('t!on- to -0,0,0 /ea$e the Rot't!on- blan; #e sure An'(-!- Coo%&!n'te F%'e is Coord0 lic; CG bac; in the Lo'&/Bon&'% Con&!t!on- :*lic; Se(e)t App(!)'t!on Re"!on
9
a S* called Se(e)t App(!)'t!on Re"!on appears with a Select menu on its left edge. In the Se(e)t App(!)'t!on Re"!on S* Turn on the Geoet% button downlic; in bo+ under Se(e)t Geoet%!) Ent!t!eIn the Select *enu which is Fust to the left of the S*lic; on the picture with a point In the main $iew port, clic; on point left most point on the bottom edge A Selection hoices menu will appear. hoose !oint . This will cause the words &!oint & to appear in the Se(e)t Geoet%!) Ent!t!e- bo+ in the :*lic; on A&& Fust below this bo+ This will remo$e the words &!oint & from the Se(e)t Geoet%!) Ent!t!e- bo+ and add them to the App(!)'t!on Re"!on bo+lic; CG The Lo'& / Bon&'% Con&!t!on :* appears againlic; App( 5 displacement constraint arrows and the numbers ,2,5 should now appear in the main $iewport window on the e+treme right point on the bottom of the truss-
#ac; in the :* called Lo'&/Bon&'% Con&!t!onSet A)t!on = Create O$e)t = (is)lace#ent Tpe = *odal Set C%%ent Lo'& C'-e = (e"ault Enter Ne, Set N'e as ri:ht"i This is for the clamping of the right most bottom nodeslic; Inpt D't'... a S* appears Set Lo'&/BC S)'(e F')to% = 1. Set T%'n-('t!on- to - ,0,0 (ote the space left in before the first comma in the T%'n-('t!on$ector. This ensures that the P direction is (CT constrained /ea$e the Rot't!on- blan; #e sure An'(-!- Coo%&!n'te F%'e is Coord0 lic; CG bac; in the Lo'&/Bon&'% Con&!t!on- :*lic; Se(e)t App(!)'t!on Re"!on a S* called Se(e)t App(!)'t!on Re"!on appears with a Select menu on its left edge. In the Se(e)t App(!)'t!on Re"!on S* Turn on the Geoet% button downlic; in bo+ under Se(e)t Geoet%!) Ent!t!eIn the Select *enu which is Fust to the left of the S*lic; on the picture with a point In the main $iew port, clic; on point 8 right most point on the bottom edge A Selection hoices menu will appear. hoose !oint 8. This will cause the words &!oint 8& to appear in the Se(e)t Geoet%!) Ent!t!e- bo+ in the :*lic; on A&& Fust below this bo+
"
This will remo$e the words &!oint 8& from the Se(e)t Geoet%!) Ent!t!e- bo+ and add them to the App(!)'t!on Re"!on bo+lic; CG The Lo'& / Bon&'% Con&!t!on :* appears againlic; App( 2 displacement constraint arrows and the numbers 2,5 should now appear in the main $iewport window on the e+treme right point on the bottom of the truss6. The loads are specified ne+t ontinuing on in the Lo'&/BC5- :*change A)t!on = Create O$e)t = /orce Tpe = *odal hange the Ne, Set N'e to to)load lic; Inpt D't'... a S* appears Enter the force $ector -0 , ;100 , 0 lea$e the moments - i.e. blan;lic; O0 ontinuing on in the Lo'&/BC5- :*lic; Se(e)t App(!)'t!on Re"!on A S* called Se(e)t App(!)'t!on Re"!on appears with a select menu Fust to its left In the Se(e)t App(!)'t!on Re"!on menu Select the Geoet% F!(te% =
8. The finite element mesh is specified ne+t 'rom the T* choose E(eent A :* appears called F!n!te E(eentSet A)t!on = Create O$e)t = Mesh eed Tpe = !ni"or# Select N$e% o+ E(eent- button downN$e% = Turn off the Ato E2e)te button uplic; in C%3e- L!-t bo+ lic; on cur$e in the main $iewport cur$e is the line between point and point 2. This is the bottom left part of the trussThe words &ur$e & will be added to the C%3e L!-t-
H
lic; App( circles which represent finite element nodes will appear on points and 2No the same for cur$es 2). The nodes created abo$e must now be tied together with elementsup at the top of the :*Set A)t!on = Create O$e)t = Mesh Tpe = Curve lic; on #ar2 under E(eent Topo(o" lic; C%3e L!-t #o+ lic; cur$e in the main $iewport lic; App( No the same for cur$es 2) To see the element numbers on the truss, clic; the K/abel ontrolL button /oo;s li;e an K/L- on the top row menu. This adds a label control tool bar which allows you to turn on>off labels for different geometric and>or finite element entities.
up at the top of the :*Set A)t!on = $%uivalence O$e)t = &ll Tpe = 'olerance Cube The purpose here is to tie the nodes together that lie on top of one another/ea$e the No&e- to $e E2)(&e& list blan; Set the E4!3'(en)!n" To(e%'n)e to .001 lic; App( The command window at the bottom of the !AT:A( des;top will tell you that 2 nodes were deleted-
9. The materials are specified ne+t Cn the T* select M'te%!'(a :* will appear called M'te%!'(Set A)t!on = Create O$e)t = Isotro)ic Meto& = Manual In)ut lic; M'te%!'( N'e bo+ Input the name to be &lu#inu# lic; Inpt P%ope%t!e- bo+ S* called Inpt Opt!on- appears Input E('-t!) Mo&(- = 4.0$10 Input Po!--on = 0. O0 #ac; in the *aterials :* lic; App( The E2!-t!n" M'te%!'(- bo+ should ha$e &lu#inu# in it-
". The properties for each element are assigned ne+t Cn the T* select E(eent P%ope%t!e-
a :* will appear called E(eent P%ope%t!eSet A)t!on = Create D!en-!on = 1d Tpe = +od lic; P%ope%t Set N'e bo+ Enter truss1 lic; Inpt P%ope%t!ea S* appears called Inpt P%ope%t!elic; in the M'te%!'( N'e bo+ lic; on the word &Aluminum& in the M'te%!'(- P%ope%t Set bo+ the words mAluminum will appear in the M'te%!'( N'e bo+lic; in the A%e' bo+ Enter .000= recall that the members cross section was 5cm + 5cm s%uarelic; O0 #ac; in the E(eent P%ope%t!e- :*lic; Se(e)t Me$e%- bo+ In the select menu Fust to the left of the S* lic; in the bo+ which contains finite element with 2 end nodes This allows you to pic; finite element entities as opposed to the geometric entities in the other bo+*o$e the cursor arrow to a point to the left and abo$e the highest, left) most point on the truss. lic; and hold down the left mouse button. Nrag the cursor while holding down the mouse button- to a point to the right of and below the right)most bottom node. A &selection bo+& is formed while you drag. :elease the button. The words Elm will appear in the Se(e)t Me$e%- bo+lic; A&& The words Element appears in the App(!)'t!on Re"!on bo+lic; App( in the E(eent P%ope%t!e- menu truss will be added to the E2!-t!n" P%ope%t Set- bo+-
H. The analysis is to be done is specified ne+t Cn the T* select An'(-!a :* will appear called An'(-!Set A)t!on = &nal6e O$e)t = $ntire Model Meto& = /ull +un lic; on So(t!on Tpe a S* will appear lic; on T%'n-('t!on P'%'ete% A S* called T%'n-('t!on P'%'ete%- will appear Set D't' Otpt to 7P2 and Print lic; O0 #ac; in the An'(-!- :* Set So(t!on Tpe = St't!) button downlic; O0 bac; in the :* An'(-!-lic; App( The analysis will ta;e a few seconds to run-
20
(ow well read the results into the graphics database bac; in the :* An'(-!-Set A)t!on = +ead 7ut)ut2 O$e)t = +esult $ntities Meto& = 'ranslate lic; on Se(e)t Re-(t- F!(e hoose truss.o)2 you may need to go to the root or home directory to find this. If this file does not e+ist, then there was an error in your model. o to the file truss.log or truss.f09 to attempt to find out what error occurred.#ac; in the An'(-!- :* lic; App( . RisualiBe the results 'rom the T* choose Re-(t A :* called Re-(t- appears Set Action = reate CbFect = ?uic; !lot @nder Se(e)t F%!n"e Re-(t hoose (is)lace#ents, 'ranslational et 8'nt!t > Y Co#)onent @nder Se(e)t De+o%'t!on Re-(t-, choose (is)lace#ents, 'ranslational lic; App( A deformed plot appears with colors indicating the le$el of deformation. (ote that the $isual deformation of the truss is magnified so that you can see the deformation KmodeL. The actual truss deformations are $ery small< as can be seen by the numerical $alues, which are (CT scaled(ote that you can also $iew the stress results in this manner. Simply choose St%e--< Ten-o% from the Se(e)t F%!n"e Re-(t options. :ecall that there are a number of ways to compute and e+trapolate the stresses for a bar and these will ma;e significant differences in the $alues which are plotted. 0. hec; the written report of the truss results. The file containing the written results from the analysis is scaled truss.f09. Cpen the file by simply double clic;ing on it-. The file might be in the root or home directory or in the directory from which you ran the analysis. In this file find the displacement $ectors and record the numerical $alues. These will help you answer some of the %uestion below. Also, find the $ectors for the stresses and constraint forces and record these $alues.
(e+t you will end your *S !AT:A( session by sa$ing your database and e+iting Cn the T* select F!(e 'rom the pull down menu select S'3e Cn the T* select F!(e 'rom the pull down menu select 8!t
VII.
8UESTIONS FROM THE TUTORIAL: MODELING A TRUSS
The %uestions below refer to the truss model described at the beginning of this tutorial. Also, information from the output file truss.f09 will be needed in order to answer many of these
2
%uestions. As used below, the term &e$e% & refers to the portion of a truss structure between two Foints. 'or e+ample, the top of this structure has two horiBontal members which are connected by the Foint at which the load is applied. 1'. 3hat is the ma+imum displacement for the structure 4 1$. Is this displacement consistent in location, magnitude and direction with your physical intuition 4 6'. 3hat is the ma+imum stress in the structure 4 6$. Is this stress consistent in location, magnitude and direction with your physical intuition 4 . Are there any members with $ery low stresses4 Noes this ma;e physical sense4 >. 7ow many e%uations are sol$ed in order to determine the displacements for this structure 4 ?. 3hat assumptions are in$ol$ed in using this specific element as opposed to using a 2 node beam element with 9 degrees of freedom 5 displacements and 5 rotations- per node 4 @. The present model uses a single 2)node bar element for each truss member. 3ould the accuracy of the model increase if two bar elements were used to model each truss member 4 Vustify your answer. '. The resultant forces sometimes called constraint, restoring or reaction forces-, are located at the nodes where the boundary conditions are applied. State how these resultant forces can be used as a &necessary but not sufficient& test of the accuracy of your analysis. $. Noes your analysis pass this test 4 . If two nodes in your final truss structure ha$e the e+act same physical location but different node numbers, what part of the !AT:A( analysis procedure has been left out 4 '. 7ow could the element properties be changed to model this truss if the members in the structure were circular hollow aluminum bars. Assume that the outside diameter is 5 cm and the inside diameter is 2 cm. :emember that this structure only models the membrane a+ialdeformation not the bending deformation of each member. $. If you wanted to account for bending deformation in your model, could you use this same adFustment to the physical properties to model the truss with hollow members 4 1;. Assume that the cross sectional area of the truss members is incorrectly input in s%uare cm as opposed to s%uare meters. If the other data for the problem is input using meters, what would the ma+imum deflection of the truss be 4 11. Assuming that the rotations of the cross sections of the bars are small, what will be the difference between the results of your !AT:A( analysis and the e+act analysis 4 &e+act& here refers to the analytic analysis using standard structural analysis methods16'. Some truss structures may be designed so that, if certain members of the truss are damaged to the e+tent that they no longer ha$e significant stiffness, the structure will still be able to handle reasonable loading. This type of truss assembly is said to ha$e redundant members. 3ithout changing the number of elements in the structure, suggest a method of using *S !AT:A( to determine if there are redundant members in this truss structure. 16$. @se the method de$eloped in 5a- to determine if one of the diagonal members is redundant. 16). @se the method de$eloped in 5a- to determine if one of the $ertical members is redundant. 1'. !redict the deflection if the direction of the load is changed from the negati$e 1 direction, to the O direction note from your nodal location information that this truss is located in the P ) 1 plane-. 1$. :un the analysis and e+plain the displacement results. 1>'. !redict the effect of remo$ing the displacement boundary condition on the lower right node of the truss structure 4 1>$. :un the analysis and e+plain the displacement results.
22
MSC/PATRAN TUTORIAL # MODELING A CANTILEVERED BEAM ITH END LOAD USING > NODE SHELL ELEMENTS I. THE PHYSICAL PROBLEM The beam below is cantile$ered or &built in& on the left edge. This means that both the translations and the rotations are held to Bero along this edge. A point or concentrated load of magnitude 000 ( appro+imately 228 lb- in the negati$e 1 direction is found at the tip of the beam. This problem is part of a standard set of test cases for finite elements published in a paper by *ac(eal and 7arder *ac(eal founded the company that ma;es the 'EA code *S>(AST:A( *S>(AST:A( and *S>!AT:A(-. The set of problems is called & The *ac(eal ) 7arder Test ases&. The material properties for the beam are E= 200 + 0 !ascals typical for steel- and
ν = 0.0 as the analytic beam theory we use below does not ta;e !oisons ration effects into account-. The beam has a solid rectangular cross section section with thic;ness in the O)direction O)direction t = 0. meters and height in the 1)direction h = 0.2 meters.
1
25
P=1000 N
h=20 cm
+
L= 6.0 m
II. THINKING ABOUT THE MECHANICS The analytic solution for stresses stresses and displacements for this problem problem is readily a$ailable. Any *echanics of *aterials te+t will pro$ide e%uations for the ma+ stress located at the bu ilt in edge and on either the top fiber for ma+ tensile stress or the bottom fiber for ma+ compressi$e stressand the ma+ displacement located, located, of course, at the free tip where the the load is applied-. These e%uations are gi$en below. 'or the normal stress due to bending
σ xx ( x% =
M ( x % y I
so that the ma+ ma+ $alue located at the built)in edge is
σ xx MAX −
=
PL( h" % ) )"
bh
.
'or the displacement at the tip of the beam ma+imum displacement-
δ Y ( x = L% =
PL EI
Some basic %uestions to consider before creating the computational model are a3her 3here e wil willl the the str stres esse ses s be be tens tensil ile e and and wher where e wil willl the they y be be com compr pres essi si$e $e4 4 b3hat 3hat wil willl be the the magn magnit itude ude and and dire direct ctio ion n of the the rea react ctio ion n forc forces> es>mo mome ment nts4 s4 c3here will the stresses be Bero4 d7ow 7ow do the the disp displa lace ceme ment nts s $ary $ary alo along ng the the len lengt gth h li linea near, r, %uad %uadra rati tic c etc. etc.-4 -4 e3hat 3hat will will the the loc local al effe effect ct of the the conc concen entr trat ated ed loa load d be be on on the the stre stress sses es4 4 fIs the the mod model el full fully y con const stra rain ined ed fro from m rig rigid id body body rot rotat atio ions ns and and dis displ plac acem emen ents ts4 4 Answering these %uestions %uestions %ualitati$ely, %ualitati$ely, along with the the %uantitati$e analytical analytical solutions solutions for the ma+ stress and displacement will pro$ide reinforcement that your computational model is correctly constructed.
III. GEOMETRIC AND FINITE ELEMENT MODEL As is the standard standard procedure for building building *S>!atran *S>!atran models, we will will build the geometry first and then construct a finite element element mesh on that geometry. The geometry will proceed proceed from creation of points to lines to surfaces for this this simple model. (e+t, we will use 6 node shell elements deforming in their membrane membrane mode to model the beam. In this e+ercise, we will will $ary the e+act number and configuration of these elements. elements. This is discussed in detail in in the ne+t paragraph. (e+t, the material and element element properties will be entered. entered. 3e will constrain the the 5 displacement and 5 rotational degrees of freedom on the left left edge for both nodes-. This creates the cantile$ered or built)in, built)in, end condition. Then we will, place a point point load of magnitude 000 on the
26
top right node of the tip or right)mostright)most- element. This load will be in the negati$e negati$e 1 direction. 'inally, the nodes must be e%ui$alenced before the analysis is ready to run. #elow, we show 8 mesh configurations configurations for the beam labeled KaL through through KeL-. omparison of results between mesh KaL and mesh KbL will indicate of how the number of elements affects the models ability to correctly correctly model a beam problem. Increasing the number of elements in in a mesh in order to increase the accuracy of the results results is called KhL con$ergence. *eshes KbL U KeL all ha$e 9 elements< but the elements ha$e different different orientations. Elements that ha$e non)regular non)regular shapes are said to be distorted. distorted. Nistorted elements elements can cause errors in the 'EA results. This can be a significant problem in comple+ meshes as e$en the best automatic mesh generators often produce some distorted elements. elements. The elements in *S>(astran *S>(astran ha$e been specifically specifically designed to minimiBe this unfortunate effect, but some sensiti$ity to element distortion may still remain. Nifferent types types of element distortion distortion result in in different le$els le$els of error. E$aluating results results from the meshes KbL ) KeL will pro$ide you with some feel for how these elements perform when they are distorted.
Me-e- +o% te Con3e%"en)e D!-to%t!on An'(-!-
I.
Re)t Re)t'n 'n" "(' ('%% 6 E(e E(een entt MeMe-: :
1000 N
20 cm
6.0
m
$7 Re)t'n"('% @ E(eent Me-:
1000 N
20 cm
6.0 m
28
)7 1; De"%ee P'%'((e(o"%' Me-:
10 Degrees Typical
1000 N
20 cm
6.0 m
&7 >? De"%ee P'%'((e(o"%' Me-:
45 Deg. Typ.
1000 N
20 cm
6.0
m
e7 >? De"%ee T%'peo!& Me-:
45 Deg. Typ.
1000 N
20 cm
6.0 m
29
IV. FINITE ELEMENT THEORY The exact details of the formulation of the 4 node shell elements in MSC/Nastran is rather complicated. However, the basic formulation of an isoparametric 4 node membrane element is not extremely difficult and will provide us with sufficient background information to begin to understand the “h” c onvergence and distortion sensitivity studies. This basic form is constructed as follows:
Isoparametric Formulation of a 2-D Membrane Element [K] Matrix Assume the element has the configuration shown below:
Y 3
4.0
4
2.0
X 1
2
The physical and natural coordinate locations of the 6 nodes are (CNE
+,y-
( ξ, η )
2 5 6
0,06,06,20,2-
),),),),-
Cur goal is to find the element stiffness matri+ ASS@*E K -
= ∫ B-T E - B- dV V
ASS@*E 2 displacement degrees of freedom dof- per node 3ith #J = the strain ) displacement matri+ such that [ B]{u} = {ε } where WuX is the dof $ector and W X is the strain $ector EJ = the constituti$e matri+ such that [ E ]{ε} = {σ } where W σ X is the stress $ector and R = $olume.
2"
u T ≈ N -u) , v) , u" , v" , u , v , u1 , v1 / = N -u/ v N ) 0 N " 0 N 0 N 1 0 where (J is the shape function matri+ N - = 0 N ) 0 N " 0 N 0 N 1 Step 1: Interpolate the dof
and the rules for the shape functions are - N i must be = at node &i& 2- N i must be =0 at any node not = &i& This leads to the shape functions N ) N 3
1
= (1 + ξ )(1 + η ) 4
< N 4
1
)
= () − ξ%() − η % < 1
N 2
1
= (1 + ξ )(1 − η ) 4
<
= (1 − ξ )(1 + η ) 4
Step 6: 'ind the #J matri+
0 ε xx ∂ ∂ x ∂ u = D-u < 0 :ele$ant strains are ε / = ε yy = ∂ y v v γ ∂ ∂ xy ∂ x ∂ y u ≈ N -u/ v
but from step
So ε / ≈ D- N-u/ = B-u/ with [ B ] = [ D][ N ] Therefore,
N ), x 0 N ", x 0 N , x 0 N 1, x 0 B- = 0 N ), y 0 N ", y 0 N , y 0 N 1, y where the commas denote N ), y N ), x N ", y N ", x N , y N , x N 1, y N 1, x partial differentiation.
Step : @se the Vacobian to find deri$ati$es Isoparametric Assumption
x T = N - x) , y), x" , y", x , y, x1 , y1 / y
i.e. the isoparametric assumption is that geometry can be interpolated using the same interpolation functions as the displacements.
x) ∂ y ∂ x ∂ξ ∂ξ N ),ξ N ",ξ N ,ξ N 1,ξ x" ≈ The Vacobian matri+ J - = ∂ y N ),η N ",η N ,η N 1,η x ∂ x ∂η ∂η x1
2H
y)
y y1 y"
and from chain rule
N N i , x ξ , x η , x N i ,ξ −) i ,ξ N = ξ η N = J - N i , y , y , y i ,η i ,η
So in this particular case
0 ) − ) + η ) − η ) + η − ) − η 1 J - = 1 − ) + ξ − ) − ξ ) + ξ ) − ξ 1 0
0
= " " 0
) 2
0 " 0 = 1 0 1 0 )
which implies that
)" 0 J - = 0 ) −)
This allows us to find the entries in #J Step >: !erform the numerical integration
∫
Assume that the element has constant thic;ness = t implies K - = t B - E - B- dx dy T
A
3hich, according to the rules of calculus can be written
∫
K - = t B-T E - B- J d ξ d η
where J is the determinant of the Vacobian matri+. aussian numerical integration is then used to find the final numbers for the element stiffness. This ta;es the form
K- = h
nj
ni
∑∑ j=)
B -T E - B - J wi w j
i =)
( ξ i ,n j %
3here ng F and ngi are the number of gaussian integration points in the KFL and KiL directions respecti$ely and w F and wi are the associated gaussian weighting factors. Un&e%-t'n&!n" te Con3e%"en)e E2pe%!ent: 'rom step abo$e we gain insight into the KhL con$ergence study. :emember that the that the analytic formula for the displacements as a function P distance from built)in edge- is δ y ( x %
Px " (, L =
−
3 EI
x %
where ! is the load, / is the length, E is the Elastic *odulus and I is the
bending moment in inertia. This e%uation shows that the displacement is a cubic function of the distance from the cantile$er. As the bi)linear linear in both and η - shape functions are used to interpolate the displacements for this 6 node element, the elements are attempting to capture a cubic beha$ior by using a series of linear appro+imations. The number of linear appro+imations is e%ual to the number of elements we use the actual situation when using *S>(astrans 6 node shell element is a little better than this due to the inno$ati$e element formulation, but this is a good way to conceptually grasp the idea of KhL con$ergence-. This is the reason why 2 elements gi$e a higher error than do 9 elements. Un&e%-t'n&!n" te D!-to%t!on Sen-!t!3!t E2pe%!ent:
2
en 'n e(eent !- %e)t'n"('%< !t- ')o$!'n 't%!2 J-e& !n -tep- 'n& > '$o3e7 !ne%!)'(( e2')t. Ho,e3e%< !+ te e(eent $e)oe- &!-to%te&< te $!K(!ne'% -'pe +n)t!on- -e& to +o% )'n no (on"e% e2')t( )'pt%e te "eoet% 'n& te ')o$!'n !- no (on"e% ne%!)'(( e2')t. T!- !nt%o&)e- e%%o% !nto -tep- 'n& > '$o3e. Te e2')t +o% o+ te e(eent- &!-to%t!on &ete%!ne- te 'ont o+ e%%o% ,!) !- !nt%o&)e&. A- ent!one& p%e3!o-(< te e(eent- !n MSC/N'-t%'n '%e !nt%!)'te( &e-!"ne& to %eo3e '- ) o+ t!- &!-to%t!on $'-e& e%%o% '- po--!$(e. I+ te -!p(e -t'n&'%& !-op'%'et%!) +o%('t!on -o,n '$o3e !- -e&< te t%'p'!o&'( e(eent- Je- e '$o3e7 ,o(& ')t'(( (o)* J$e)oe 3e% -t!++7 'n& te e%%o%- !n te &!-p(')eent- ,o(& $e "e Jo3e% ;7. Fo% t!- %e'-on< !t !- )%!t!)'( t't -op!-t!)'te&< ,e((Kte-te& +!n!te e(eent )o&e- $e -e& +o% 'n )%!t!)'( 'n'(-!-. E3en ten< !t !- ,!-e to !n-pe)t e-e- +o% %e"!on- ,e%e e(eent- '%e !"( &!-to%te& 'n& 'ttept to )%e'te ' (e-- &!-to%te& e- !n t't '%e'.
R. STE! #1 STE! I(ST:@TIC(S 'C: *CNE/I( T7E A(TI/ERE:EN #EA* @SI( *S>!AT:A( !reliminaries for using !AT:A( include a- /og on to the computer b- lic; STA:T lower left corner of the 3indows Nes;top-, go to !rograms, Select *S common-, Select *S !atran.0. The instructions below give details for modeling the beam problem discussed above. Specifically, the 6 rectangular elements (mesh “b” above) is constructed. If one wishes to create any of the other meshes, the mesh creation section must be adapted to fit that mesh.
In the instructions below, the following abbre$iations and terms will be used TM = Top Men. This refers to the horiBontal menu options residing at the top of the screen after !AT:A( has been initiated. RM = R!"t Men. This refers to the menus that pop up after an option has been chosen from the top menu. These menus reside on the far right side of the !AT:A( des;top. SM = S$o%&!n'te Men. This referees to the menus that pop up from options selected in the right menu. C(!)* = @nless otherwise stated, this indicates a clic; with the left mouse button. Bo(&+')e will indicate te+t that occurs in the !AT:A( menus. Italics te+t will indicate te+t that you must enter into te+t bo+es in the !AT:A( menus or te+t that you choose in a menu scroll bo+. . Cur first step is to create a new database 'rom the T* choose F!(e In the resulting pull down menu choose Ne, A S* called Ne, D't'$'-e pops up Turn on chec;ed- Mo&!+ P%e+e%en)e@nder F!(e N'e enter bea#.db lic; O0 2. (e+t set the analysis preference A Ne, Mo&e( P%e+e%en)e- window will appear as a :* @nder To(e%'n)e choose ?ased on Model
50
Set Mo&e( D!en-!on to @.0 @nder An'(-!- Co&e choose MCA*&'+&* hoose An'(-!- Tpe = tructural clic; O0 5. The geometry of the beam will be determined ne+t 'rom the T* choose Geoet% A :* called Geoet% will result Set A)t!on = Create O$e)t = Point Meto& = XYZ Set the Po!nt ID list to 1 Set Re+e%en)e Coo%&!n'te F%'e to Coord 0 Turn off the Ato E2e)te button Enter the following into the Po!nt Coo%&!n'te- list [0,0,0] note that !AT:A( will accept either commas or blan;s as separators between coordinateslic; App( A point will appear in the main $iewport at coordinates 0,0,0J #ac; at the top of the :* called Geoet% Set A)t!on = Create O$e)t = Point Meto& = XYZ Set the Po!nt ID list to 2 Set Re+e%en)e Coo%&!n'te F%'e to Coord 0 Turn off the Ato E2e)te button Enter the following into the Po!nt Coo%&!n'te- list [@,0,0] note that !AT:A( will accept either commas or blan;s as separators between coordinateslic; App( A point will appear in the main $iewport at coordinates 9,0,0J #ac; at the top of the :* called Geoet% Set A)t!on = Create O$e)t = Point Meto& = XYZ Set the Po!nt ID list to Set Re+e%en)e Coo%&!n'te F%'e to Coord 0 Turn off the Ato E2e)te button Enter the following into the Po!nt Coo%&!n'te- list [0,0.2,0] note that !AT:A( will accept either commas or blan;s as separators between coordinateslic; App( A point will appear in the main $iewport at coordinates 0,0.2,0J #ac; at the top of the :* called Geoet% Set A)t!on = Create O$e)t = Point Meto& = XYZ Set the Po!nt ID list to 3 Set Re+e%en)e Coo%&!n'te F%'e to Coord 0 Turn off the Ato E2e)te button
5
Enter the following into the Po!nt Coo%&!n'te- list [@,0.2,0] note that !AT:A( will accept either commas or blan;s as separators between coordinateslic; App( A po!nt ,!(( 'ppe'% !n te '!n 3!e,po%t 't )oo%&!n'te- @<;.6<; #ac; at the top of the :* called Geoet% Set A)t!on = Create O$e)t = Curve Meto& = Point Set the C%3e ID list to 1 Turn Atoe2e)te off Set St'%t!n" Po!nt L!-t = Point 1 Set Ending !oint /ist = Point 2 lic; App( #ac; at the top of the :* called Geoet% Set A)t!on = Create O$e)t = Curve Meto& = Point Set the C%3e ID list to 2 Turn Atoe2e)te off Set St'%t!n" Po!nt L!-t = Point Set Ending !oint /ist = Point 4 lic; App( #ac; at the top of the :* called Geoet% Set A)t!on = Create O$e)t = ur"ace Meto& = Curve Set the S%+')e ID list to 1 Set P't%'n 6 Con3ent!on o"" Opt!on = 2 Curve Set M'n!+o(& o"" not chec;edSet St'%t!n" C%3e L!-t = Curve 1 Set Ending ur$e /ist = Curve 2 lic; App(
6. The boundary conditions are specified ne+t 'rom the T* choose Lo'&/BC5 A :* called Lo'&/Bon&'% Con&!t!on- will appear Set A)t!on = Create O$e)t = (is)lace#ent Tpe = *odal Set C%%ent Lo'& C'-e = (e"ault Enter Ne, Set N'e as lBcant The name can be whate$er name you wish. The name lBcant is chosen as this is for the cantile$er of the left most nodeslic; Inpt D't'... a S* called Input Nata appears Set Lo'&/BC S)'(e +')to% =1 Set T%'n-('t!on- to -0,0,0 Set Rot't!on- to -0,0,0 #e sure An'(-!- Coo%&!n'te F%'e is Coord0
52
lic; CG bac; in the Lo'&/Bon&'% Con&!t!on- :*lic; Se(e)t App(!)'t!on Re"!on A SM )'((e& Se(e)t App(!)'t!on Re"!on 'ppe'%Turn on the Geoet% button downlic; in bo+ under Se(e)t Geoet%!) Ent!t!eIn the !atran Se(e)t Men J Fust to the left of the :*lic; on the cur$e icon Fust under the point iconIn the main $iew port, select the left most $ertical edge of the beam. A Se(e)t!on Co!)e- S* appears hoose ur"ace 1.1 This will cause the words &Surface .& to appear in the Se(e)t Geoet%!) Ent!t!e- bo+ in the :*lic; on A&& Fust below this bo+ This will remo$e the words & Surface . & from the Se(e)t Geoet%!) Ent!t!e- bo+ and adds them to the App(!)'t!on Re"!on bo+lic; CG The Lo'& / Bon&'% Con&!t!on :* appears againlic; App( 5 displacement constraint arrows and 5 rotation constraint arrows should now appear on each point in the main $iewport window on the e+treme left edge of the beam. (umbers ,2,5,6,8,9 will appear with the arrows to show that all 9 of the dof are constrained there8. The loads are specified ne+t ontinuing on in the Lo'&/BC5- :*change A)t!on = Create O$e)t = /orce Tpe = *odal hange the Ne, Set N'e to rB)oint lic; Inpt D't'... a S* appears Enter the force $ector -0 , ;1000 , 0 lea$e the moments - i.e. blan;lic; O0 ontinuing on in the Lo'&/BC5- :*lic; Se(e)t App(!)'t!on Re"!on a small !atran select menu appears to the left edge of the :* lic; in this !atran select menu on the point icon In the main $iewport, clic; on the point 6 top right corner of the beam A S* called Se(e)t!on Co!)e- menu appears. hoose the Po!nt > option, not the C%3e or S%+')e option!oint 6 will be added to the Se(e)t Geoet%!) Ent!t!e- listlic; A&& !oint 6 will be added to the App(!)'t!on Re"!on listlic; O0 Lo'&/BC5- menu now reappearslic; App( A $ector with the 000 unit downward load should appear on point 6 in the main $iewport-
55
9. The finite element mesh is specified ne+t 'rom the T* choose E(eent A :* appears called E(eentSet A)t!on = Create O$e)t = Mesh Tpe = ur"ace Set No&e I& > 1 Set E(eent I& L!-t > 1 Set G(o$'( E&"e Len"t > 1.0 This will create 9 elements. If you want to create only 2 elements as is needed to answer %uestion Y below- then set the lobal edge length to 5.0Set E(eent Topo(o" > 8uad3 Set Me-e% > Iso#esh lic; in the S%+')e L!-t bo+ lic; and drag to select the entire structure The 3ords &Surface & should appear in the S%+')e L!-t lic; App( S!2 e(eent- ,!(( 'ppe'% on te -t%)t%e. Set A)t!on = $%uivalence O$e)t = &ll Tpe = 'olerance Cube The purpose here is to tie the nodes together that lie on top of one anotherSet the E4!3'(en)!n" To(e%'n)e to .00 lic; App( The command window at the bottom of the !AT:A( des;top will tell you that 0 nodes were deleted. This step will become critical if, in more complicated models, you are attempting to Foin portions of a model which ha$e been meshed separately.-
". The materials are specified ne+t Cn the T* select M'te%!'(a :* will appear called M'te%!'(Set A)t!on = Create O$e)t = Isotro)ic Meto& = Manual In)ut lic; M'te%!'( N'e bo+ Input the name to be bea#B#atl lic; Inpt P%ope%t!e- bo+ S* called Inpt Opt!on- appears Input E('-t!) Mo&(- =200.0$= Input Po!--on = 0.0 lic; O0 #ac; in the M'te%!'(- :* lic; App(
H. The properties for each element are assigned ne+t Cn the T* select P%ope%t!ea :* will appear called E(eent P%ope%t!eSet A)t!on = Create D!en-!on = 2d Tpe = hell lic; P%ope%t Set N'e bo+
56
Enter bea#B)ro) lic; Inpt P%ope%t!ea S* appears called Inpt P%ope%t!elic; in the M'te%!'( N'e bo+ lic; on the word &beammatl& in the M'te%!'( P%ope%t Set- bo+ at the bottom of the S* the words mbeammatl will appear in the M'te%!'( N'e bo+ at the top of the S*lic; in the T!)*ne-- bo+ Enter 0.1 lic; O0 #ac; in the E(eent P%ope%t!e- :*lic; Se(e)t Me$e%- bo+ a !atran Se(e)t en will appear on the left edge of the :* lic; on the icon which contains the surface or face icon *o$e the cursor arrow to a point to the left and abo$e the highest, left) most point on the beam. lic; and hold down the left mouse button. Nrag the cursor while holding down the mouse button- to a point to the right of and below the right)most bottom node. A &selection bo+& is formed while you drag. :elease the button. The words Surface will appear in the Se(e)t Me$e%- bo+lic; A&& The words Surface appears in the App(!)'t!on Re"!on bo+lic; App( in the E(eent P%ope%t!e- menu beamprop will be added to the E2!-t!n" P%ope%t Set- bo+-
. The analysis is to be done is specified ne+t Cn the T* select An'(-!a :* will appear called An'(-!Set A)t!on = &nal6e O$e)t = $ntire Model Meto& = /ull +un lic; Translation !arameters In the S* that appears, set D't' Otpt = 7)2 and Print lic; O0 #ac; in the :* An'(-!Set So(t!on Tpe = inear tatic button downlic; O0 lic; App( The analysis will ta;e a few seconds to run. A S* indicating that *S>(astran is wor;ing may appear-
0. A graphical representation of the deformation can be produced. A graphical representation of the deformation pro$ides an easy way to help determine if you ha$e constructed your model correctly. Cn the T* select An'(-!Set A)t!on = +ead 7ut)ut2 O$e)t = +esults $ntities Meto& = 'ranslate lic; Se(e)t Re-(t- F!(e A S* appears called Se(e)t F!(e
58
lic; the file $e'.op6 J1ou may need to loo; in your home or root directory to find the file. If this file does not e+ist, then you ha$e made a mista;e in constructing your model. o to E+plorer right)clic; on Start and choose E+plore- and find the file beam.log and beam.f09. Cpen these files by double clic;ing on them and search for the word KerrorL to determine what your mista;e is-. bea#.o)2 then appears in the F!(e N'e bo+ lic; O0 bac; in the An'(-!- menulic; App(
Cn the T* select Re-(t A :* will appear called Re-(tSet A)t!on = Create O$e)t = 8uic9 Plot In te Select 'ringe :esult $o2 )(!)* Displacements, translational In te Apply 'ringe :esult $o2 )(!)* Displacements, translational Set ?uantity = Y Component lic; App( (This will create the deformed plot) (ote that stresses can also be plotted from the Re-(t- menu by specifying them in the Se(e)t F%!n"e Re-(t section. . (e+t you will end your *S>!AT:A( session by sa$ing your database and e+iting. Cn the T* select F!(e 'rom the pull down menu select S'3e Cn the T* select F!(e 'rom the pull down menu select 8!t
VI. E9ERCISES: Fo% 'n o+ te e2e%)!-e- $e(o,< !t ' $e e(p+( to -e te Re-(t- Tep('te !n)(&e& '+te% te e2e%)!-e-. a- ompare the 'EA results with the analytic results for the tip deflection and stresses using two elements and using 9 elements along the a+is of the beam see figures KaL U KeL abo$e-. This is a small h con$ergence test. !lot Z error- Rs number of elements-. Assume a linear function from your 2 data points. If this linear assumption is correct, what is the least number of elements you would need to get Z error in the displacements4 3hat is the least number of elements you would need to get 0Z error in the stresses4 (ote Z error in displacements and 0Z error in stresses are sometimes used for standard error goals. In addition, because stresses usually con$erge more slowly than displacements, these two errors often occur for appro+imately the same number of elements.b- :eturn to your &*ac(eal ) 7arder& beam model. :erun the analysis using the same structural geometry, boundary conditions, loading conditions and material properties as you used pre$iously. *odel the structure with the 6 meshes specified as meshes b)e in the Keometric !ropertiesL section abo$e. ompare both the displacement and stress solutions from the 'EA with their analytic counterpart. Netermine which type of distortion appears to be most detrimental to the 'EA results by recording specific error percentages for all 6 meshes for both displacements and stresses.
59
c-
(oting that the elements we are using are &shell& elements that is they ha$e both membrane A(N bending dof-, rerun the four 9)node meshes. This time load the structure in the &out)of) plane& or O direction. To do this you will need to apply 2 e%ual loads to the 2 nodes on the tip of the beam. These loads must be in the O)direction. As the thic;ness is not the same as the width of the beam, your analytic answers for the tip deflection will be different than when you loaded the beam in the )1 direction. Again, compare the percent errors for both displacements and stresses for the meshes b)e.
d- Netermine the numerical $alues for the Vacobian matri+ for an element in one of the distorted meshes. e- :un the 9)element distorted)mesh problems with the load parallel to the long a+is in a+ial loading- and discuss the resulting errors for both displacements and stresses. f-
:erun the analysis using only rectangular elements. hange the !oissons ratio to 0.5 normal !oissons ratio for steel-. :un the analysis using 2, then 9 then 6H0 elements by setting the global edge length to 5, then then 0.08 respecti$ely-. :ecord the displacement and stress results for the 5 meshes. ompute the percent errors for the stresses using the analytic results as the baseline-. ompare these errors with those found while using a !oissons ratio of Bero, !ropose an e+planation for the differences,
g- :un the 9)element distorted)mesh problems with loads that create torsion and discuss the resulting errors for both displacements and stresses. (ote that you will need to consult a *echanics of *aterials te+t for the analytic e+pressions for the displacements and stresses of a shaft with rectangular cross section.
[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[ :ES@/T TE*!/ATE [[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[ Analytic tip deflection for the membrane)based case = Analytic tip deflection for the bending )based case = Analytic ma+. stress for the membrane)based case = Analytic ma+. stress for the bending )based case =
Lo'&!n" Tpe: MESH
J$en&!n" ,!t (o'& !n < $en&!n" ,!t (o'& !n < '2!'(< to%-!on7 TIP DISPL. MA9. STRESS DISPL. ERROR STRESS ERROR 2 element rectangular mesh 9 element rectangular mesh 0 degree parallelograms 68 degree parallelograms 68 degree trapeBoids
MSC/PATRAN TUTORIAL# > MODELING A FRAME STRUCTURE JEIGHT BENCH7
5"
USING BEAM ELEMENTS
I. THE PHYSICAL PROBLEM The frame structure weight lifting bench- below has the 6 legs that are attached to the floor. The weight of a user is assumed to be distributed across the rectangular bo+ which sits in the horiBontal plane. The weight of this user and accompanying weights is accounted for by a H lb per inch load distributed across the 0H inches of the horiBontal rectangle. The weight on the uprights is assumed to be 800 lb ma+ on each upright. This accounts for some impact load as well as the static force of a fully loaded bar. In addition to the $ertical force, there is a 00 lb per upright force in the horiBontal direction. This is intended to model the physics of someone pushing the bar horiBontally in the 1 direction- against the cradle supports as they remo$e the bar to begin the bench press e+ercise.
II. THINKING ABOUT THE MECHANICS
5H
The analytic solution for stresses and displacements for this problem is readily a$ailable if we thin; about the problem in sections. Any *echanics of *aterials te+t will pro$ide e%uations for the stress and the displacements for built in and simply supported beams as well as a+ial loads. These results can be used to gi$e basic analytic comparison solutions for certain sections of the structure.
III. GEOMETRIC AND FINITE ELEMENT MODEL As is the standard procedure for building *S>!atran models, we will build the geometry first and then construct a finite element mesh on that geometry. The geometry will proceed from creation of points to cur$es for this simple model. (e+t, we will use 2 node beam elements to model the frame. (e+t, the material and element properties will be entered. 3e will constrain the 5 displacement and 5 rotational degrees of freedom on the 6 legs. This creates the cantile$ered or built)in, end conditions for these sections of the frame. Then we will place a point load of magnitude 800 in the U1 direction on the top nodes of each of the uprights where the weight bar would rest-. A 00 lb load in the horiBontal direction is also placed at that same node. A $ertical load of H lb per inch is placed on the horiBontal bench section rectangle in the P1 plane-. 'inally, the nodes must be e%ui$alenced before the analysis is ready to run.
As can be seen in the step by step instructions below, !atran has a library of beam cross sections that can be used for frame analysis. These properties include $arious cross sections and wall thic;ness. Cne particular feature of note is the manner in which the orientation of the cross section is specified. The menu that allows you to pic; the properties of the beam cross section re%uires a $alue for K#eam CrientationL . This $alue determines how the cross section will oriented. In particular, imagine that the graphic of the cross section which is shown on the library menu- has a local coordinate system with P/ being the horiBontal and1/ being the $ertical coordinates respecti$ely see figure below-. Cb$iously, this means that O/ is the coordinate down the long a+is of the beam. If we label the K#eam CrientationL $ector WboX, then the following relationship can be used to specify our $alues for the components of WboX. WboX P WO/X = WP/X. An E+ample is shown below onsider the following cross section and the orientation of the cross section on the 2 beams in the picture.
1/
P/
5
'or the section of the beam that has its long a+is down the global P a+is, the #eam Crientation $ector WboX is set to W0,,0X This results in the orientation of the cross section as shown because WboX P WO /X = WP/X W0,,0X P W,0,0X = W0,0,X. So the choice of WboX = W0,,0X results in the global O a+is i.e. W0,0,X- being the local P)a+is as seen in the graphic of the cross section. (ote that this same choice for WboX will result in the orientation for the section of the beam that has its long a+is in the W,,0X direction abo$e. This is because, for that case WboX P WO/X = WP/X. = W0,,0X P W,,0X = W0,0,X. This procedure is used below, in the step)by)step procedure, to determine the choice ofWboX in the beam library menu.
IV. FINITE ELEMENT THEORY The exact details of the formulation of the 2 node beam elements in MSC/Nastran is rather complicated. However, the basic formulation of an isoparametric 2 node beam element is not extremely difficult and will provide us with sufficient background information to begin to understand the general application areas and “h” convergence of these elements. This basic formulation for the 2 node isoparametric beam can be found in the almost any Finite Elements text (see for example Finite Elements for Stress Analysis, R.D. Cook, John Wiley & Sons, 1995) .
60
R.
STE! #1 STE! I(ST:@TIC(S 'C: *CNE/I( T7E ':A*E @SI( *S>!AT:A( \ *S>(AST:A(
!reliminaries for using !AT:A( include a- /og on to the computer b- lic; STA:T lower left corner of the 3indows Nes;top-, go to !rograms, Select *S common-, Select *S !atran.0. The instructions below give details for modeling the beam problem discussed above. The instructions are NOT as detailed as I have given in other problems as I expect that you have begun to get a feel for how to do certain tasks in Patran.
In the instructions below, the following abbre$iations and terms will be used TM = Top Men. This refers to the horiBontal menu options residing at the top of the screen after !AT:A( has been initiated. RM = R!"t Men. This refers to the menus that pop up after an option has been chosen from the top menu. These menus reside on the far right side of the !AT:A( des;top. SM = S$o%&!n'te Men. This referees to the menus that pop up from options selected in the right menu. C(!)* = @nless otherwise stated, this indicates a clic; with the left mouse button. Bo(&+')e will indicate te+t that occurs in the !AT:A( menus. Italics te+t will indicate te+t that you must enter into te+t bo+es in the !AT:A( menus or te+t that you choose in a menu scroll bo+. . Cur first step is to create a new database 'rom the T* choose F!(e In the resulting pull down menu choose Ne, A S* called Ne, D't'$'-e pops up Turn on chec;ed- Mo&!+ P%e+e%en)e@nder F!(e N'e enter bench.db lic; O0 2. (e+t set the analysis preference A Ne, Mo&e( P%e+e%en)e- window will appear as a :* @nder To(e%'n)e choose ?ased on Model Set Mo&e( D!en-!on to 60.0 @nder An'(-!- Co&e choose MCA*&'+&* hoose An'(-!- Tpe = tructural clic; O0
5. The geometry of the beam will be determined ne+t 'rom the T* choose Geoet% A :* called Geoet% will result Set A)t!on = Create O$e)t = Point Meto& = XYZ
6
Set the Po!nt ID list to 1 Set Re+e%en)e Coo%&!n'te F%'e to Coord 0 Turn off the Ato E2e)te button Enter the following into the Po!nt Coo%&!n'te- list [2,0,0] note that !AT:A( will accept either commas or blan;s as separators between coordinateslic; App( A point will appear in the main $iewport at coordinates 2,0,0J
@sing the same approach, create each of the other points in this table Point 2 5 6 8 9 " H 0 2
P
1 2 9 2 9 H 0 H 0 9 2 H 0
O 0 0 0 0 62 62 62 62 62 62 62 62
0 0 H H 0 0 5H 5H H H H H
#ac; at the top of the :* called Geoet% Set A)t!on = Create O$e)t = Curve Meto& = Point Set the C%3e ID list to 1 Turn Atoe2e)te off Set St'%t!n" Po!nt L!-t = Point 1 Set Ending !oint /ist = Point 3 lic; App(
@sing the same approach, create each of the other cur$es in this table Curve
2 5 6 8 9 " H
#eginning !o int 2 6 6 2
Ending !oint
5 6 5 " 8 0 0
62
0 2
2 2 5
H 9 0
6. The boundary conditions are specified ne+t 'rom the T* choose Lo'&/BC5 A :* called Lo'&/Bon&'% Con&!t!on- will appear Set A)t!on = Create O$e)t = (is)lace#ent Tpe = *odal Set C%%ent Lo'& C'-e = (e"ault Enter Ne, Set N'e as cant The name can be whate$er name you wish. The name cant is chosen as this is for the cantile$er of the leg ends which contact the floorlic; Inpt D't'... a S* called Input Nata appears Set Lo'&/BC S)'(e +')to% =1 Set T%'n-('t!on- to -0,0,0 Set Rot't!on- to -0,0,0 #e sure An'(-!- Coo%&!n'te F%'e is Coord0 lic; O0 bac; in the Lo'&/Bon&'% Con&!t!on- :*lic; Se(e)t App(!)'t!on Re"!on A SM )'((e& Se(e)t App(!)'t!on Re"!on 'ppe'%Turn on the Geoet% button downlic; in bo+ under Se(e)t Geoet%!) Ent!t!e A Se(e)t!on Co!)e- S* appears hoose )oints 1,2,5,@ lic; on A&& Fust below this bo+ lic; O0 The Lo'& / Bon&'% Con&!t!on :* appears againlic; App( 5 displacement constraint arrows and 5 rotation constraint arrows should now appear on each point in the main $iewport window on the e+treme lower edge of the benchs legs. (umbers ,2,5,6,8,9 will appear with the arrows to show that all 9 of the dof are constrained there8. The finite element mesh is specified ne+t 'rom the T* choose E(eent A :* appears called E(eentSet A)t!on = Create O$e)t = Mesh eed Tpe = !ni"or# hoose the N$e% o+ E(eent- option Set the number of elements to 3 3e want each of the 2 cur$es to ha $e 6 elements. To ensure this, in the C%3e L!-t Bo2 enter Curve 112
C(!)* A!!/1 A set of mesh seeds will appear to show the density of nodes.
#ac; at the top of the :* called Elements Set A)t!on = Create O$e)t = Mesh
65
Tpe = Curve Set No&e I& > 1 Set E(eent I& L!-t > 1 Set G(o$'( E&"e Len"t > 1.0 Set E(eent Topo(o" > ?ar 2 lic; in the C%3e L!-t bo+ lic; and drag to select the entire structure lic; App( Fo% e(eent- ,!(( 'ppe'% on e') o+ te )%3e- !n te -t%)t%e.
#ac; at the top of the :* called Elements
Set A)t!on = $%uivalence O$e)t = &ll Tpe = 'olerance Cube The purpose here is to tie the nodes together that lie on top of one anotherSet the E4!3'(en)!n" To(e%'n)e to .02 lic; App( The command window at the bottom of the !AT:A( des;top will tell you that some nodes were deleted. This step is :ITIA/ as it KattachesL the nodes together at the frame Functions9. The materials are specified ne+t Cn the T* select M'te%!'(a :* will appear called M'te%!'(Set A)t!on = Create O$e)t = Isotro)ic Meto& = Manual In)ut lic; M'te%!'( N'e bo+ Input the name to be bea#B#atl lic; Inpt P%ope%t!e- bo+ S* called Inpt Opt!on- appears Input E('-t!) Mo&(- 50.0$@ Input Po!--on = 0. lic; O0 #ac; in the M'te%!'(- :* lic; App( ". The properties for each element are assigned ne+t Cn the T* select P%ope%t!ea :* will appear called E(eent P%ope%t!eSet A)t!on = Create D!en-!on = 1d Tpe = ?ea# lic; P%ope%t Set N'e bo+ Enter s%uareB)ro) We will now create the cross sectional properties for the parts of the bench that have square cross sections. These parts are the 4 legs and the 2 uprights(which would hold the actual weight bar) lic; Inpt P%ope%t!ea S* appears called Inpt P%ope%t!elic; in the M'te%!'( N'e bo+ lic; on the word &beammatl& in the M'te%!'( P%ope%t Set- bo+ at the bottom of the S* the words mbeammatl will appear in the M'te%!'( N'e bo+ at the top of the S*-
66
Vust to the right of the Se)t!on N'e bo+, set the option to D!en-!onlic; in the Se)t!on n'e bo+ and input s%uareBsect Vust to the right of the B'% O%!ent't!on bo+, set the option to Ve)to% lic; in the B'% O%!ent't!on bo+ and enter the $ector -1,0,0 lic; on the ICLBe' L!$%'% button A SM 'ppe'%- )'((e& Be' L!$%'% Set A)t!on = Create D!en-!on = tandard ha)e Tpe = *astran tandard Set the Ne, Se)t!on N'e to %uare1 Scroll through the $arious possible cross sections using the and buttons under the 5+5 set of cross section pictures- until you find the hollow rectangular picture with constant wall thic;ness on the lowest row-. lic; this graphic. In the upper right part of the window Set > 1.0 Set H > 1.0 Set t1 > .125 Set t6 > .125 If you want to see the information on the cross sectional properties which will come in handy when doing the analytical comparison calculation later- clic; on the C'()('te/D!-p(' button. lic; App( lic; O0 if a menu as;s if you wish to o$er write say YES7 lic; C'n)e( #ac; in the Input !roperties *enu, clic; O0 #ac; in the !roperties :* lic; in the Se(e)t Me$e%- bo+ hoose the 6 legs and the 2 uprights this is 9 cur$es and all the $ertical memberslic; A&& lic; App( (ow well create the properties for the horiBontal members. These members will ha$e a 2 in + in hollow cross section with .28 wall thic;ness. In this case it is critical that the large dimension of the cross section be oriented to pro$ide the ma+ bending moment of inertia KIL , so the larger 2 in- dimension must be the $ertical dimension of the cross section. #ac; in the :* called E(eent P%ope%t!eSet A)t!on = Create D!en-!on = 1d Tpe = ?ea# lic; P%ope%t Set N'e bo+ Enter rectYB)ro) We will now create the cross sectional properties for the parts of the bench that have rectangular cross sections and run in the Y direction lic; Inpt P%ope%t!ea S* appears called Inpt P%ope%t!elic; in the M'te%!'( N'e bo+ lic; on the word &beammatl& in the M'te%!'( P%ope%t Set- bo+ at the bottom of the S* the words mbeammatl will appear in the M'te%!'( N'e bo+ at the top of the S*Vust to the right of the Se)t!on N'e bo+, set the option to D!en-!onlic; in the Se)t!on n'e bo+ and input rectYBsect
68
Vust to the right of the B'% O%!ent't!on bo+, set the option to Ve)to% lic; in the B'% O%!ent't!on bo+ and enter the $ector -1,0,0 lic; on the ICLBe' L!$%'% button A SM 'ppe'%- )'((e& Be' L!$%'% Set A)t!on = Create D!en-!on = tandard ha)e Tpe = *astran tandard Set the Ne, Se)t!on N'e to +ectY Scroll through the $arious possible cross sections using the and buttons under the 5+5 set of cross section pictures- until you find the hollow rectangular picture with constant wall thic;ness on the lowest row-. lic; this graphic Set > 2.0 Set H > 1.0 Set t1 > .125 Set t6 > .125 If you want to see the information on the cross sectional properties which will come in handy when doing the analytical comparison calculation later- clic; on the C'()('te/D!-p(' button. lic; App( lic; O0 if a menu as;s if you wish to o$er write -' YES7 lic; C'n)e( #ac; in the Input !roperties *enu, clic; O0 #ac; in the !roperties :* lic; in the Se(e)t Me$e%- bo+ hoose the 2 horiBontal members that ha$e their long a+is in the 1 direction cur$es 5 \ 2lic; A&& lic; App(
#ac; in the :* called E(eent P%ope%t!eSet A)t!on = Create D!en-!on = 1d Tpe = ?ea# lic; P%ope%t Set N'e bo+ Enter rectXB)ro) We will now create the cross sectional properties for the parts of the bench that have rectangular cross sections and run in the X direction lic; Inpt P%ope%t!ea S* appears called Inpt P%ope%t!elic; in the M'te%!'( N'e bo+ lic; on the word &beammatl& in the M'te%!'( P%ope%t Set- bo+ at the bottom of the S* the words mbeammatl will appear in the M'te%!'( N'e bo+ at the top of the S*Vust to the right of the Se)t!on N'e bo+, set the option to D!en-!onlic; in the Se)t!on n'e bo+ and input rectXBsect Vust to the right of the B'% O%!ent't!on bo+, set the option to Ve)to% lic; in the B'% O%!ent't!on bo+ and enter the $ector -0,1,0 lic; on the ICLBe' L!$%'% button A SM 'ppe'%- )'((e& Be' L!$%'% D!en-!on = tandard ha)e Tpe = *astran tandard Set the Ne, Se)t!on N'e to +ectX
69
Scroll through the $arious possible cross sections using the and buttons under the 5+5 set of cross section pictures- until you find the hollow rectangular picture with constant wall thic;ness on the lowest row-. lic; this graphic Set >2.0 Set H > 1.0 Set t1 > .125 Set t6 > .125 If you want to see the information on the cross sectional properties which will come in handy when doing the analytical comparison calculation later- clic; on the C'()('te button. lic; App( lic; O0 if you are as;ed to o $erwrite, say YES lic; C'n)e( #ac; in the Input !roperties *enu, clic; O0 #ac; in the !roperties :* lic; in the Se(e)t Me$e%- bo+ hoose the 6 horiBontal members that ha$e their long a+is in the P direction cur$es 6,",H,(ote that there are 6 members that ha$e their long a+is aligned with the P a+is< not Fust 2. These 6 include 2 cur$es that attach the uprights to the rectangular horiBontal supports. lic; A&& lic; App( In order to see if the cross sections are correctly aligned, go to the T* = Nisplay, then select /oad>#>Elem !rops] in the :* that appears, @nder #eam Nisplay, change the default )N /ine to 5)N 'ull Span and hit Apply at the bottom of the S* -. This will turn on display of the cross sections. If you wish to see the cross sections shaded, you can use the T* shading icon solid shaded bo+, Fust to the right of the little wire frame icons2. The loads are specified ne+t C(!)* te TM = Lo'&-/BC The :* /oads># pops up. Set A)t!on = Create O$e)t = /orce Tpe = *odal hange the Ne, Set N'e to Dei:hts lic; Inpt D't'... a S* appears Enter the force $ector -0, 100 , ;500 /ea$e the moments - i.e. blan;lic; O0
ontinuing on in the Lo'&/BC5- :*lic; Se(e)t App(!)'t!on Re"!on a small !atran select menu appears close to the :* lic; in this !atran select menu on the point icon In the main $iewport, clic; on the points " \ H top of the uprights on the benchA&& these points to the application region lic; O0 Lo'&/BC5- menu now reappearslic; App( (A vector with the 510 unit downward and backward load should appear on points 7 & 8 in the main viewport)
6"
#ac; in the main :* /oads># A)t!on = Create O$e)t = (istributed oad Tpe = $le#ent !ni"or# Set Ne,Set N'e = &K(o'& Set Target Element Type > 1;d lic; Inpt D't' In te %e-(t!n" SM Set the +o%)e- to -0,0, /ea$e the oent- blan; lic; O0 B')* !n te Lo'&-/BC RM lic; Se(e)t App(!)'t!on Re"!on In te %e-(t!n" RM Turn on FEM as the Geoet% +!(te% Select all the elements along the cur$es 5,6,H,2 these are the 6 beams in the P1 plane that form the rectanglelic; A&& lic; O0 #ac; in the :* clic; App( Note: if the forces that appear on the main view screen are not in the correct direction, then you probably flipped one of the curve beginning/ending points. The easiest way to fix this is to remove the distributed load from those elements where it is in the wrong directions and create a second distributed force set that has the values <0,0,-8> and apply it to these elements. . The analysis is to be done is specified ne+t Cn the T* select An'(-!a :* will appear called An'(-!Set A)t!on = &nal6e O$e)t = $ntire Model Meto& = /ull +un lic; Translation !arameters In the S* that appears, set D't' Otpt = 7)2 and Print lic; O0 #ac; in the :* An'(-!Set So(t!on Tpe = inear tatic button downlic; O0 lic; App( The analysis will ta;e a few seconds to run. A S* indicating that *S>(astran is wor;ing may appear-
0. A graphical representation of the deformation can be produced. A graphical representation of the deformation pro$ides an easy way to help determine if you ha$e constructed your model correctly. Cn the T* select An'(-!Set A)t!on = +ead 7ut)ut2 O$e)t = +esults $ntities Meto& = 'ranslate lic; Se(e)t Re-(t- F!(e A S* appears called Se(e)t F!(e lic; the file $en).op6 J1ou may need to loo; in your home or root directory to find the file. If this file does not e+ist, then you ha$e made a mista;e in constructing your model. o to E+plorer right)clic; on Start and choose E+plore- and
6H
find the file bench.log and bench.f09. Cpen these files by double clic;ing on them and search for the word KerrorL or KfatalL to determine what your mista;e is-. bea#.o)2 then appears in the F!(e N'e bo+ lic; O0 bac; in the An'(-!- menulic; App(
Select the T* Re-(t A :* will appear called Re-(tSet A)t!on = Create O$e)t = 8uic9 Plot In te Select 'ringe :esult $o2 )(!)* Displacements, translational In te Apply Nisplacement :esult $o2 )(!)* Displacements, translational Set ?uantity = magnitude lic; App( (This will create the deformed plot) (ote that stresses can also be plotted from the Re-(t- menu by specifying them in the Se(e)t F%!n"e Re-(t section. 1ou will want to use the Ron*ises stresses in this case as the P, 1 or O based stresses are, by default, in the local coordinate system for that beam and are not in the global oord 0- frame. . (e+t you will end your *S>!AT:A( session by sa$ing your database and e+iting. Cn the T* select F!(e 'rom the pull down menu select S'3e Cn the T* select F!(e 'rom the pull down menu select 8!t
VI. E9ERCISES: .
ompare the 'EA results with the analytic results for the mid)span deflection and stresses of a simply supported beam. To do this loo; at the mid)span deflection and stresses of either of the long horiBontal members. (ote that the # of the ends of these members are (ot really simply supported. There is some resistance to rotation of the cross section. 7owe$er, neither is it truly a cantile$ered #. Therefore, if you calculate the midspan displacements sing simply supported #, the analytic displacement will be an upper bound. 2. reate the Ron *ises stress plot and the displacement plot. No these ma;e physical sense4 5. ompare the stresses in the uprights with the analytical !>A appro+imation using only the a+ial O component- part of the load. 3hat do you conclude4 6. ompare the stresses in the uprights with the analytical *y>I appro+imation using only the bending y component- part of the load. 3hat do you conclude4
MSC/PATRAN TUTORIAL # ? MODELING A STABELIATION FI9TURE ITH END PRESSURE USING SOLID ELEMENTS
6
I. THE PHYSICAL PROBLEM The structure below is designed to support a bearing on its right, cur$ed edge. A similar part e+ists to hold the bearing on the other side. The left edge is cantile$ered or &built in&. This means that both the translations and the rotations are held to Bero along this edge. A pressure load of magnitude 00 lb>in2 in the negati$e P direction results from the bearing reaction. The material properties for the beam are E= 0 + 0 9 psi typical for aluminum- and ν 0., . The part has a solid cross section with thic;ness in the O)direction t = 5 in. =
II. THINKING ABOUT THE MECHANICS The analytic solution for stresses and displacements for this problem is not readily a$ailable. 7owe$er, any *echanics of *aterials te+t will pro$ide e%uations for the ma+ stress and the ma+ displacement of simple problems that will pro$ide upper or lower bounds for stresses and displacements. These analytic $erifications will be discussed below.
Some basic %uestions to consider before creating the computational model are . 3here will the stresses be tensile and where will they be compressi$e4 2. 3hat will be the magnitude and direction of the reaction forces>moments4 5. 3here will the stresses be Bero4 6. 7ow do the displacements $ary along the length linear, %uadratic etc.-4 8. 3hat will the local effect of the pressure load be on the stresses4 9. Is the model fully constrained from rigid body rotations and displacements4 Answering these %uestions %ualitati$ely, along with the %uantitati$e analytical solutions for the ma+ stress and displacement will pro$ide reinforcement that your computational model is correctly constructed. III.
CREATING THE GEOMETRIC AND FINITE ELEMENT MODEL
1. C%e'te te Geoet% reate the 5)d obFect below according to the following steps
80
reate the points shown with coordinates as in the table !oint +)coord y)coord 0 0 2 0 0 5 ) 6 9 ) 8 5 2 9 9 8 " 8 H 0 6 0 6
B)coord 0 0 0 0 0 0 0 0 0
(e+t create cur$es between points and 2, 5 and another cur$e between 6, 9 and another cur$e between ", H and , 2 and another cur$e between H, 5 and ". reate the cur$e between points 2 and 5 and between points "and H using the 2)d arc 2point using a radius of . reate the arc between points 6, 8 and 9 using the 2d arc5point option. (ow create 5 surfaces. The instructions will use the cur$e numbers in the picture below. !lease substitute the cur$e numbers form the cur$es you created.
8
reate the first surface between the cur$es ,2,8 and 0 using the reate>Surface>Edge command. reate the 2nd surface between the cur$es ", 0, 9 and and the 5rd surface between the cur$es 5, , 6, and H. (ow create solids of thic;ness 5 in the O direction- from each of the 5 surfaces using the reate>Solid>E+trude command. The translation $ector will need to be 0,0,5. 3hen you are done, the part will loo; li;e this.
82
6. C%e'te te F!n!te E(eent Me- The first tas; is to seed the mesh. This is critical in this model as the model contains 5 separate solids which will need to be meshes separately. Then the nodes will need to be e%ui$alenced so that the 5 solids are KattachedL computationally. If this e%ui$alencing is to wor; correctly, nodes along the interface between 2 solids will need to be coincident. The mesh seed will ensure this. @sing the reate>*esh Seed>@niform option in the Element menu, create mesh seeds as shown below. (ote that is your mesh seeds are a little different than the ones shown below, it will simply mean that you end up with a slightly different number and placement of elements. This should (CT affect the results of your analysis substantially e+cept in one case. The distribution of elements in the 1 direction must be constant across the part. 'or e+ample if you ha$e 9 elements across the far left edge, then you need to ha$e 9 elements across the right cur$ed edge and across other P=constant planes in the part. The reason this is important is that if the element pattern is not symmetric in the in the 1 direction, the part will e+perience a non)symmetric distribution of loads in the 1 direction, resulting in non)physical displacements in the 1 direction and also resulting in non)physical bending stresses.
(e+t place the actual mesh on the solids using the reate>*esh>Solid. If the mesh seeds are done as shown, it will not matter what the global edge length is. @se the 7e+H elements. @se the isomesh mesh generator. (e+t e%ui$alence the nodes using the E%ui$alence>All>Tolerance cube command. The defaults tolerance is fine. This should indicate appro+imately 96 nodes were deleted. The graphics will show these nodes along the interface between the 5 solids. The completed mesh should loo; appro+imately as shown below.
85
. C%e'te te BC 'n& Lo'&To clamp the left edge edge away from the rounded bearing surface- use the reate>Nisplacement>(odal command in the /oads># menu. Set all 5 displacements and all 5 rotations to Bero and select apply to the left edge. (e+t create the pressure load on the bearing surface by using the reate>!ressure>element @niform command. *a;e sure the element target type is 5d. hoose a pressure of 00. To select the application surface in the Select Application Surface- turn on the geometry button and then select the icon for K'ace of a SolidL and choose the cur$ed surface shown highlighted below. The # and loads graphics will appear as shown.
The # on the left and the pressure load on the right might loo; different on your part depending on whether you ha$e applied the # or pressure to the geometry .
86
>. C%e'te te M'te%!'( 'n& P%ope%t The material for the part is aluminum which has a E of 0e9 psi and a !oissons ratio of 0.5. @sing the *aterials menu create an isotropic homogeneous material with these properties. The properties set is made using the command reate>5N>Solid in the properties menu. Input the properties simply as the material you Fust created. Select the entire part to ha$e these properties. ?. Do te An'(-!In the analysis menu, use the command AnalyBe>Entire *odel>'ull :un . Set the Translation !arameters to output the M.op2 file. :ead in the analysis results @sing the command :ead Cutput2>:esult Entities> Translate. Select the appropriate results M.op2- file. @. V!e, te Re-(tIn the results menu, use the command reate>?uic; !lot. *a;e plots of the displacements ad the appropriate stresses. VI. E9ERCISES 1. T%n !n te p(ot- +o% te &!-p(')eent- 'n& -t%e--e-. Do te '*e p-!)'( -en-eQ 6. F!n& ' ,' to "et -oe -$-t'nt!'( 'n'(t!) 3e%!+!)'t!on +o% te o&e(. . Loo* 't te -t%e-- %e-(t- 'n& p%e-)%!$e ' ,e!"t -'3!n"- e'-%e t't -o(& not )%e'te -t%e-- %e('te& p%o$(e- J!.e. &ete%!ne ,e%e 'te%!'( )'n p%o$'$( $e %eo3e&7. Copt't!on'(( te-t o% ne, &e-!"n.
88
MSC/PATRAN TUTORIAL # @ MODELING A CANTILEVERED BEAMS VIBRATION USING > NODE SHELL ELEMENTS I. THE PHYSICAL PROBLEM The beam below is cantile$ered or &built in& on the left edge. This means that both the translations and the rotations are held to Bero along this edge. The material properties for the
beam are E= "0 + 0 !ascals typical for Aluminum- and ν = 0. . The beam has a solid rectangular cross section with thic;ness in the O)direction t = 0.0 meters and height in the 1) direction h = 0. meters. 3e wish to find the mode shapes and associated $ibration fre%uencies for this beam. 1
89
h=10 cm
+
L= 1.0 m II. THINKING ABOUT THE MECHANICS The analytic solution modes shapes and natural fre%uencies- for this problem is readily a$ailable. Any $ibrations te+t will pro$ide e%uations for the mode shapes eigen$ectors- and the natural fre%uencies eigen$alues-. These e%uations are gi$en below. 'or the cantile$ered beam with bending moment o f inertia KIL, Elastic 1oungs- modulus KEL, mass per unit length KmL and /ength K/L, the first 5 natural fre%uencies 3 )5 rad>sec- are gi$en by
ω ) = ).24"
EI 1
mL
ω "
= 1.3*1 "
EI 1
mL
ω
= .244 "
EI mL1
(ote that these correspond to the following 5 mode shapes which are all bending modes in the plane of the smallest $alue of KIL. *odeshape
*odeshape 2
8"
*odeshape 5
Some basic %uestions to consider before creating the computational model are . Are there any other types of mode shapes that might occur torsional, a+ial or bending in a different plane-4 2. 3hat would be a reasonable fre%uency for the first mode shape4 5. Are there any constraint force chec;s that will help me $alidate the accuracy of my model4 Answering these %uestions %ualitati$ely, along with the %uantitati$e analytical solutions for the mode shapes and their associated natural fre%uencies will pro$ide reinforcement that your computational model is correctly constructed.
III. GEOMETRIC AND FINITE ELEMENT MODEL As is the standard procedure for building *S>!atran models, we will build the geometry first and then construct a finite element mesh on that geometry. The geometry will proceed from creation of points to cur$es to surfaces for this simple model. (e+t, we will use 6 node shell elements to model the beam. (e+t, the material and element properties will be entered. 3e will constrain the 5 displacement and 5 rotational degrees of freedom on the left edge for all nodes-. This creates the cantile$ered or built)in, end condition. 'inally, the nodes must be e%ui$alenced before the analysis is ready to run.
IV. FINITE ELEMENT THEORY The exact details of the formulation of the 4 node shell elements in MSC/Nastran is rather complicated. However, the basic formulation of an isoparametric 4 node membrane element is not extremely difficult and will provide us with sufficient background information to begin to understand the vibration model studies. This basic form is constructed as follows:
8H
Isoparametric Formulation of a 2-D Membrane Element [K] Matrix Assume the element has the configuration shown below:
Y 3
4.0
4
2.0
X 1
2
The physical and natural coordinate locations of the 6 nodes are (CNE
+,y-
( ξ, η )
2 5 6
0,06,06,20,2-
),),),),-
Cur goal is to find the element stiffness matri+ ASS@*E K -
= ∫ B-T E - B- dV V
ASS@*E 2 displacement degrees of freedom dof- per node 3ith #J = the strain ) displacement matri+ such that [ B]{u} = {ε } where WuX is the dof $ector and W X is the strain $ector EJ = the constituti$e matri+ such that [ E ]{ε} = {σ } where W σ X is the stress $ector and R = $olume.
u T ≈ N -u) , v) , u" , v" , u , v , u1 , v1 / = N -u/ v N ) 0 N " 0 N 0 N 1 0 where (J is the shape function matri+ N - = 0 N ) 0 N " 0 N 0 N 1 Step 1: Interpolate the dof
and the rules for the shape functions are - N i must be = at node &i& 2- N i must be =0 at any node not = &i&
8
This leads to the shape functions N ) N 3
1
= (1 + ξ )(1 + η ) 4
< N 4
1
)
= () − ξ%() − η % < 1
N 2
1
= (1 + ξ )(1 − η ) 4
<
= (1 − ξ )(1 + η ) 4
Step 6: 'ind the #J matri+
0 ε xx ∂ ∂ x ∂ u = D-u < 0 :ele$ant strains are ε / = ε yy = ∂ y v v γ ∂ ∂ xy ∂ x ∂ y u ≈ N -u/ v
but from step
So ε / ≈ D- N-u/ = B-u/ with [ B ] = [ D][ N ] Therefore,
N ), x 0 N ", x 0 N , x 0 N 1, x 0 B- = 0 N ), y 0 N ", y 0 N , y 0 N 1, y where the commas denote N ), y N ), x N ", y N ", x N , y N , x N 1, y N 1, x partial differentiation.
Step : @se the Vacobian to find deri$ati$es Isoparametric Assumption
x T = N - x) , y), x" , y", x , y, x1 , y1 / y
i.e. the isoparametric assumption is that geometry can be interpolated using the same interpolation functions as the displacements.
x) ∂ y ∂ x ∂ξ ∂ξ N ),ξ N ",ξ N ,ξ N 1,ξ x" ≈ The Vacobian matri+ J - = ∂ x ∂ y N ),η N ",η N ,η N 1,η x ∂η ∂η x1 and from chain rule
N N i , x ξ , x η , x N i ,ξ −) i ,ξ N = ξ η N = J - N i , y , y , y i ,η i ,η
90
y)
y y1 y"
So in this particular case
) 2
0 ) − ) + η ) − η ) + η − ) − η 1 J - = 1 − ) + ξ − ) − ξ ) + ξ ) − ξ 1 0
0
= " " 0
0
" 0 = 1 0 1 0 )
which implies that
)" 0 J - = 0 ) −)
This allows us to find the entries in #J Step >: !erform the numerical integration
∫
Assume that the element has constant thic;ness = t implies K - = t B - E - B- dx dy T
A
3hich, according to the rules of calculus can be written
∫
K - = t B-T E - B- J d ξ d η
where J is the determinant of the Vacobian matri+. aussian numerical integration is then used to find the final numbers for the element stiffness. This ta;es the form
K- = h
nj
ni
∑∑ j=)
B -T E - B - J wi w j
i =)
( ξ i ,n j %
3here ng F and ngi are the number of gaussian integration points in the KFL and KiL directions respecti$ely and w F and wi are the associated gaussian weighting factors. Un&e%-t'n&!n" te Copt't!on'( V!$%'t!on An'(-!- : The elements as formed above must be assembled into a global stiffness matrix. In the same manner, element mass matrices are formed using the equation
∫
M - = ρ N -T N - J d ξ d η . A similar form e+ists for the :ayleigh damping matri+ J. The stiffness, mass and damping matrices are then used in the dynamics e%uilibrium relationship / + " - d / + K - d / = ! / where the o$er)dots indicated deri$ati$es with respect to M - d
time and WfX is the forcing function. This set of e%uations can be sol$ed for the time history of the motion transient dynamics- or for the eigen$alues and eigen$ectors. 'or the $ibration analysis, the damping and the forcing function are assumed to be Bero. The resulting eigen$alue problem of the second ;ind is
M - ω / + K - d / = 0/ where eigen$alues are the natural fre%uencies ω and the eigen$ectors WdX gi$e the node shapes. R. STE! #1 STE! I(ST:@TIC(S 'C: *CNE/I( T7E RI#:ATIC( C' T7E A(TI/ERE:EN #EA* @SI( *S>!AT:A( !reliminaries for using !AT:A( include a- /og on to the computer b- lic; STA:T lower left corner of the 3indows Nes;top-, go to !rograms, Select *S common-, Select *S !atran.0.
9
In the instructions below, the following abbre$iations and terms will be used TM = Top Men. This refers to the horiBontal menu options residing at the top of the screen after !AT:A( has been initiated. RM = R!"t Men. This refers to the menus that pop up after an option has been chosen from the top menu. These menus reside on the far right side of the !AT:A( des;top. SM = S$o%&!n'te Men. This referees to the menus that pop up from options selected in the right menu. C(!)* = @nless otherwise stated, this indicates a clic; with the left mouse button. Bo(&+')e will indicate te+t that occurs in the !AT:A( menus. Italics te+t will indicate te+t that you must enter into te+t bo+es in the !AT:A( menus or te+t that you choose in a menu scroll bo+. . Cur first step is to create a new database 'rom the T* choose F!(e In the resulting pull down menu choose Ne, A S* called Ne, D't'$'-e pops up Turn on chec;ed- Mo&!+ P%e+e%en)e@nder F!(e N'e enter bea#;vib.db lic; O0 2. (e+t set the analysis preference A Ne, Mo&e( P%e+e%en)e- window will appear as a :* @nder To(e%'n)e choose ?ased on Model Set Mo&e( D!en-!on to10.0 @nder An'(-!- Co&e choose MCA*&'+&* hoose An'(-!- Tpe = tructural clic; O0 5. The geometry of the beam will be determined ne+t 'rom the T* choose Geoet% A :* called Geoet% will result Set A)t!on = Create O$e)t = Point Meto& = XYZ Set the Po!nt ID list to 1 Set Re+e%en)e Coo%&!n'te F%'e to Coord 0 Turn off the Ato E2e)te button Enter the following into the Po!nt Coo%&!n'te- list [0,0,0] note that !AT:A( will accept either commas or blan;s as separators between coordinateslic; App( A point will appear in the main $iewport at coordinates 0,0,0J @se this same procedure to create points at coordinates ,0,0J, ,0.,0J and 0,0.,0J #ac; at the top of the :* called Geoet% Set A)t!on = Create O$e)t = Curve Meto& = Point Set the C%3e ID list to 1
92
Turn Atoe2e)te off Set St'%t!n" Po!nt L!-t = Point 1 Set Ending !oint /ist = Point 2 lic; App( #ac; at the top of the :* called Geoet% Set A)t!on = Create O$e)t = Curve Meto& = Point Set the C%3e ID list to 2 Turn Atoe2e)te off Set St'%t!n" Po!nt L!-t = Point Set Ending !oint /ist = Point 4 lic; App( #ac; at the top of the :* called Geoet% Set A)t!on = Create O$e)t = ur"ace Meto& = Curve Set the S%+')e ID list to 1 Set P't%'n 6 Con3ent!on o"" Opt!on = 2 Curve Set M'n!+o(& o"" not chec;edSet St'%t!n" C%3e L!-t = Curve 1 Set Ending ur$e /ist = Curve 2 lic; App(
2. The finite element mesh is specified ne+t 'rom the T* choose E(eent A :* appears called E(eentSet A)t!on = Create O$e)t = Mesh Tpe = ur"ace Set No&e I& > 1 Set E(eent I& L!-t > 1 Set G(o$'( E&"e Len"t > 0.025 Set E(eent Topo(o" > 8uad3 Set Me-e% > Iso#esh lic; in the S%+')e L!-t bo+ lic; and drag to select the entire structure The 3ords &Surface & should appear in the S%+')e L!-t lic; App( Set A)t!on = $%uivalence O$e)t = &ll Tpe = 'olerance Cube The purpose here is to tie the nodes together that lie on top of one anotherSet the E4!3'(en)!n" To(e%'n)e to .00 lic; App( The command window at the bottom of the !AT:A( des;top will tell you that 0 nodes were deleted. This step will become critical if, in more complicated models, you are attempting to Foin portions of a model which ha$e been meshed separately.5. The boundary conditions are specified ne+t 'rom the T* choose Lo'&/BC5-
95
A :* called Lo'&/Bon&'% Con&!t!on- will appear Set A)t!on = Create O$e)t = (is)lace#ent Tpe = *odal Set C%%ent Lo'& C'-e = (e"ault Enter Ne, Set N'e as lBcant The name can be whate$er name you wish. The name lBcant is chosen as this is for the cantile$er of the left most nodeslic; Inpt D't'... a S* called Input Nata appears Set Lo'&/BC S)'(e +')to% =1 Set T%'n-('t!on- to -0,0,0 Set Rot't!on- to -0,0,0 #e sure An'(-!- Coo%&!n'te F%'e is Coord0 lic; CG bac; in the Lo'&/Bon&'% Con&!t!on- :*lic; Se(e)t App(!)'t!on Re"!on A SM )'((e& Se(e)t App(!)'t!on Re"!on 'ppe'%Turn on the FEM button downlic; in bo+ under Se(e)t No&e@se the cursor to highlight the set of nodes along the left $ertical edge of the beam. There should be 8 nodes there. lic; CG The Lo'& / Bon&'% Con&!t!on :* appears againlic; App( 5 displacement constraint arrows and 5 rotation constraint arrows should now appear on each node in the main $iewport window on the e+treme left edge of the beam. (umbers ,2,5,6,8,9 will appear with the arrows to show that all 9 of the dof are constrained there-
6. The materials are specified ne+t Cn the T* select M'te%!'(a :* will appear called M'te%!'(Set A)t!on = Create O$e)t = Isotro)ic Meto& = Manual In)ut lic; M'te%!'( N'e bo+ Input the name to be alu#inu# lic; Inpt P%ope%t!e- bo+ S* called Inpt Opt!on- appears Input E('-t!) Mo&(- =40.0$= Input Po!--on = 0. Input the Den-!t to be 2400 lic; O0 #ac; in the M'te%!'(- :* lic; App(
8. The properties for each element are assigned ne+t Cn the T* select P%ope%t!e-
96
a :* will appear called E(eent P%ope%t!eSet A)t!on = Create D!en-!on = 2d Tpe = hell lic; P%ope%t Set N'e bo+ Enter bea#B)ro) lic; Inpt P%ope%t!ea S* appears called Inpt P%ope%t!elic; in the M'te%!'( N'e bo+ lic; on the word &aluminum& in the M'te%!'( P%ope%t Set- bo+ at the bottom of the S* the words maluminum will appear in the M'te%!'( N'e bo+ at the top of the S*lic; in the T!)*ne-- bo+ Enter 0.01 lic; O0 #ac; in the E(eent P%ope%t!e- :*lic; Se(e)t Me$e%- bo+ a !atran Se(e)t en will appear on the left edge of the :* lic; on the icon which contains the surface or face icon *o$e the cursor arrow to a point to the left and abo$e the highest, left) most point on the beam. lic; and hold down the left mouse button. Nrag the cursor while holding down the mouse button- to a point to the right of and below the right)most bottom node. A &selection bo+& is formed while you drag. :elease the button. The words Surface will appear in the Se(e)t Me$e%- bo+lic; A&& The words Surface appears in the App(!)'t!on Re"!on bo+lic; App( in the E(eent P%ope%t!e- menu beamprop will be added to the E2!-t!n" P%ope%t Set- bo+-
9. The analysis is to be done is specified ne+t Cn the T* select An'(-!a :* will appear called An'(-!Set A)t!on = &nal6e O$e)t = $ntire Model Meto& = /ull +un lic; Translation !arameters In the S* that appears, set D't' Otpt = 7)2 and Print lic; O0 #ac; in the :* An'(-!Set So(t!on Tpe = *or#al Modes button downlic; O0 lic; App( The analysis will ta;e a few seconds to run. A S* indicating that *S>(astran is wor;ing may appear-
". A graphical representation of the mode shapes can be produced. A graphical representation of the mode shapes pro$ides an easy way to begin to determine if you ha$e constructed your model correctly. Cn the T* select An'(-!-
98
Set A)t!on = +ead 7ut)ut2 O$e)t = +esults $ntities Meto& = 'ranslate lic; Se(e)t Re-(t- F!(e A S* appears called Se(e)t F!(e lic; the file $e'K3!$.op6 J1ou may need to loo; in your home or root directory to find the file. If this file does not e+ist, then you ha$e made a mista;e in constructing your model. o to E+plorer right)clic; on Start and choose E+plore- and find the file beam)$ib.log and beam.f09. Cpen these files by double clic;ing on them and search for the word KerrorL to determine what your mista;e is-. ?ea#;vib.o)2 then appears in the F!(e N'e bo+ lic; O0 bac; in the An'(-!- menulic; App(
Cn the T* select Re-(t A :* will appear called Re-(tSet A)t!on = Create O$e)t = 8uic9 Plot In te Select :esult ase $o2 )(!)* De+'(t< Mode 1… In te Select 'ringe :esult $o2 )(!)* Eigenvectors, translational In te Apply 'ringe :esult $o2 )(!)* Eigenvectors, translational Set ?uantity = Magnitude Turn on the animation button so it displays a chec;lic; App( (This will create the animation of the first mode) Investigate other, higher order mode shapes. Be sure to record data and screen captures needed to answer the questions below.
H. (e+t you will end your *S>!AT:A( session by sa$ing your database and e+iting. Cn the T* select F!(e 'rom the pull down menu select S'3e Cn the T* select F!(e 'rom the pull down menu select 8!t
VI. E9ERCISES: a- ompare the 'EA results with the analytic results for the first 5 pairs of mode shapes and fre%uencies which are associated with bending of the beam in the direction of minimum KIL. 1ou can use the analytic e%uations shown earlier to produce the analytic results. b- Study the first 8 mode shapes produced by the (astran and comment on which modes are not associated with bending about the minimum KIL direction.
99
c-
:erun the analysis using only .00928 as the global edge length produces 6 times as many elements-. Noes a refinement in the mesh appear to produce more closely con$erged results4
d- hange the !oissons ratio to 0.0. :erun the analysis using the original global edge length of 0.028. ompare these errors with those found while using a !oissons ratio of 0.05, !ropose an e+planation for the differences. e- Identify the possible sources of that might ma;e our results a poor model of the actual physical structure.
MSC/PATRAN TUTORIAL # THERMAL ANALYSIS OF A COOLING FIN USING SHELL ELEMENTS
I. THE PHYSICAL PROBLEM The problem you will model is a fin of aluminum alloy, 0.2 m long, 0.002 m thic; and large width. This is the type of fin that might pro$ide air)cooling on a motorcycle engine. 'or the finite element model, we consider a representati$e strip of the fin 0.0 m in depth shown as the region between the dotted lines in the drawing-. The 200)degree wall is representati$e of the hot temperature of the engine. Cur goal is to find the temperature distribution down the fin. If the outside tip of the engine is too hot, it can be a safety concern. 7eat is conducted down the fin away from the heat source of the engine- and heat is also lost through con$ection from the top and bottom surfaces to the air. The ambient temperature of the air is ;nown to be 28 o and the con$ection coefficient film coefficient- is ;nown to be 50 3>m2- . The fin itself is made of aluminum which has a conducti$ity of "" 3>m2 G-.
3all 200
9" 0.20
0.0
0.002
II. THINKING ABOUT THE MECHANICS
The analytic solution for the temperatures for this problem is readily a$ailable. Any 7eat Transfer te+t will pro$ide e%uations for the temperature distribution of a fin considering conduction away from the heat source and con$ection from the top and bottom surfaces. These results can be used to gi$e basic analytic comparison solutions for certain sections of the structure. (ote that we assume no radiation occurs and that only the top and bottom surfaces ha$e significant con$ection heat transfer the con$ection from the edges of the fin is neglected-. These assumptions are normal for a first le$el analysis where the temperatures are in the ranges used in this problem.
III. GEOMETRIC AND FINITE ELEMENT MODEL As is the standard procedure for building *S>!atran models, we will build the geometry first and then construct a finite element mesh on that geometry. The geometry will proceed from creation of cur$es to a surface for this simple model. (e+t, we will use 6 node 2)dimensional elements to model the fin. (e+t, the material and element properties will be entered. 3e will set the wall temperature and the con$ection characteristics for the top and bottom of the fin. 'inally, the nodes must be e%ui$alenced before the analysis is ready to run. IV. FINITE ELEMENT THEORY The e&act details of the formulation of the 1 node "5d elements in 67'+astran is rather complicated. 8owever, the basic formulation of the "5d thermal element is not e&tremely difficult and will provide us with sufficient bac!ground information to begin to understand the general application areas and convergence of these elements. This basic formulation for the "5d thermal, linear, quasistatic element can be found in most any 9inite :lement Analysis te&t (see for e&le 9inite :lements for 7tress Analysis, by R.;. 'oo!, 7ons, )**4.% .
R. I(ST:@TIC(S 'C: *CNE/I( T7E 'I( @SI( *S>!AT:A( \ *S>(AST:A( !reliminaries for using !AT:A( include a- /og on to the computer b- lic; STA:T lower left corner of the 3indows Nes;top-, go to !rograms, Select *S common-, Select *S !atran.0. The instructions below give details for modeling the thermal fin problem discussed above. The instructions are ?T as detailed as have been given in other problems as it is e&pected that you have begun to get a feel for how to do certain tas!s in Patran.
In the instructions below, the following abbre$iations and terms will be used TM = Top Men. This refers to the horiBontal menu options residing at the top of the screen after !AT:A( has been initiated.
9H
RM = R!"t Men. This refers to the menus that pop up after an option has been chosen from the top menu. These menus reside on the far right side of the !AT:A( des;top. SM = S$o%&!n'te Men. This referees to the menus that pop up from options selected in the right menu. C(!)* = @nless otherwise stated, this indicates a clic; with the left mouse button. Bo(&+')e will indicate te+t that occurs in the !AT:A( menus. Italics te+t will indicate te+t that you must enter into te+t bo+es in the !AT:A( menus or te+t that you choose in a menu scroll bo+. . Cur first step is to create a new database 'rom the T* choose F!(e In the resulting pull down menu choose Ne, A S* called Ne, D't'$'-e pops up Turn on chec;ed- Mo&!+ P%e+e%en)e@nder F!(e N'e enter "in.db lic; O0 2. (e+t set the analysis preference A Ne, Mo&e( P%e+e%en)e- window will appear as a :* @nder To(e%'n)e choose ?ased on Model Set Mo&e( D!en-!on to 0.2 @nder An'(-!- Co&e choose MCA*&'+&* hoose An'(-!- Tpe = 'her#al clic; O0 5. The geometry of the beam will be determined ne+t Select Geoet% from T*. Cn :*, select A)t!on= reate, O$e)t= ur$e, Meto&= P1O (ote C%3e ID L!-t has a . Re+e%. Coo%&!n'te F%'e should be oord 0 Set Ve)to% Coo%&!n'te- L!-t to 0.2 0 0 1ou will be drawing lines $ectors- with these +yB components.O%!"!n Coo%&!n'te- L!-t = 0 0 0 lic; APPLY. A line from origin to point 0.2,0,0 should appear on screen.*a;e second cur$e 3ith same $ector, set O%!"!n Coo%&!n'te- L!-t to 0 0.0 0. lic; App(. A second cur$e appears on the screen.(ow create a surface between the cur$es. Cn the Geoet% :*, choose A)t!on= reate< O$e)t= Surface< Meto&= ur$e. Set Opt!on to 2 ur$e. (ote there is a St'%t!n" C%3e L!-t and En&!n" C%3e L!-t. lic; in the St'%t!n" C%3e L!-t bo+. .Select the first cur$e by using the mouse. lic; the small bo+ on cur$e on the screen. lic; in the En&!n" C%3e L!-t bo+. Then clic; on cur$e 2. (ote a surface is created. 6. reate the finite elements. Cn the T* select E(eent- and get a :*. hoose A)t!on= reate< O$e)t=*esh< Tpe= Surface hoose the siBe of the elements. Type in G(o$'( E&"e Len"t 0.0 Select I-oe-. lic; in S%+')e L!-t bo+. Select the Surface with the cursor. lic; App(. (ote the model has 20 elements.
9
8. reate #oundary conditions At T*, select Lo'&/BC-. et :*. (ow create the con$ection characteristics for the bottom of the fin hose A)t!on=create, O$e)t=con$ection, tpe=element uniform (ame the con$ection #. In Ne, Set N'e, type top)convec Select T'%"et E(eent Tpe = 2N lic; Inpt D't'. et submenu. Type 0 for con$ection coefficient w>m 2c- for top surface con$ection. Type 25 for ambient temp. lic; O0. #ac; in Lo'&/ BC menu, clic; Se(e)t App(!)'t!on Re"!on bo+ Select FEM as the eometry 'ilter. lic; in Se(e)t 6D E(eent- o% E&"e- bo+ @sing mouse, clic; on all the elements. 7old shift down for multiple selections.- lic; A&&. The application region bo+ should list the elements 20. lic; O0 #ac; in Lo'&/BC menu clic; App(.
(ow create the con$ection characteristics for the bottom of the fin hose A)t!on=create, O$e)t=con$ection, tpe=element uniform (ame the con$ection #. In Ne, Set N'e, type bot)convec Select T'%"et E(eent Tpe = 2N lic; Inpt D't'. et submenu. Type 0 for con$ection coefficient w>m 2c- for bottom surface con$ection. Type 25 for ambient temp. lic; O0. #ac; in Lo'&/ BC menu, clic; Se(e)t App(!)'t!on Re"!on bo+ Select FEM as the eometry 'ilter. lic; in Se(e)t 6D E(eent- o% E&"e- bo+ @sing mouse, clic; on all the elements. 7old shift down for multiple selections.- lic; A&&. The application region bo+ should list the elements 20. lic; O0 #ac; in Lo'&/BC menu clic; App(.
(ow create the base temperature #. In Lo'&/BC :* A)t!on=create, O$e)t=Temp, tpe=nodal In Ne, Set N'e type ?asete#). lic; on Inpt D't'. In submenu Inpt D't', type 200 in Tepe%'t%e bo+. lic; O0. #ac; in Lo'&/BC S*, clic; on Se(e)t App(!)'t!on Re"!on. In submenu, select FEM as Geoet% F!(te% . lic; on Se(e)t No&e-. @sing mouse, select the nodes and 22 at the e+treme left of the model. lic; A&&. lic; O0. #ac; in Lo'&/BC menu, clic; App(. The screen should show 200 at nodes a nd 22.9. reate and select material Cn T* select M'te%!'(-. In submenu, A)t!on=create, O$e)t=isotropic, eto&=manual input. In M'te%!'( N'e bo+, type alu#inu#. lic; Inpt P%ope%t!e-. In submenu, Inpt Opt!on-, enter thermal conducti$ity as 144 . w>m2;-. lic; O0. If S* does not disappear, lic; C'n)e(. #ac; in the :* , lic; App( In T*, select P%ope%t!eIn submenu A)t!on=create, O$e)t=2N, Tpe=shell. In P%ope%t Set N'e type shellB)ro). lic; on Inpt P%ope%t!e- In submenu, clic; on Aluminum in the *aterial !roperty Sets bo+. * Aluminum appears in the *aterial (ame bo+ at the top of the form.
"0
Set T!)*ne--= 0.002 lic; O0. #ac; in E(eent P%ope%t!e-, clic; Se(e)t e$e%-. @se mouse to select the entire model. 1ou can clic; and draw a bo+ around the entire model to select it.- lic; A&&. lic; App(. ". /oad #oundary onditions In order to ha$e both the con$ection on top and on the bottom as well as the and base temperature # on the model, all 5 boundary conditions must be combined into a single load case. In T*, select Lo'& C'-e-. In S*, A)t!on=reate, Lo'& )'-e n'e, type "inBcase. In De-)%!pt!on, type h>0 on "in Dith base> 200C. and a#bient>25C. lic; on A--!"n/P%!o%!t!e BC under the Se(e)t In&!3!&'( Lo'&-/BC lic; on )on3e$otK)on3e) and then on )on3etopK)on3e) and then on tep$'-etep As you clic; on these each of the 5 is added to the A--!"ne& Lo'&/BC
At the bottom of the menu, clic; O0 #ac; in the /oad ase :*, clic; App(
H. AnalyBe sol$e- for temperature. In T* select An'(-!-. In S*, A)t!on= Analysis O$e)t = entire model, Meto& = 'ull :un, o$ n'e = "in lic; t%'n-('t!on P'%'ete%- and set output to Cp2 \ !rint lic;, CG #ac; in the Analysis :*, clic; So(t!on Tpe hoose Ste'& St'te An'(-!lic; O0 #ac; in the Analysis :*, choose S$)'-e C%e'te @nder A3'!('$(e S$)'-e-, select fincase @nder A3'!('$(e Lo'&)'-e-, select fincase lic; App( lic; C'n)e( #ac; in the Analysis :*, clic; S$)'-e Se(e)t @nder S$)'-e- +o% So(t!on Se4en)e 1? , select fincase @nder S$)'-e- Se(e)te&, clic; on Nefault this remo$es default from the listlic; O0 #ac; in Analysis S* lic; App( . To read in the results for post)processing .In the :*=Analysis Set A)t!on = +ead 7ut)ut2E O$e)t = +esults $ntitiesE Meto& = 'ranslate lic; Se(e)t Re-(t- F!(e A S* appears called Se(e)t F!(e lic; the file +!n.op6 J1ou may need to loo; in your home or root directory to find the file. If this file does not e+ist, then you ha$e made a mista;e in constructing your model. o to E+plorer right)clic; on Start and choose E+plore- and find the file fin.log and fin .f09. Cpen these files by double clic;ing on them and search for the word KerrorL or KfatalL to determine what your mista;e is-. f in.o)2 then appears in the F!(e N'e bo+ lic; O0 bac; in the An'(-!- menu-
"
