Residual Stresses of Plate With Holes by ANSYS Analysis- Hani Aziz Ameen

Dr. Hani Aziz Ameen

AN SYS Analysis of Residual Stresses in Plate with Holes

Residual Stresses of Plate with Holes by ANSYS Analysis Asst. Prof. Dr. Hani Aziz Ameen Technical College- Baghdad Dies and Tools Engineering Department E-mail: [email protected] Introduction The finite element methods has a powerful tool of numerical solution of a wide range of engineering problems. It is used to calculate stress and temperature distribution in solid structures of complex geometries subjected to complicated loadings.[1] The basic ideas of the finite elements methods originated from advances in structural analysis in 1941, Hrenikoof [2] presented a solution of elasticity problems using the “ frame work method “ . Courant’s paper [3], which used it to solve model torsion problems appeared in 1943. Turner..et al [4], derived stiffness matrices for plate ,truss, beam and other elements and presented their finding in 1956. In the late 1960 and early 1970, finite element analysis was applied to nonlinear problems and large deformations. Oden’s Book [5] on nonlinear continuer appeared in 1972. Today, the developments in mainframe computers and availability of powerful microcomputer has brought this method within reach of engineers working.[1].

ANSYS Software ANSYS V10 ( Analysis System Software ) is a finite element analysis software enables engineers to perform the following tasks [6]: • Build computer models or transfer CAD models of structures, products, components or systems. • Apply operating loads or other design performance conditions. • Study physical responses, such as stress levels, temperature distributions, or the impact of electromagnetic fields. • Optimize a design early in the development process to reduce production costs. • Do prototype testing in environments where it otherwise would be undesirable or impossible (for example biomedical applications ) .

Using The ANSYS V10 Program[7] : The ANSYS program is designed to run by three methods which are : 1- Interactive method, which is also called Graphical User Interface (GUI). 1

Dr. Hani Aziz Ameen


2- ANSYS Parametric Design Language (APDL).the advance methods in programmable engineering design.

ANSYS Structural Analyses [7] : Structural analysis is probably the most application of the finite element method. The term structural implies not only civil engineering structures such as bridges, building and foundations, but also mechanical structures such as ship hulls, aircraft, bodies and machine housings as well as mechanical components such as pistons, machine parts and tools…etc. • The procedure for a static structural analysis consists of three main steps: 1- Build the model and its meshing . 2- Apply loads and obtain the solution . 3- Review the results . the type of problem involved, an ANSYS analysis consists of the same steps: modeling, meshing, solution, and post processing. The modeling is drawing in a 2D or 3D representation of the problem. During the meshing phase you will define material properties and choose an element suitable for the problem. The last step of the meshing phase is to discredited the model i.e. create the mesh. In the solution phase, boundary conditions and loads need to be defined. The types of loads and boundary conditions you select depend on the simplifications being made. then attempt to solve the system of equations defined by the mesh and boundary conditions. Finally, when the solution is complete, you will need to review the results using the post processor. These results may be color contour plots, line plots, or simply a list of DOF results for each node. The easiest way to do and learn my problems is by using the pictures doing step – by – step in ANSYS output : Say we would like to analyze a plate with four holes that is being loaded in the center of plane.

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Dr. Hani Aziz Ameen


Goal of the research: Study of plate deflection behavior and stress distribution during static load. The plate has four supported holes with thickness t . the deflection δ is determined at concentrated load F1 = 100 N when the deflections are elastic in all plate. When the plate is loaded to F2 =2000 N or more , Plastic zone is checked. The plate is made of 1015 steel, cold drawn with mechanical properties as shown in table ( 1) . Table (1) Mechanical properties Tensile Strength ,Yield Tensile Strength ,Ultimate Poisson’s Ratio Elongation at Break

value 325 MPa 385 Mpa 0.29 18 %

The chemical composition for 1015 steel, cold draw indicated in the table(2 ). Table (2) Component C Fe Mn P S

Wt. % 0.12 – 0.18 99.13 – 99.58 0.3 – 0.6 Max 0.04 Max 0.05

Work Procedures: 1. 2. 3. 45-

Build the Model Take element type . Mesh operation . Apply Boundary conditions and loads. Solve and Review the Resultants

1. Build the Model (A): Create rectangular shape (150 * 100 ) mm2 with operation on edges ( 0.025 )m radius the coordinates as below :Fig(1). x1,0 y1,0 x2,0.15 y2,0 3

Dr. Hani Aziz Ameen


x3,0.15 y3,0.10 x4,0 y4,0.10

Fig ( 1

)

(B): Built four holes 12.5 mm radius with thickness t = 2.5 mm :

Fig ( 2

)

2. Take element type ( solid 45) has properties as below: SOLID45 Element Description SOLID45 is used for the 3-D modeling of solid structures. The element is defined by eight nodes having three degrees of freedom at each node: translations in the nodal x, y, and z directions. The element has plasticity, creep, swelling, stress stiffening, large deflection, and large strain capabilities. A reduced integration option with hourglass control is available.

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Nodes : I, J, K, L, M, N, O, P Degrees of Freedom : UX, UY, UZ

Fig.(3 ), show SOLID45 Geometry

Fig.(3) SOLID45 Geometry

3- Mesh operation (free mesh) as Fig.(4 ).

Fig.(4) mesh operation

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4-Apply Boundary conditions as Figs. (5) and (6) Four holes Supported , with load at plate center.

Fig( 5 ) mesh operation with supporting for four holes

Fig.(6) supporting for four holes with concentrated load in front view.

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Results and Discussion 1- Deflection Fig.(7a) shows the deflection of plate( in z- direction – 3D view) with the concentrated load at center of plate (100 N) , and Fig.(7b) shows the (2D view)

(a)

(b) Fig.(7)

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Stress Distribution Case – 1 – Concentrated load =100 N Our aim is to find the distribution of stresses in the plate under several loading and with fixed holes. Fig.(8) shows the contours of equivalent stresses in the plate, and its obvious from figure that the max. stress consternate on the center which is (4.9MPa) which is less that the yield point . and the other values decreases when far away from the center but it can be shown that the ( green area) beside the holes represent the amount of stress concentration which value is ( 2.18MPa) this is due to the fixed holes.

Fig.(8)

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Case -2- Concentrated load = 2kN Fig( 9 ) shows the deflection of the plate under 2000 N and the adjacent figure (Fig.(10)) shows the contours of equivalent stresses in the plate , and its obvious from figure that the max. stress consternate on the center which is (98MPa) which is less that the yield point . and the other values decreases when far away from the center but it can be shown that the ( green area) beside the holes represent the amount of stress concentration which value is ( 43.6MPa) this is due to the fixed holes. a-Deflection = 0.0490 mm

Fig. (9) Deflection values

b-Stress =98 MPa

Fig. ( 10

9

) Stresses distribution values

Dr. Hani Aziz Ameen


Case -3- Concentrated load = 7kN Fig(11) shows the deflection of the plate under 7kN which is 0.172 mm in a maximum , and Fig.(12) shows the contours of equivalent stresses in the plate , and its obvious from figure that the max. stress consternate on the center which is (329MPa) which is greater that the yield point . i.e. the plate undergoes the plastic deformation and the amount of plastic yield represented by the red color at the center of plate and the other values decreases when far away from the center but it can be shown that the ( green area) beside the holes represent the amount of stress concentration which value is ( 146MPa) this is due to the fixed holes.

Fig( 11 ) Deflection at load 7000 N

Fig.( 12 ) Stress Distribution at load 7000 N

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Through the applied load and re-loading the stress residual will be existed,, so these values plotted in Fig.(13 ) as shown

Fig.(13) Residual Stress Distribution along the plate thickness at it’s center

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Dr. Hani Aziz Ameen


Case -4- Concentrated load = 2.1kN If the radius of holes is reduced to 0.005, and keep the other dimensions: Fig.(14) shows the contours of equivalent stresses in the plate , and its obvious from figure that the max. stress consternate on the edge of holes which is (337MPa) which is greater that the yield point . i.e. the plate undergoes the plastic deformation and the amount of plastic yield represented by the red color not at the center of plate as before cases but the stresses values decreases when far away from the edges. It can be shown that the ( blue area) beside the holes represent the amount of stress concentration which value is ( 1.3 to 113MPa) this is due to the reducing fixed area on plate.

Fig(14 ) Stress Distribution at load 2.1K N at 0.005 mm holes radius 12

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Fig.(15 ) shows the deflection of the plate under 2.1kN which is 0.068 mm in a maximum .

Fig.(15) Deflection at load 2.1K N at 0.005 mm holes radius

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Conclusions From this study, it can be concluded that: 1we can use ANSYS software to analyze the structural problem including residual stresses . 2relative to our plate’s size (15 cm x 10 cm ) the plastic zone occurs at load 7kN 3the max. deflection for the plate is 0.17 mm 4the value of equivalent stress near the holes is greater than the other points due the concentration of stress due to the changing the area . 5there is a relation between the fixed area on the plate and the stress distribution and the amount of deflection made the plate undergoes the plastic deformation under static concentrated load.

References [1] Tim Langlais , “ ANSYS Short Course “, [email protected] August 16, 1999. from internet . [2] Hrenikoff, A.,” Solution of problems in elasticity by the frame work method”. J. of Appl. Mech.,8: 169-175 (1941). [3] Courant, R. “ Variation methods for the solution of problems of equilibrium and vibrations “, Bulletin of American Mathematical Society, 49:1-23 (1943) . [4] Turner ,M.J.,R.W.clough,H.C.Martin and L.J. Topp “ stiffness and deflection analysis of complex structures” J. of Aero. Science 23(9):805-824(1956). [5] Oden, J.T. “ Finite elements of Nonlinear Continuer “ ,New York, McGraw-Hill, 1972. [6] Saeed Moaveni : Finite Element Analysis” , theory and application with ANSYS, 1999 . [7] ANSYS, Structural Manual , 2005, ANSYS, Inc.

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Residual Stresses of Plate With Holes by ANSYS Analysis- Hani Aziz Ameen

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