Modelling and Analysis Laboratory Manual VTU

Computer Aided Modeling and Analysis Laboratory

Department Of Mechanical Engineering, Don Bosco Institute o f Technology

1

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,QWURGXFWLRQWRWKH)LQLWH(OHPHQW0HWKRG In thermo mechanical members and structures, finite-element analysis (FEA) is typically invoked to compute displacement and temperature fields from known applied loads and heat fluxes. FEA has emerged in recent years as an essential resource for mechanical and structural designers. Its use is often mandated by standards such as the ASME Pressure Vessel Code, by insurance requirements, and even by law. Its acceptance has benefited from rapid progress in related computer hardware and software, especially computer-aided design (CAD) systems. Today, a number of highly developed, user-friendly finite-element codes are available commercially. The purpose of this chapter is to introduce finite-element theory and practice. The next three chapters focus on linear elasticity and thermal response, both static and dynamic, of basic structural members. After that, nonlinear thermo mechanical response is considered. In FEA practice, a design file developed using CAD is often “imported” into finite element codes, from which point little or no additional effort is required to develop the finite-element model and perform sophisticated thermo mechanical analysis and simulation. CAD integrated with an analysis tool, such as FEA, is an example of computer-aided engineering (CAE). CAE is a powerful resource with the potential of identifying design problems much more efficiently and rapidly than by “trial and error.” A major FEM application is the determination of stresses and temperatures in a component or member in locations where failure is thought most likely. If the stresses or temperatures exceed allowable or safe values, the product can be redesigned and then reanalyzed. Analysis can be diagnostic, supporting interpretation of product-failure data. Analysis also can be used to assess performance, for example, by determining whether the design-stiffness coefficient for a rubber spring is attained. OVERVIEW OF THE FINITE-ELEMENT METHOD

Consider a thermo elastic body with force and heat app lied to its exterior boundary. The finite-element method serves to determine the displacement vector u(X,t ) and the temperature T( X,t ) as functions of the un deformed position X and time t . The process of creating a finite-element model to support the design of a mechanical system can be viewed as having (at least) eight steps: 1. The body is first discretized, i.e., it is modeled as a mesh of finite elements connected at nodes. 2. Within each element, interpolation models are introduced to provide approximate expressions for the unknowns, typically u(X,t ) and T(X, t ), ), in terms of their nodal values, which now become the unknowns in the finite-element model. 3. The strain-displacement relation and its thermal analog are applied to the approximations for u and T to furnish approximations for the (Lagrangian (Lagrangian)) strain and the thermal gradient. 4. The stress-strain relation and its thermal analog (Fourier’s Law) are applied to obtain approximations to stress S and heat flux q in terms of the nodal values of u and T. 5. Equilibrium principles principles in variational form are applied using the variou s approximations within each element, leading to element equilibrium equations
















7. Prescribed kinematic and temperature conditions on the boundaries ( constraints ) are applied to the global equilibrium equations, thereby reducing the number of d egrees of freedom and elimin eliminating ating “rigid-body” modes. 8. The resulting global equilibrium equations are then solved using u sing computer algorithms. algorithms. The output is post processed. Initially, the output should be compared to data or benchmarks, or otherwise validated, to establish that the model correctly represents the underlying mechanical system. If not satisfied, the analyst a nalyst can revise the finite-element model and r epeat the computations. When the model is validated, post processing, with heavy reliance on graphics, then serves to interpret the results, for example, d etermi etermining ning whether the underlying design is satisfactory. If problems with the design are identified, the analyst can then choose to revise the design. The revised design is modeled, and the process of validation and interpretation is repeated. MESH DEVELOPMENT

Finite-element simulation has classically been viewed as having three stages: preprocessing, analysis, and post processing. The input file developed at the preprocessing stage consists of several elements: 1. control information (type of analysis, etc.) 2. material properties (e.g., elastic modulus) 3. mesh (element types, nodal coordinates, connectivities) 4. applied force and heat flux data 5. supports and constrain constraints ts (e.g., prescribed displacements) 6. initial conditions (dynamic problems) In problems without severe stress concentrations, much of the mesh data can be developed conveniently using automatic-mesh generation. With the input file developed, the analysis processor is activated and “raw” output files are generated. The postprocessor module typically contains (interfaces to) graphical utilities, thus facilitating display of output in the form chosen by the analyst, for example, contours of the Von Mises stress. Two problems arise at this stage: Validation and interpretation. The analyst can use benchmark solutions, special cases, or experimental data to validate the analysis. With validation, the analyst gains confidence in, for example, the mesh. He or she still may face problems p roblems of interpretation, particularly if the output is voluminous. Fortunately, current graphical-display systems make interpretation easier and more reliable, such as by displaying high stress regions in vivid colors. Postprocessors o ften allow the analyst to “zoom in” on regions of high interest, for example, where rubber is highly confined. More recent methods based on virtual-reality technology enable the analyst to fly through and otherwise become immersed in the model. mod el. The goal of mesh design is to select the number and location of finite-element nodes and element types so that the associated analyses are s ufficiently accurate. Several methods include automatic-mesh generation with adaptive capabilities, which serve to produce and iteratively refine the mesh based on a user-selected error tolerance. Even so, satisfactory meshes are not necessarily obtained, so that model editing by the analyst may be
















2. Nodes should be located where displacements and temperatures are constrained or prescribed in a concentrated manner, for example, where “pins” p revent movement. 3. Nodes should be located where concentrated springs and masses and their thermal analogs are present. 4. Nodes should be located along lines and surface patches, over which pressures, shear stresses, compliant foundations, distributed heat fluxes, and surface convection are applied. 5. Nodes should be located at boundary points where the applied tractions and heat fluxes experience discontinuities. 6. Nodes should be located along lines of symmetry symmetry.. 7. Nodes should be located along interfaces between different materials or co mponents. 8. Element-aspect ratios (ratio of largest to smallest element dimensions) should be no greater than, for example, five. 9. Symmetric configurations should have symmetric meshes. 10. The density of elements should be greater in domains with higher gradients. 11. Interior angles in elements should not be excessively acute or obtuse, for example, less than 45 or greater than 135 . 12. Element-density variations should be gradual rather than abrupt. 13. Meshes should be uniform in subdomains with low gradients. 14. Element orientations should be staggered to prevent “bias.” °

°

In modeling a configuration, a good practice is initially to develop the mesh locally in domains expected to have high gradients, and thereafter to develop the mesh in the intervening low-gradient domains, thereby “reconciling” the high-gradi high-gradient ent do mains. There are two classes of errors in finite-element analysis: Modeling error ensues from inaccuracies in such input data as the material properties, boundary conditions, and initial values. In addition, there often are compromises in the me sh, for example, modeling sharp corners as rounded. Numerical error is primarily due to truncation and round-off. As a practical matter, error in a finite-element simulation is often assessed by comparing solutions from two meshes, the second of which is a refinement of the first. The sensitivity of finite-element computations to error is to some extent controllable. If the condition number of the stiffness matrix (the ratio of the maximum to the minimum eigen value) is modest, sensitivity is reduced. Typically, the condition number increases rapidly as the number of nodes in a system grows. In addition, highly irregular meshes tend to produce high-condition numbers. Models mixing soft components, for example, rubber, with stiff components, such as steel plates, are also likely to have high-condition numbers. Where possible, the model should be designed to reduce r educe the condition number.
















Types of supports

Sl. No

Type of support

1

Fixed

2

Roller

3

Hinged Or pinned

4

Simply support

Degrees of Freedom to be Restricted Tx Ty Tz Rx Ry Rz

¥ x-y plane x-y plane x-y plane

¥

¥

¥

¥

¥

¥

¥

¥

¥

¥

¥

¥

¥

¥

¥

¥

¥ ¥

































TRUSS Determine the force in each member of the following truss. Indicate if the member is in tension or compression. The cross-sectional area of each member is 0.01 m and the Young’s modulus is 200x109 N/m2 

.

Step1: Start Algor – Start- Program files-Algor22- Fempro

appear. Select the Step2: Select the "File: New" command. The "New" dialog will appear. "FEA Model" icon and press the "New" button. Step3: Select Linear – Statics Stress With Linear Material model


















Step5: Create a new Analysis file truss1 and save-this will open u s the Working environment environment

Step6: Go for Plane 1 , right click it and select Sketch. Now the Drawing Environment Environ ment opens.


















Step 8: uncheck the USE AS CONSTRUCTION box..

Step9: Start the line by pressing enter i.e start from 0,0. T hen Y=2.8– Enter

Then X=1.5 and Y=2.0- Enter


















Step 11: A New Part 1 Will be generated. In Part1 kindly select Element type and right click to define it . Select Truss from the list.

Step 12: Select the Element Definition, right click for Modify Element Definition, A new 2 dialog box opens give cross-sectional area as 0.01m .


















Defining ning boundary b oundary condition: Step14: Defi Select the Vertices from Selection-S Selection-Select elect from menu bar

Move the cursor to near the A node and select it. The Node will highlight, then right click in the screen and select Nodal Boundary Boundar y condition condition and select fixed.




















Select Node C and right click for applying Force

.




















Move the cursor to near the C node and select it. The Node will highlight, then right click in the screen and select Nodal Boundary Boundar y condition condition and select all expect TY.

Step15: Go for Analysis in the menu bar and select Parameters. Select all in the output tab.



















Computer Aided Modeling and Analysis Laboratory Step16: After analysis completes, Go for Results Element Force And moments –Axial Forces. The Model will show the results.

Select Nodes from selection-select menu bar Select all nodes and right click to add probe to selection:







































Exercises on Truss 1) Determine the reaction force, displacement and elemental stress for the truss shown below. Given: Material : Mild steel 3 2 E = 209X10 N/mm 2 A= 100mm

2) Determine the reaction force displacement and elemental stress for the truss shown below.

Given: Material : Mild steel 3 2 E = 209X10 N/mm Section A –A : 10X10 Sq 100






















BARS Determine the Displacement in the direction of force applied for a bar of constant cross Section area.

Step1: Start Algor – Start- Program files-Algor22- Fempro



















Computer Aided Modeling and Analysis Laboratory Step5: Create a new Analysis file Bar 1 and save-this will open us the Working environment. Step6: To create the bar we need to draw line in YZ plane, to go to drawing environment right Click the YZ plane and select sketch.

Step 7: To create Line go for geometry – add line




















Step12: Select Material, right click to modify material and select AISI 1005 Steel from the




















Click on the left side end vertices and right Click to add the constraints. Select Fixed.








































Computer Aided Modeling and Analysis Laboratory Step 16: Now the result window opens. Select the Results- displacement -magnitude to know the displacement




















Exercises on Bars Case 1: Bars with uniform cross section 1) A circular rod of dia 20 mm and 500 mm long is subjected to a tensile force of 45 KN. The modulus of elasticity for steel may be taken as 200 KN/mm 2. Find stress, strain and elongation of the bar due to applied load. 2

2

( Ans: A=314.159 mm , stress = 143.24 mm , strain = 0.0007162 , Elongation = 0.358 mm)




















Case 3: Compound bars 5) A compound bar of length 500 mm consists of a strip of Aluminum 50 mm wide X 20 mm thick and a strip of steel 50 mm wide X 15 mm thick rigidly joined at ends. If the bar is subjected to a load of 50KN, find the stress developed in each materials and extension of the bar. Take EAl = 1x105N/mm2 and ESteel = 2x10 5N/mm2 ( Ans: Deformation = 0.1 mm)




















Beams 1) Determine the maximum bending stress and strain developed in the beam and Maximum deflection of the beam due to applied load. Also plot SFD and BMD for the cantilever beam shown below. Material used is Steel AISI 4130.



















Computer Aided Modeling and Analysis Laboratory Step6: To create the bar we need to draw line in XY plane, to go to drawing environment right Click the XY plane and select sketch.

Step 7: To create Line go for geometry – add line












































































































































































































































Modelling and Analysis Laboratory Manual VTU

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