CAE lab manual

MVSR ENGINEERING COLLEGE DEPARTMENT OF MECHANICAL ENGINEERINGANSYS

(Analysis Software)

1.0 FINITE ELEMENT CONCEPTFinite element analysis simulates physical system and their loading conditions mathematically. Analysis seeks to approximate the behavior of an arbitrary shaped structure under general loading and constrain conditions. A continuum is divided into discrete number of small regions called finite elements, whose behavior is easily understood. The entire system is then co-related to such elements to study the integrated behavior.

1.2 ADVANTAGES OF FEMAny complex structure can be analyzedDifferent boundary conditions can be incorporated suitablyComplicated material properties such as anisotropy, non-linearity can be incorporatedThe conventional method of analysis of beam, plates, shells etc are distinctly different from one another, FEM on other hand adopts uniform approach for all type of structures

1.3 STEPS IN FEM Discretization of continuum Selection of displacement model Derivation of element stiffness matrix Assembly of element stiffness matrix & application of boundary Solution for unknown displacements Computation of element strains & stress from nodal displacement

Element: Element is an entity, into which a system under study can be divided into. An element definition can be specified by nodes. The shape (area, length and volume) of the element depends upon the nodes with which it is made up of.

Nodes: Nodes are the corner points of the element. Nodes are independent entities in the space. These are similar to points in geometry. By moving a node in space an element shape can be changed.

.Degrees of freedom: The mobility at each node, which is used to represent the behavior of the systems, called the degrees of freedom or the number of independent co-ordinates required to describe the motion of a system is called degrees of freedom of the system. Thus a free particle undergoing a general motion will have three degrees of freedom, while a rigid body will have six degrees of freedom. i.e., three components of position and three angles defining the orientation. Further more, a continuous elastic body will require an infinite number of co-ordinates to describe its motion; hence, its degree of freedom is infinite.

In ANSYS the transnational degrees of freedom is represented by U (say Ux, Uy, Uz) and rotational degrees of freedom is represented by ROT (say ROTx, ROTy, ROTz).

Units and consistency:Almost all the software’s are independent of the system of units to be used. So it is the responsibility of the user to use consistent units, CAE software’s won’t take care the consistency of units. Depending on the model dimensions, material properties are to be supplied.

1.4 H- Adaptivity and P-Adaptivity: In traditional finite element analysis as the number of elements increases, the accuracy of the solution improves. The accuracy of the solution can be measured quantitatively with various entities, such as strain energies, displacements, and stresses and so on.

H-Method (Hierarchy Method): In this, to improve the accuracy of the solution we go for a smaller element size than the existing size there by increasing the number of elements. This is the usual h-adaptivity method. Each element is formulated mathematically with a certain predetermined order of shape functions. This polynomial order does not change in the h-adaptivity method. The elements associated with this type of capability are called the h-elements.

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MVSR ENGINEERING COLLEGE DEPARTMENT OF MECHANICAL ENGINEERINGP-Method (Polynomial Method): A different method to modify the subsequent finite element analysis on the same problem is to increase the polynomial order in each element while maintaining the original finite element size and mesh.The increase of the interpolation order is internal, and the solution stops automatically once a specified error tolerance is satisfied. This is known as the p-adaptivity method. The elements associated with this capability are called the p-elements.

H-P Method: These two methods can be combined to modify the subsequent analysis on the same model by simultaneously reducing the element size and increasing the interpolation order in each element.This combination is called mixed hp-adaptively.

All the fem packages do the following tasks1. Accepting input data2. Calculation of element stiffness matrices3. Assembly of element stiffness matrices4. Solution of simultaneous equations5. Calculation of stresses from displacement

1.5 VARIOUS STAGES IN FE ANALYSIS

1. PREPROCESSINGa) Create or import model geometryb) Define material propertiesc) Choose element typed) Define geometric constantse) Generate Finite element Mesh

2. SOLUTIONa) Apply boundary conditionsb) Apply loadc) Solve for unknowns

3. POSTPROCESSINGa) Review results like displacement, stresses, reactions etc.b) Check validity of solution

Structural analysis is the most common application of the finite element method. The term structural implies naval, aeronautical and mechanical & civil structures. Various types of structural analyses are carried out using FEM.

Following are the various types of analysis Structural Analysis Thermal Analysis Vibrations and Dynamics Modal Analysis. Buckling Analysis Harmonic Analysis Acoustics Fluid flow simulations Crash simulations Mold flow simulations

The primary unknowns (nodal degrees of freedom) calculated in a structural analysis are displacements. Other quantities, such as strains, stresses, and reaction forces, are then derived from the nodal displacements.1.6 Available FEM software Packages

ANSYS (General purpose, PC and workstations) SDRC/I-DEAS (Complete CAD/CAM/CAE package) NASTRAN (General purpose FEA on Mainframes) LS-DYNA 3D (Crash/impact simulations) ABAQUS (Nonlinear dynamic Analysis) NISA (A General-purpose FEA tool) PATRAN (Pre/post processor) HYPERMESH (Pre/post processor) SOLIDWORKS/COSMOS (Complete CAD/CAM/CAE package)

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MVSR ENGINEERING COLLEGE DEPARTMENT OF MECHANICAL ENGINEERING

Expt.No: 1 Date: Static Analysis of 2D Transmission Tower

Aim: To perform static Analysis of 2D Transmission Tower as shown in fig.

Discipline: Structural

Analysis Type: Static

Element Type: Link 180

Problem Description:

Material Properties: E= 200GPa

Geometrical Properties: Cross-section area of Truss = 6.25x10-3 sq. m

Diagram:

Results:

1. The Deflection at each joint = ------------

2. The stress in each member = -------------

3. Reaction forces at the base = ------------

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Practice Problems

1. Static Analysis of Truss Member

Aim: To perform static Analysis on Truss as shown in fig.




Given data:

Cross-section area of Truss = 3x10-4 sq m

E= 2.07x1011 N /sq m

Diagram:

4


Results:

1. The Maximum stress = --------- Pa

2. Reaction forces at Node 1 and Node5.

3. Compare the above results with the theoretical values.

2. Static Analysis of 2D Four-bar Truss

Aim: To perform static Analysis on Truss as shown in fig.




Given data:

Cross-section area of Truss = 60 sq.mm

E= 20000N/mm2

Diagram:

Results:

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MVSR ENGINEERING COLLEGE DEPARTMENT OF MECHANICAL ENGINEERING1. The Maximum stress = --------- Pa

2. Nodal Displacements

3. Reaction at the joints

Expt.No: 2 Date: Static Analysis of 3D Space Truss

Aim: To perform static Analysis on 3D space truss as shown in fig.




Given data:

Cross-section area of Truss = 10x10-4 m2

E= 210GPa

All dimensions are in meters

Diagram:

Results:

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MVSR ENGINEERING COLLEGE DEPARTMENT OF MECHANICAL ENGINEERING1. The Maximum stress = ---------

2. The Maximum displacement = ----------

Practice Problem

1. Static Analysis of 3D Space Truss

Aim: To perform Static Analysis on 3D space truss as shown in fig




Given data:

Cross-section area of Truss = 4in2

E= 30x106 Psi

All Dimensions are in inches

Diagram:

Nodes 1-4 are supported by ball and socket joints

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MVSR ENGINEERING COLLEGE DEPARTMENT OF MECHANICAL ENGINEERINGResults:

1. The Maximum stress = ---------

2. Reaction forces at end supports

Expt.No: 3 Date: Bending Stress Analysis on Beam

Aim: To perform Bending stress analysis on beam



Element Type: Beam 188 and Beam 189

Given data:

Width and Height of the Beam =0.346 meters (Square Cross-section)

E= 2.8X1010 Pa

Diagram:

Results:


2. Deformation of the Beam

3. Maximum bending stress along the beam

4. Bending moment along the beam

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Practice Problems1. Static Analysis of Overhanging Beam

Aim: To perform Static analysis of an overhanging beam




Given data:

Breadth = 300mm and Height of the Beam =0.346 meters, E= 2x105N/mm2. Poisson’s

ratio=0.25

Diagram:

Results:


2. Deformation of the Beam

3. Reaction Forces

4. Bending moment along the beam

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2. Structural Analysis of a Beam with Distributed Loads

Aim: To perform Structural analysis of a beam with distributed loads





Material Properties: E = 206.7 X 109 Pa

Geometric Properties: l = 6.096m; a = 3.048m; h = 0.762m; A= 0.0326 m2;

Izz= 3.283 x10-3m4

Loading: w = 145.9 x103 N/m

Test Case: A beam ,with a cross sectional area A, is supported as shown below and loaded on

the overhangs by a uniformly distributed load w.Determine the maximum bending stress in the

middle portion of the beam and the deflection at the middle of the beam

Results:


2. The Maximum deflections = ----------


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MVSR ENGINEERING COLLEGE DEPARTMENT OF MECHANICAL ENGINEERING4. Solve the problem by increasing the number of elements and compare the results

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MVSR ENGINEERING COLLEGE DEPARTMENT OF MECHANICAL ENGINEERINGExpt.No: 4 Date:

Static Analysis of an Axisymmetric Pressure vessel

Aim: To perform Static analysis of an Axisymmetric Pressure Vessel



Element Type: 8node183 (Plane183)


Material Properties: E = 14.5 Msi, Poisson’s ratio = 0.21

Geometric Properties: Pressure P=1700psi

Test Case:

The pressure vessel shown below is made of cast iron (E = 14.5 Msi, ν = 0.21) and contains an

internal pressure of p = 1700 psi. The cylindrical vessel has an inner diameter of 8 in with

spherical end caps. The end caps have a wall thickness of 0.25 in, while the cylinder walls are

0.5 in thick. In addition, there are two small circumferential grooves of 1/8 in radius along the

inner surface, and a 2 in wide by 0.25 in deep circumferential groove at the center of the

cylinder along the outer surface.

Diagram:

Results:



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Static Analysis of a Curved Shell due to Internal Pressure

Aim: To perform Static analysis of a shell subjected to internal pressure



Element Type: 8node183 (Plane183)


Material Properties: E = 30x106psi, Poisson’s ratio = 0.3

Geometric Properties: Pressure P= 1 Psi

Diagram:

Results:



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MVSR ENGINEERING COLLEGE DEPARTMENT OF MECHANICAL ENGINEERINGExpt.No:6 Date:

Buckling Analysis of a Column

Aim: To perform Buckling analysis of a column


Analysis Type: Buckling

Element Type: Beam 188 or Beam 189


Material Properties: E = 2.1x105 Pa, Poisson’s ratio =0.3

Geometric Properties Length= 1000mm; Cross-section 10 mm x 10mm

Diagram:

LOAD = 1 NEWTON

Results:

1. The fundamental frequency of the system is -------------

2. Draw at least three modes of the system.

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Modal Analysis of a Cantilever Beam

Aim: To perform Modal analysis of a cantilever beam


Analysis Type: Modal

Element Type: Beam 188 or Beam 189


Material Properties: E = 206.8 x109 Pa; Poisson’s ratio = 0.3; Density =7830 kg/m3

Geometrical Properties: Izz= 8.333x10-10m4 ; A= 1x10-4m2, Height =0.01m

Test Case: A simple cantilever beam of 1.0 m, length is considered. Modal analysis is required

to be performed. The frequencies in both reduced and subspace method are to be determined.

Results:

1. The fundamental frequency of the system is -------------

2. Draw at least three modes of frequency of the system.


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Harmonic Analysis of a Cantilever Beam

Aim: To perform Harmonic analysis of a cantilever beam

Discipline: Harmonic


Element Type: Beam 188 or Beam189


Material Properties: E = 206.8 X 109 Pa; Poisson’s ratio = 0.3; Density =7830 kg/m3

Geometrical Properties: I zz= 8.333e-10 m4 ; A= 1 x10-4m2, Height =0.01m

Test Case: A simple cantilever beam of 1.0 m, length is considered. Modal analysis is required

to be performed. The frequencies in both reduced and subspace method are to be determined.

Results: 1. The fundamental frequency of the system is -------------

2. Draw at least three modes of frequency of the system.

3. Compare the above results with the theoretical values

Expt.No: 9 Date: Steady state Heat Transfer Analysis in a Composite Material

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Aim: To perform Steady state heat transfer analysis in a composite material

Analysis Type: Thermal

Element Type: Plane 2D quad-8-node

Given data:

Material Properties: k1 (brick) = 0.8 kcal/m-hr-oc; k2 (cork) = 0.038 kcal/m-hr-oc;

k3 (wood) = 0.15 kcal/m-hr-oc

Test Case: This is a steady state transfer analysis of set of insulators, whose outer face

temperatures are defined. Conduction occurs in-between the insulators. The results of interest

are to plot nodal solutions and read the temperatures at the interfaces and also to obtain heat

flux value.

Results: 1. The interface temperatures = ---------------- 0C

2. The heat flux = ------------------Kcal/m2 hr 0 C

3. Plot the graphs between the Temperature Vs Distance & Heat flux Vs Distance.

4. Compare the above results with the theoretical results.

5. Consider Plane 2D quad-4-node element and check the results.

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Flow Analysis of Gases in a Venturimeter

Aim: To perform flow analysis of gasses in a venturimeter.


Analysis Type: CFD

Software used: Solid works 2013, Ansys workbench (fluent)

Given data: Dimensions of venturimeter, initial velocity = 40 m/s, gauge pressure = 1 pa

Solidworks sketch

Results:

1. Maximum pressure = ------------

2. Minimum pressure = ------------

3. Maximum velocity = -------------

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CFD Analysis of an Aerofoil

Aim: To perform CFD analysis of an aerofoil

Analysis Type: CFD

Software used: Ansys workbench (fluent)

Given data:

Profile of an aerofoil is shown in figure below; also the flow velocity of air is 2 m/s

Figure

Results:

1. Compute and plot the velocity distribution over the airfoil2. Compute Lift and drag force

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MVSR ENGINEERING COLLEGE DEPARTMENT OF MECHANICAL ENGINEERINGMATLAB Exercises

Expt.No: 12 Date: Structural Analysis of a Bar using Link Element

Aim: To determine the nodal displacement, stresses in each material and reaction forces of the

given structural problem using link element also solve the problem in MATLAB and compare with

ANSYS solution.

Test Case:

Element type: Link 180

Geometrical and material specifications:

Aluminum: A1=2400 mm2, E1=70x109 N/m2; Steel: A2=600 mm2, E2=200x109 N/m2

Finite element model:

Result:

Parameter MATLAB ANSYS1.Nodal displacement in mm

q1

q2

q3

2. Stress in N/m2 s1

s2

3. Reaction forces in N r1

r2

2. Plot the maximum stress positions

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MVSR ENGINEERING COLLEGE DEPARTMENT OF MECHANICAL ENGINEERINGB) Structural Analysis of a Beam using Beam Element

Aim: To determine the nodal displacement, bending moment’s and bending stresses for a given

beam problem. Solve the problem in MATLAB and compare with ANSYS solution.

Test Case:

Element type: Beam 188 and Beam 189

Geometrical and material specifications: E= 200GPa, I=24x10-6


Result:

Parameter MATLAB ANSYS

1.Nodal Displacement in

mm

2.Bending stress N/mm2

3.Bending moment N-m

Comment:

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MVSR ENGINEERING COLLEGE DEPARTMENT OF MECHANICAL ENGINEERINGC) Structural Analysis of a Plate using 2D Plane Element

Aim: To determine the displacement of node 1 and node 2 and the element stresses for plane

stress conditions using 2D CST elements. Solve the problem in MATLAB and compare with

ANSYS solution.

Test Case:

Geometrical and material specifications:

T= 0.5mm, E= 200x109N/mm2

Element type: Constant strain triangle


Results:

1.

2. Plot the maximum stress position.

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Parameter MATLAB ANSYS

1.Displacement at node 2 in mm

2.Displacement at node 2 in mm

3.Element stress in element 1 in

mm

4.Element stress in element 2 in

mm

MVSR ENGINEERING COLLEGE DEPARTMENT OF MECHANICAL ENGINEERINGComment:

TUTORIALS

1. Nonlinear Analysis of a Cantilever Beam

Aim: To perform Nonlinear analysis of a cantilever beam


Discipline: Nonlinear



Material Properties: Ex = 34000 MPa; Ey = 6530MPa; Ez= 6530MPa; vxy = 0.217;

Vyz = 0.366; vzx = 0.217; density = 2.6x10-6 kg/mm3

Diagram:

Results: 1. The Translation displacements = ---------- mm

2. The maximum Stress = ----------

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MVSR ENGINEERING COLLEGE DEPARTMENT OF MECHANICAL ENGINEERING2. Coupled Field (Structural/Thermal) Analysis

Aim: To perform couple field analysis on a solid structure connected with a link

Element Types: Thermal mass (Link33)

Discipline: Structural-Thermal

Analysis Type: Static and Thermal


Material Properties: E = 206.8 X 109 Pa; Thermal conductivity= 60.5W/m *K

Thermal Expansion Coefficient = 12e-06/K.

A steel link, with no internal stresses, is pinned between two solid structures at a reference

temperature of 0 C (273 K). One of the solid structures is heated to a temperature of 75 C (348

K). As heat is transferred from the solid structure into the link, the link will attempt to expand.

However, since it is pinned this cannot occur and as such, stress is created in the link.

Results:

1. The stress in the link = ---------------- MPa.

2. Compare the above result with theoretical result.

3. Static Analysis of Plate with a Hole

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Aim: To perform Static analysis of a plate with a hole

Element Type: 2D Quad, PLANE 145



Material Properties: E=200GPa, Poisson’s Ratio=0.29.

Geometrical Properties:

Height =10mm

Width =20mm

Radius =5mm


A steel plate with a hole in the center is subjected to a tensile pressure. Due to the symmetric

nature of the geometry and loading, only ¼ of the structure modeled (as shown below).

Symmetry boundary conditions are to be applied, and local convergence criteria be specified.

Results:

1. The Maximum stress = --------- Pa

2. The Maximum displacement = ---------- mm

3. Stress concentration Factor deformations


5. Solve the problem by increasing the number of elements and compare the results

4. Heat Transfer Analysis of Chimney

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MVSR ENGINEERING COLLEGE DEPARTMENT OF MECHANICAL ENGINEERINGAim: To perform Steady state heat transfer Analysis of Cross section of Chimney.

Discipline: Thermal

Analysis Type: Steady state heat transfer (h method)

Element Type: Solid, Quad 4 node, Plane 55


Material Properties: K=1.0 Btu/hr-ft-0F, hi=12 Btu/hr-ft2-0F,h0=3.0 Btu/hr-ft2-0F(1Btu=0.293

watt-hr)

Geometrical Properties: a=4 ft, b=1 ft (1 Ft=30.48 cm)

Loading: Tg=1000 F, Ta=0oF

Result:

5. Solidification of a Casting

Aim: To perform analysis during solidification of casting

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MVSR ENGINEERING COLLEGE DEPARTMENT OF MECHANICAL ENGINEERINGGiven data:

Material Properties for Sand: (1Btu=0.293 watt-hr), 1lb/in3=271 KN/m3, 1lb = 4.451N)

Conductivity (KXX) = 0.025Btu/ (hr-in-0 F);

Density (DENS) = 0.054 lb/in3

Specific heat (c) = 0.28 Btu/ (lb-0 F)

Conductivity for Steel (KXX):

At 00 F = 1.44Btu (hr-in-0 F) at 26430 F = 1.54 Btu (hr-in-0 F);

At 27500 F = 1.22 Btu (hr-in-0 F) at 28750 F = 1.22 Btu (hr-in-0 F)

Enthalpy for steel:

At 00 F = 0.0 Btu/in3; at 26430 F =128.1 Btu/in3; at 27500 F = 163.8 Btu/in3

At 28750 F =174.2 Btu/in3

Initial conditions:

Temperature of steel = 28750 F; Temperature of sand = 800 F

Convection Properties:

Film coefficient = 0.014 Btu (hr-in2 - 0 F)

Ambient temperature =800 F

Test Case: This is a transient heat transfer analysis of a casting process. The objective is to

track the temperature distribution in the steel casting and the mold during the solidification

process, which occurs over duration of 3 hours. The casting is made in an L-shaped sand mold

with 4 inch thick walls. Conduction occurs between the sand mold and the ambient air.

Results:

1. The maximum temperature is ------------------------

2. Indicate the temperature distribution

6. Static Analysis of a Connecting rod

Aim: To determine the Maximum Stress locations in the given connecting rod.


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MVSR ENGINEERING COLLEGE DEPARTMENT OF MECHANICAL ENGINEERINGAnalysis type: Static

Element Type: 3D tetrahedron element.

Given data:

Material Properties: E = 206.8 X 109 Pa; Poisson ratio = 0.3; Density =7830 kg/m3

Note: All Dimensions are in mm.

Results:

1. Indicate the maximum stress locations in the component.

2. The Von-Misses Stress -------------------

3. The maximum deflection in the component ---------------------

VIVA Questions

1. What are the different approximate solution methods?

2. What do you mean by continuum?

3. Define term node?

4. Define term element?

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MVSR ENGINEERING COLLEGE DEPARTMENT OF MECHANICAL ENGINEERING5. What is convergence?

6. What are the types of convergence?

7. What is p-convergence?

8. What is h convergence?

9. What is a higher order element?

10. Give example for higher order elements.

11. What do you mean by compatible elements?

12. What is geometric invariance?

13. Why do we use Pascal’s triangle in FEA?

14. What are the steps involved in FEA?

15. What is stiffness matrix?

16. How to obtain stiffness matrix?

17. What are the properties of stiffness matrix?

18. What is displacement function?

19. How to identify order of elements?

20. Mention different types of elements.

21. Mention some application of FEA.

22. What is connectivity?

23. What are the methods to improve problem solution?

24. Define symmetry in matrix.

25. What is plane stress?

26. What is plane strain?

27. Compare FEA with solid mechanics.

28. What are the packages available for FEA?

29. Define potential energy.

30. Define minimum potential energy.

31. Write potential energy equation for cantilever beam.

32. Mention two different methods to approach the model of physical system.

33. Difference between global coordinate and local coordinate?

34. What is local coordinate?

35. What is global coordinate?

36. What is shape function?

37. What are two general natural coordinate?

38. Mention the range of natural coordinate.

39. Number of shape function in CST

40. Number of shape function in quadrilateral.

41. Explain one point formula and Explain two point formula.

42. Why we are using polynomial equation in FEA?

43. Mention two schemes to represent band width?

44. What are forces involved in work potential?

45. What are anisotropic elements?

46. What are isotropic elements?

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MVSR ENGINEERING COLLEGE DEPARTMENT OF MECHANICAL ENGINEERING47. What are the two different approaches to study elasticity?

48. List the properties of shape functions.

49. Define truss.

50. What is weighted residual methods?

51. What different methods to solve weighed residual problem?

52. Explain the principle of virtual work?

53. Mention some advantages of FEA over solid mechanics.

54. Mention different types of elastic constants.

55. Which is the most accepted form of numerical integration in

FEM?

56. List the different approaches to derive integral equation.

57. What are the different types of errors in FEA?

58. Define Beam & Its types.

59. Define Conduction, Convection and radiation.

60. Define Heat flux, Heat flow & Heat generation

61. Define adiabatic surfaces.

62. Define Density, film coefficient.

63. Define Thermal gradient & Thermal conductivity.

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CAE lab manual

Documents

element shape

element definition

nodal displacement element

smaller element size

rotational degrees of

system of units

degree of freedom

finite elements