FINITE ELEMENT ANALYSIS

1. What is meant by finite element analysis?
2. Name any four applications of FEA.
3. What is the concept of matrix algebra and in what way it is used in FEA?
4. Briefly explain Gaussion elimination method.
5. Why polynomial type interpolation functions are preferred over trigonometric functions?
6. What is meant by ‘descretization’?
7. List out the various weighted-residual methods.
8. Define the concept of potential energy
9. List out any four advantages of using FEA.
10. What is the need for FEA?
11. List out FEM software packages
12. Name the different modules of FEM and their function
13. List out the properties of stiffness matrix
14. What are the different coordinate systems used in FEM?
15. Define a simplex, complex and multiplex element
16. What are shape functions and what are their properties?
17. Define ‘Natural coordinate system’
18. What are the advantages of natural coordinate system?
19. What are 1-Dimensional scalar and vector variable problems?
20. What types of problems are treated as one-dimensional problems?
21. Write down the expressions for shape functions of 1-D bar element.
22. Define aspect ratio. State its significance.
23. Write down the expressions for the element stiffness matrix of a beam element
24. What is a higher order element? Give an example
25. Write down the shape functions for a ‘Rectangular element.
26. State a two dimensional scalar variable problem with an example.
27. What is meant by a CST element? State its properties.
28. In what way a bilinear element is different from simplex and complex element?
29. Define ‘Plane stress’ and ‘Plane strain’ with suitable example
30. Differentiate between a CST and LST element

31. What are the differences between use of linear triangular element and bilinear rectangular element? 32. What is meant by a two dimensional vector variable problem?
33. Write down the expression for the stress-strain relationship matrix for a 2-D system.
34. State the expression for stiffness matrix for a bar element subjected to torsion
35. Write down the finite element equation for one-dimensional heat conduction
36. Specify the various elasticity equations.
37. What are the ways by which a 3-dimensional problem can be reduced to a 2-D problem?
38. What is meant by axisymmetric solid?
39. Write down the expression for shape functions for a axisymmetric triangular element
40. State the conditions to be satisfied in order to use axisymmetric elements
41. State the expression used for ‘gradient matrix’ for axisymmetric triangular element
42. State the constitutive law for axisymmetric problems.
43. Sketch ring shaped axisymmetric solid formed by a triangular and quadrilateral element
44. Write down the expression for stiffness matrix for an axisymmetric triangular element
45. Distinguish between plane stress, plane strain and axisymmetric analysis in solid mechanics 46. Sketch an one-dimensional axisymmetric (shell) element and two-dimensional axisymmetric element.
47. What is an ‘Iso-parametric element’? 48. Differentiate between Isoparametric, super parametric and sub parametric elements. 49. Write down the shape functions for 4-noded linear quadrilateral element using natural coordinate system. 50. What is a ‘Jacobian transformation’? 51. What are the advantages of ‘Gaussian quadrature’ numerical integration for isoparametric elements??
52. How do you calculate the number of Gaussian points in Gaussian quadrature method?
53. Find out the number Gaussian points to be considered for (x4+3x3-x) dx
54. What is the Jacobian transformation fro a two nodded isoparametric element?
55. What is meant by isoparametric formulation?
56. Sketch an general quadrilateral element and an isoparametric quadrilateral element.
57. How do you convert Cartesian coordinates into natural coordinates?
58. Write down the expression for strain-displacement for a four-noded quadrilateral element using natural coordinates