UNIT
– I – FINITE
ELEMENT FORMULATION OF BOUNDARY VALUE
PROBLEMS PART-A
1. What is the finite element method? 2. How does the finite element method work? 3. What are the main steps involved in FEA. [AU, April / M ay – 2011] 4. Write the steps involved in developing finite element mod el. 5. What are the basic approaches to improve a finite element model? [A U, Nov / D ec – 2010]
6. Write any two advantages of FEM Analysis. [A U, Nov / Dec – 2012] 7. What are the methods generally associated with finite element analysis? 8. List any four advantages of finite element method. [AU, April / M ay – 2008] 9. What are the applications of FEA? [AU, April / M ay – 2011] 10. Define finite difference method. 11. What is the limitation of using a finite difference method? [AU, April / M ay – 2010] 12. Define finite volume method. 13. Differentiate finite element method from finite difference method. 14. Differentiate finite element method from finite volume method. 15. What do you mean by discretization in finite element method? 16. What is discretization? [A U, Nov / Dec – 2010] 2010] 17. List the types of nodes. [A U, M ay / June – 2012] 18. Define degree of freedom. 19. What is meant by degrees of freedom? [ AU , Nov / Dec – 2012]
20. State the advantage of finite element method over other numerical analysis methods. 21. State the fields to which FEA solving procedure is applicable. 22. What is a structural and non-structural problem? 23. Distinguish between 1D bar element and 1D beam element. [A U, Nov / Dec – 2009, May / Ju ne – 2011]
24. Write the equilibrium equation for an elemental volume in 3D including the body force. 25. How to write the equilibrium equation for a finite element? [A U, Nov / Dec – 2012] 26. Classify boundary conditions. [ AU , Nov / Dec – 2011] 27. What are the types of boundary conditions? 28. What do you mean by boundary condition and boundary value problem? 29. Write the difference between initial value problem and boundary value problem. 30. What are the different types of boundary conditions? Give examples. [A U, M ay / June – 2012]
31. List the various methods of solving boundary value problems. [AU, April / M ay – 2010] 32. Write down the boundary conditions of a cantilever beam AB of span L fixed at A and free at B subjected to a uniformly distributed load of P throughout the span. [AU , May / June – 2009, 2011]
33. Briefly explain force method and stiffness method. 34. What is aspect ratio? 35. Write a short note on stress – strain relation. 36. Write down the stress strain relationship for a three dimensional stress field. [AU, April / May – 2011]
37. State the effect of Poisson’s ratio. 38. Define total potential energy of an elastic bod y. 39. Write the potential energy for beam of span L simply supported at ends, subjected to a concentrated load P at mid span. Assume EI constant. [A U, Apri l / M ay, Nov / Dec – 2008]
40. State the principle of minimum potential energy. [A U, Nov / D ec – 2007, April / M ay – 2009]
41. How will you obtain total potential energy of a structural system? [AU, April / M ay – 2011, M ay / Jun e – 2012]
42. Write down the potential energy function for a three dimensional deformable body in terms of strain and displacements. [A U, M ay / June – 2009] 43. What should be considered during piecewise trial functions? [AU, April / M ay – 2011] 44. Name the weighted residual methods. [ AU , Nov / Dec – 2011] 45. What is the use of Ritz method? [ AU , Nov / Dec – 2011] 46. Mention the basic steps of Rayleigh-Ritz method. [AU, April / M ay – 2011] 47. Highlight the equivalence and the difference between Rayleigh Ritz method and the finite element method. [A U, Nov / Dec – 2012] 48. Distinguish between Rayleigh Ritz method and finite element method with regard to choosing displacement function. [A U, Nov / Dec – 2010] 49. Why are polynomial types of interpolation functions preferred over trigonometric functions? [AU, April / M ay – 2009, M ay / Jun e – 2013] 50. What is meant by weak formulation? 51. Define the principle of virtual work. 52. Differentiate Von Mises stress and principle stress. 53. What do you mean by constitutive law?[A U, Nov / Dec – 2007, Apri l / M ay – 2009] 54. What are h and p versions of finite element method? 55. What is the difference between static and dynamic analysis? 56. What is Galerkin method of approximation? [ AU , Nov / Dec – 2009] 57. What is a weighted resuidal method? [ AU , Nov / Dec – 2010] 58. Distinguish between potential energy and potential energy functional.
59. Name any four FEA software. PART
– B
1. Explain the step by step procedure of FEA. [A U, Nov / Dec – 2010] 2. Explain the general procedure of finite element a nalysis. [A U, Nov / Dec – 2011] 3. Briefly explain the stages involved in FEA. 4. Explain the step by step procedure of FEM. [A U, Nov / Dec – 2011] 5. List out the general procedure for FEA problems. [A U, M ay / June – 2012] 6. Compare FEM with other methods of analysis. [ AU , Nov / Dec – 2010] 7. Define discretization. Explain mesh refinement. [ AU , Nov / Dec – 2010] 8. Explain the process of discretization of a structure in finite element method in detail, with suitable illustrations for each aspect being & discussed. [A U, Nov / Dec – 2012] 9. Discuss procedure using the commercial package (P.C. Programs) available today for solving problems of FEM. Take a structural problem to explain the same. [A U, Nov / Dec
– 2011] 10. State the importance of locating nodes in finite element model. [A U, Nov / Dec – 2011] 11. Write a brief note on the following.
a. Isotropic material b. Orthotropic material c. Anisotropic material 12. What are initial and final boundary value problems? Explain. [A U, Nov / Dec – 2010] 13. Explain the Potential Energy Approach [ AU , Nov / Dec – 2010] 14. Explain the principle of minimization of potential energy. [A U, Nov / Dec – 2011] 15. Explain the four weighted residual methods. [A U, Nov / Dec – 2011] 16. Explain Ritz method with an example. [AU , April / May – 2011] 17. Explain Rayleigh Ritz and Galerkin formulation with example. [A U, M ay / June – 2012]
18. Write short notes on Galerkin method? [AU , April / M ay – 2009] 19. Discuss stresses and equilibrium of a three dimensional body. [A U, M ay / June – 2012]
20.Derive the element level equation for one dimensional bar element based on the station- of a functional. [AU , M ay / June – 2012] 21. Derive the characteristic equations for the one dimensional bar element by using piecewise defined interpolations and weak form of the weighted residual method? [A U, M ay / June – 2012]
22. Explain Gaussian elimination method of solving equations. [AU , April / May – 2011] 23. Write briefly about Gaussian elimination? [AU, April / M ay – 2009] 24. The following differential equation is available for a physical phenomenon.
Boundary conditions are, y (0) = 0 y (10) = 0. Find the value of the parameter a, by the following methods. (i) Collocation (ii) Sub – Domain (iii) Least Square (iv) Galerkin. 25. Discuss the following methods to solve the given differential equation:
With the boundary condition y(0) = 0 and y( H ) = 0 (i) Variant method (ii) Collocation method. [AU, April / M ay – 2010] 26. A cantilever beam of length L is loaded with a point load at the free end. Find the maximum deflection and maximum bending moment using Rayleigh-Ritz method using the function y=
Given: EI is constant. [AU, April / M ay – 2008]
27. A simply supported beam carries uniformly distributed load over the entire span. Calculate the bending moment and deflection. Assume EI is constant and compare the results with other solution. [A U, Nov / Dec – 2012] 28. Determine the expression for deflection and bending moment in a simply supported beam subjected to uniformly distributed load over entire span. Find the deflection and moment at midspan and compare with exact solution using Rayleigh-Ritz method. Use [A U, Nov / Dec – 2008]
29. Compute the value of central deflection in the figure below by assuming. The beam is uniform throughout and carries a central point load P.
