FEM

1. UNIT-1
1) Explain the Historical development of Finite element method (F .E. M)
2) Describe in detail the general steps of the F.E.M
3) List the advantages and disadvantages of F.E.M.
4) List the typical areas of Engineering where the F.E.M. is applied.
5) Describe the commonly used methods for deriving the element stiffness matrix and
element equations.
6) Explain the concept of descritization.
7) Why polynomials are used as shape functions?
8) Explain simplex and complex elements?
9) What are the locations at which nodes can be positioned during discretization?
10) What are the shape functions for the linear element?
11) Write the shape functions for a two dimensional triangular element?
12) How many primary nodes are required to define a quadrilateral element?
13) Describe the theorem of stationary potential energy.
Solve for the nodal displacement and support reactions, using the principle of Min.
Potential Energy for the system shown in Figure.
14) Describe the Raleigh-Ritz method of approximation with validation of the method
with a simply supported beam subjected to udl of w/ unit length intensity.
15) Differentiate between Raleigh-Ritz method and Finite element method.
16) Compare between Potential energy method and Raleigh – Ritz method
17) Develop the differential equations of equilibrium for a 2-dimensional stress system.
18) Develop the differential equation of equilibrium for a 3-dimensional stress system.
19) Develop strain – displacement relationship for a 3D elastic body.
20) Develop the stress-strain relationship for a 3D elastic body.
K2K1 K3
20kN
10kN
1
2
3
4
K1=1200kN/m
K2=1800kN/m
K3=1500kN/m

2. 21) Differentiate between plane stress and plane strain problem.
22) Develop the stress-strain relation for axisymmetric bodies subjected to axisymmetric
Loading
23) If a displacement field is described by u = (-x2+2y2+6xy) ×10-4; v= (3x+6y-y2) × 10-4
determine strain in x direction, strain in y direction and shear strain in xy plane.
24) For the following stepped bar, determine the nodal displacements, stresses in 3
sections and reactions at the ends, using Elimination approach for handling the
boundary conditions. Take L1= 1000mm, A1 = 500 mm2, E1 = 2 x 105 N/mm2, L2=
1500mm, A2 =300 mm2, L3= 250mm, A3 = 625 mm2, E3 = E2 = E1.
25) Discuss the methodology to develop a Finite element solution for stress analysis of a
Gravity dam.