SHARNBASVA UNIVERSITY

FACULTY OF ENGINEERING AND TECHNOLOGY

DEPARTMENT OF MECHANICAL ENGINEERING
M.TECH (MACHINE DESIGN)
FEM QUESTION BANK (23MDE21)

MODULE-1 Marks CO’S RBT

1. Explain the terms Preprocessor, solver and postprocessor. 10M CO1 L1,L2
2. Briefly explain applications of FEM in various fields. 10M CO1 L1,L2
3. Write short note on advantages of Finite Element methods. 5M CO1 L1
4. Write short note on limitations of Finite element method. 5M CO1 L1
Solve following differential equation
𝑑2𝑦 𝑑𝑦
5.
+ 3x – 6y = 0 ; 0 ≤ x ≤ 1 10M CO1 L2,L3
𝑑𝑥 2 𝑑𝑥
BCS: y (0) = 0 and yI (1)
= 0.1;
Find y (0.2) using variational method and compare with exact solution.
Solve the differential equation by Galerkin’s method.
𝜕2 𝑢
6. – 9u = x3, 0 ≤ x ≤ 1 20M CO1 L2,L3
𝜕𝑥 2
BCS: u (0) = 0 and u (1) = 2
Compare the answers with exact solution at x = 0.25, 0.5 and 0.75.
Solve the following differential equation using Galerkin method.
𝑑2𝑢
+ 5 = 0 for 0 < x < 1 CO1
7. 𝑑𝑥 2 15M L2,L3
𝑑𝑢
Boundary conditions are : u = 0 at x = 0 and + u = 0 at x = 1. Find u(0,2)
𝑑𝑥
and compare with exact solution.
Solve the following differential equation using Galerkin method.
𝑑2𝑢
+ u = x2 , 0 ≤ x ≤ 1 CO1
8. 𝑑𝑥 2 15M L2,L3
𝑑𝑢
Boundary conditions are : u = 0 at x = 0 and = 1 at x = 1. Find values for u
𝑑𝑥
(0.3) and u (0.6).
MODULE-2
Three concentric rings with given inner and outer diameter, first ring 15 and
20, second ring 25 and 35, third ring 40 and 50 respectively. The different
9. materials are joined together given E1 = 120GPa, E2 = 180GPa, E3 = 200GPa , 10M CO2 L2,L3
fixed at one end and pressure applied at other end is 80 KN. Determine the
displacement at the free end.
10. Explain the characteristics of shape function. 5M CO2 L1
11. Explain with sketches the types of elements. 15M CO2 L2
12. Explain different types of node with suitable examples. 5M CO2 L1
13. State different types of boundary conditions with examples. 10M CO2 L2
Mention the displacement boundary conditions for different support CO2
14. 5M L2
condition free, fixed, roller and pinned.
 Using FEM, analyze the taper bar as shown in figure. The cross-sectional
area to the left and right is equal to 80 mm2 and 20 mm2. Take length of bar
is equal to 60 mm, Take E = 210 GPa.

15. 15M CO2 L2,L3

500 N

For the steel block supporting rigid plates given below dimensions.
Determine displacement matrix and stresses in each element.

16. Properties Steel Aluminum Brass 10M CO2 L2,L3

C/S area
200 370 370
(mm2)
E (N/mm2) 2 x 105 7 x 104 8.8 x 104
MODULE – 3
17. Define and Explain plane stress condition with figure. 10M CO3 L2
18. Define and Explain plain strain condition with figure. 5M CO3 L1
19. Write the short note on Sub Iso parametric and super parametric FEA. 10M CO3 L2

Evaluate the shape functions N1, N2, and N3.

3(4,7)

20. P(3.85,4.8) 15M CO3 L2,L3

1(1.2,2) 2(7,3.5)
 In figure a long cylinder of inside diameter 80 mm and outside diameter 120mm
snugly fits in a hole over its full length. The cylinder is then subjected to an internal
pressure of 2 MPa. Using two elements on the 10 mm length shown, find the
displacements at the inner radius.

20M CO3 L2,L3

21.

With example explain the finite element formulation of tetrahedral element

considering four lagrange-type shape functions to find strain displacement relation 20M CO3 L2,L3
22.
matrix.
Explain the three principal stresses with example of three invariants of the stress CO3
5M L1
23. tensor.
MODULE – 4

Define in general and fundamentals of shell theory. 10M CO4 L2

24.
CO4
Explain briefly the classification of shell surface. 10M L2
25.
Write short note on design consideration of a) minimum nominal cover, b) CO4
10M L2
26. Thickness of the edge, c) Bending moments, d) Shear force.
CO4
Write the difference of CST and LST elements. 10M L2
27.
A CST element has nodal coordinates (10, 10) (70, 35) and (75,25) for nodes 1, 2
and 3 respectively. The element is 2mm thick and is of material with properties E =
70 GPa and Poisson’s ratio is 0.3. Upon loading of model, the nodal deflections CO4
20M L3
28. were found to be u1 = 0.01mm, u2 = 0.03mm, u3 = -0.02mm. v1 = -0.04mm, v2 =
0.02mm, v3 = -0.04mm. Assume plane stress condition. Determine Jacobian for
transformation, strain displacement relationship, the strains, the stresses.
MODULE – 5
What do you mean by consistent mass matrices? Derive the same for linear bar
10M CO5 L2
29. element.
What do you mean by lumped mass matrices? Derive the same for linear bar CO5
10M L2
30. element.
 Consider a uniform cross section bar of length L made up of a material whole
young,s modulus and density are given by E and 𝜌. Estimate the natural
frequencies of axial vibration of the bar using consistent mass matrices.
10M CO5 L2,L3
31.

Consider a uniform cross section bar of length L made up of a material whole

young,s modulus and density are given by E and 𝜌. Estimate the natural
frequencies of axial vibration of the bar using lumped mass matrices.
CO5
10M L2,L3
32.

L
Find the natural frequency of axial vibration of a bar of uniform cross section of 30
33. mm2 and length 1 m. Take E = 2 x 105 N/mm2 and 𝜌 = 8000 kg/m3. Take two linear 10M CO5 L3
elements. Compare the natural frequencies with exact frequencies.
Determine the eigenvalues and eigenvectors for the stepped bar shown in figure.

CO5
34. 20M L3