0) Explain Galerkin's method. (4 Marks)

6. a) Derive the stiffness matrix for a plate bending finite element. (5 Marks) 0) Write
down the shape functions for an eight noded hexahedral element in natural

coordinates. (4 Marks)
Part C

7. a) Discuss axisymmetric analysis. Explain how problems with axisymmetric
geometry having non-axisymmetric loads are handled in FEM. (8 Marks)
b) Discuss rigid body modes of vibration analysis (4 Marks)

8. a) Distinguish between lumped mass matrix and consistent mass matrix. (4 Marks)
b) Write short notes on Lagrange and serendipity elements. (8 Marks)

9. a) Explain the inverse iteration method for finding eigen values and eigen vectors.
(4 Marks)
b) Estimate the natural frequency of natural vibration of a cantilever bar using
FEM.
Length=Imeter, Young's modulus=210GPa, density=7800Kg/m 3 , Area of cross
section= 30 x 10 m (8 Marks)

ऋ के कं कं के KA के के के

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