1. Discuss in detail about the concepts of FEM formulation. Explain with step-by-step procedure. Also list out the major applications of FEM.

2.(a) What do you understand by finite element model? Explain and give an example of modelling of a mechanical component.

(b) Describe the shape functions and its characteristics. Discuss why polynomials are generously used as shape functions.

3.(a) Develop the stress-strain matrix equation and strain displacement matrix for an axi-symmetric triangular element.

(b) Distinguish between the following: Essential boundary condition and Natural boundary condition

(ii) Boundary value problem and Initial value problem


4.(a) Describe the variational functions.

(b) Two thin rods of stiffness kN/mm and 8 kN/mm are connected as shown in the figure given below and are subjected to a load of 6 kN at node 3. The system is fixed at node 1. Determine the displacement at node 2 and node 3.

<br><br> <img src='./qimages/9162-4b.jpg'>

5. A circular bar of uniform cross-section length Young's modulus and density p is vertically suspended under its own weight using four-element model. Find the state of deformations and strain under its own weight.

6.(a) Derive the element stiffness matrix for a 1-D bar problem using Galerkin approach.
Define internal and external indeterminacies. Describe with the suitable formula for degree of indeterminacy for a 2-D truss.

7. Write short notes on the following: Nodal Points Static and Dynamic Analysis Influence Coefficients Weight Factors