1. Discuss in detail about the concepts of FEM formulation. How is it that theFEM emerged as a powerful tool Discuss the major applications of FEM.

Define shape function. Write the shape function of a four-noded quadrilateral element.

Derive one-dimensional steady state heat conduction equation.

Using Galerkin approach, derive the element stiffness matrix for a I-D bar problem.

The elements of a row or a column of the stiffness matrix of a bar element sum up to zero, but this is not so for a beam element. Explain why.

Distinguish between the following:

Cartesian co-ordinate and Natural co-ordinate system

Bar and Beam element

Determine the matrix relating strain and nodal displacement for an axisymmetric triangular element.

5. A fixed beam of 5 m span carries a point load of 20 kN at a distance of 2 m from one of its ends. Determine the slope and deflection under the load [EI 10 x 10^3 kN-m^2

6. Use finite element method to calculate the displacement and stresses of a bar shown in the figure below:

<img src='./qimages/15755-6.jpg'>

7. Answer any two of the following questions:

Determine the constant load vector for the CST element under the action of gravity acting in the plane of the element.

Explain the steps involved in the analysis of beams.

Derive the constitutive relation matrices for plane stress and plane strain situations.