1. Stress strain and deformation relations , plane - stress, planes strain, Principles of minimum Potential Energy, principle of virtual work.

2. Stiffness method for steady state problems of discrete systems (Bar, trusses, one dimensional heat transfer system) Element stiffness matrix, Assembly of elements, global stiffness matrix and its properties, Node numbering, Displacement and force Boundary conditions, Transformations matrix, Gauss elimination method

3. Displacement - Based FEM for solid mechanics;

   1. Derivation of finite element equilibirium equations, Langrangian elements (I-D & 2-D elements); CST, rectangle, aspect ratio shape functions, lumping of loads, comptability and convergence requirements. Stress calculations

   2. Isopohmetric Derivation of Stiffness matrices, bar and plane bilinear elements, Seredipity elements, natural coordinates, numerical integration, Co-continuity p and h refinement

4. Variational Method: Variational Approach for known functional of field problems
   Weighted Reidual Methods: Point collection, subdomain collocation, methods of least square, Galerkin
   Application of these methods to one dimensional boundary value problems; Structures, fluid mechanics and heat transfer.

5. Finite Elements in Dynamics and Vibrations: Introduction, Dynamic Equations, Mass and Damping Matrics, Mass Matrics, Consistent and Diagonal, Damping, Natural frequencies and Mode Shapes.

Recommended Books:

1. Introduction to Finite Elements in Engineering, Tirupathi R. Chandrapatla and Ashok D. Belagundu, Prentice Hall of India. Ltd.

2. Comcept and Applications of Finite Element Analysis, Robert D. Cook. David S. Malkus. Michaiel E. Palesha, John Wiley & Sons.

3. Finite Element Procedures, Klaus Jurgan Bathe, Prentice Hall of India, New Delhi