History of the Finite Element Analysis, solid mechanics stress equilibrium equation, strain-displacement equations, stress-strain Temperature Relations, Plane stress, plane starin and strain energy, Total potential energy, Essential and natural boundary conditions. Variation formulation in FEM – Rayleigh Ritz method - Weighted residual techniques -General FEA Process- FEA Solution Process.

Types of 1D element, Displacement function, Global and local coordinate systems, order of element, shape function and its properties. Formulation of element stiffness matrix and load vector for spring, bar, beam, truss and plane frame. Transformation matrix for truss and plane frame, Assembly of global stiffness matrix and load vector, properties of stiffness matrix, half bandwidth, Boundary conditions elimination method and penalty approach, stress calculations- example problems.

Types of 2D elements, Formulation of elemental stiffness matrix and load vector and load vector for Plane stress/strain such as Constant Strain Triangles (CST), Pascal‗s triangle , primary and secondary variables, properties of shape functions. Assembly of global stiffness matrix and load vector, Boundary conditions, solving for primary variables (displacement) - example problems, Overview of axi-symmetric elements.

Concept of isoperimetric elements, Terms Isoperimetric, super parametric and sub-parametric. Isoperimetric formulation of bar element. Coordinate mapping-Natural coordinates, higher order elements – lagrangean and serendipity elements. Convergence requirements-patch test, uniqueness of mapping-Jacobian matrix. Numerical integration- 2 and 3 point quadrature, full and reduced integration- example problems.

Introduction, Governing differential equation, steady-state heat transfer formulation of 1D element for conduction and convection problem, boundary conditions and solving for temperature distribution- example problems. Types of dynamic analysis, General dynamic equation of motion, point and distributed mass, lumped and Consistent mass, Mass matrices formulation of bar and beam element, Un-damped-free vibration- example problems