Theory: Historical Background – Mathematical Modeling of field problems in Engineering – Governing Equations – Discrete and continuous models – Boundary, Initial and Eigen Value problems– Variation formulation in FEM – Rayleigh Ritz method - weighted residual techniques - FEA General procedure –Discretization of the domain – advantages, limitations and applications of FEA- Hypermesh abaqus Tool. Practical: Structural analysis of cantilever beam and simply supported beam under different boundary conditions Structural analysis of fixed beam under different boundary conditions

Theory: 1 –D bar element - shape function using natural coordinates and generalized coordinates, stiffness matrix of a 1-D bar element –Springs - finite element formulation of stiffness matrix, load vector and assembly of globalequations, Temperature effects – example problems. Stiffness matrix and finite element equation for a two node Truss element – Beams - example problems. Practical: Structural Analysis of simple trusses Structural analysis of composite trusses

Theory: Finite element modeling – 2-D element under plane stress and plane strain condition - shape function for the Constant Strain Triangular element using natural coordinates and generalized coordinates - strain displacement matrix of CST element – axisymmetric element - example problems Practical: Stress analysis under plane stress condition - pressure vessel subjected to an internal pressure. Model frequency analysis of 2D Components.

Theory: Basic equations of heat transfer - Shape function of 1-D heat conduction, stiffness matrix for 1-D heat conduction, with free end convection, with internal heat generation- assembly of global equations and load vector, Finite element formulation - Example problems. Higher order elements – Quadrilateral elements Practical: Heat transfer analysis of 2D components under different boundary conditions Heat transfer analysis of 3D components under different boundary conditions

Theory: Natural co-ordinate systems – Isoparametric elements – shape functions for a 2-D four noded and eight noded Isoparametric rectangular element using natural coordinate system - Serendipity elements – Numerical integration – Gaussian Quadrature – example problems. Practical: Modal analysis of Cantilever, Simply supported and Fixed beams under different boundary conditions Harmonic analysis of Cantilever, Simply supported and Fixed beams under different boundary conditions