Introduction to FEM, basic concept, historical background, general applicability, engineering Applications. Boundary conditions. Potential energy and equilibrium, Rayleigh-Ritz method and Galerkin method-applied to simple problems on axially loaded members, cantilever, simply supported beams, with point loads and distributed loads.

Introduction; Finite Element Modelling – Element Division; Numbering Scheme; Coordinate and Shape Functions; The Potential Energy Approach; Assembly of Global Stiffness Matrix and Load Vector; Treatment of Boundary Conditions; Temperature Effects; Numericals. Stiffness matrix of bar element by direct method, Properties of stiffness matrix.

Local and Global co-ordinate systems, Trusses – assumptions, formulation of Truss element, Hermite functions, formulation of beam. Numericals on Trusses and beams.

Second Order 2D Equations involving Scalar Variable Functions – Variational formulation –Finite Element formulation – Triangular elements – Shape functions and element matrices and vectors. Equations of elasticity – Plane stress, plane strain and axisymmetric problems.

Steady state heat transfer, 1D heat conduction governing equation, boundary conditions, One dimensional element, Galerkin approach for heat conduction, heat flux boundary condition, 1D heat transfer in thin fins. Numericals.