Finite Element Method

Week 1: Introduction, Boundary value problems and solution methods, Direct approach – example, advantage and limitations.Week 2: Elements of calculus of variation, Strong form and weak form, equivalence between strong and weak forms, Rayleigh-Ritz method.Week 3: Method of weighted residuals – Galerkin and Petrov-Galerkin approach; Axially loaded bar, governing equations, discretization, derivation of element equation, assembly, imposition of boundary condition and solution, examples.Week 4: Finite element formulation for Euler-Bernoulli beams.Week 5: Finite element formulation for Timoshenko beams.Week 6: Finite element formulation for plane trusses and frames computer implementation.Week 7: Finite element formulation for two-dimensional problems - completeness and continuity, different elements (triangular, rectangular, quadrilateral etc.), shape functions, Gauss quadrature technique for numerical integration.Week 8: Finite element formulation for two-dimensional scalar field problems; Iso-parametric formulation Application to Heat conduction and torsion problems.Week 9: Finite element formulation for two-dimensional problems in linear elasticity; Formulation.Week 10: Finite element formulation for two-dimensional problems in linear elasticity; Examples and computer implementation.Week 11: Implementation issues, locking, reduced integration, B-Bar method.Week 12: Finite element formulation for three-dimensional problems; Different elements, shape functions, Gauss quadrature in three dimension, examples.