Finite Element Method
Indian Institute of Technology, Kharagpur and NPTEL via Swayam
This course may be unavailable.
This is an introductory level course on Finite Element Method. After attending the course, the students will be able to comprehend FEM as a numerical technique to solve partial differential equations representing various physical phenomena in structural engineering. The proposed course also provides a hands-on training on translating FEM formulation into computational code in MATLAB.INTENDED-AUDIENCE:BE/B.Tech (Elective), M.Tech, PhD.PRE-REQUISITES :Solid Mechanics/Numerical methods in Engineering.INDUSTRY-SUPPORT :Civil/Mechanical/Aerospace/Ocean and naval Architecture.
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.
Prof. Biswanath Banerjee, Prof. Amit Shaw