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# Finite Element Method

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### Overview

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.

### Syllabus

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.

### Taught by

Prof. Biswanath Banerjee, Prof. Amit Shaw

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