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Finite Element Analysis I

Lecture 1: Mod-01 Lec-01 Lecture 01

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Lecture Details :

Finite Element Analysis by Dr. B.N. RAO, Department of Civil Engineering, IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in

Course Description :

Contents:
Approximate solution of boundary value problems-Methods of weighted residuals, Approximate solution using variational method, Modified Galerkin method, Boundary conditions and general comments

Basic finite element concepts-Basic ideas in a finite element solution, General finite element solution procedure, Finite element equations using modified Galerkin method, Application: Axial deformation of bars, Axial spring element - Analysis of trusses-Two dimensional truss element, Three dimensional space truss element, Stresses due to lack of fit and temperature changes

Beam bending-Governing differential equation for beam bending, Two node beam element, Exact solution for uniform beams subjected to distributed loads using superposition, Calculation of stresses in beams, Thermal stresses in beams - Analysis of structural frames-Plane frame element, Thermal stresses in frames, Three dimensional space frame element

General one dimensional boundary value problem and its applications-One dimensional heat flow, Fluid flow between flat plates-Lubrication Problem, Column buckling - Higher order elements for one dimensional problems-Shape functions for second order problems, Isoparametric mapping concept, Quadratic isoparametric element for general one dimensional boundary value problem, One dimensional numerical integration, Application: Heat conduction through a thin film

Two dimensional boundary value problems using triangular elements, Equivalent functional for general 2D BVP, A triangular element for general 2D BVP, Numerical examples - Isoparametric quadrilateral elements-Shape functions for rectangular elements, Isoparametric mapping for quadrilateral elements, Numerical integration for quadrilateral elements, Four node quadrilateral element for 2D BVP, Eight node serendipity element for 2D BVP

Isoparametric triangular elements-Natural (or Area) coordinates for triangles, Shape functions for triangular elements, Natural coordinate mapping for triangles, Numerical integration for triangles, Six node triangular element for general 2D BVP - Numerical integration-Newton-Cotes rules, Trapezium rule, Simpsonís rule, Error term, Gauss-Legendre rules, Changing limits of integration, Gauss-Leguerre rule, Multiple integrals, Numerical integration for quadrilateral elements, Numerical integration for triangular elements

Applications based on general two dimensional boundary value problem-Ideal fluid flow around an irregular object, Two dimensional steady state heat flow, Torsion of prismatic bars - Two dimensional elasticity-Governing differential equations, Constant strain triangular element, Four node quadrilateral element, Eight node isoparametric element

Axisymmetric elasticity problems-Governing equations for axisymmetric elasticity, Axisymmetric linear triangular element, Axisymmetric four node isoparametric element - Three dimensional elasticity-Governing differential equations, Four node tetrahedral element, Eight node hexahedral (brick) element, Twenty node isoparametric solid element, Prestressing, initial strains and thermal effects

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