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Other university, Civil Engineering , Finite Element Method Syllabus
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Unit - 1 Calculus Of Variation
Unit 1
Calculus of variation
1.1 Introduction to calculus of variations
1.2 Introduction to equilibrium equations in elasticity
1.3 Eulers Lagrange’s equations
1.4 Principal of virtual work
1.5 Virtual displacements
1.6 Principles of minimum potential energy
1.7 Boundary value
1.8 Initial value problems
1.9 Flexibility approach
1.10 Displacement approach
1.11 Different problems in structural analysis
Unit - 2 FEM Procedure
Unit 2
FEM Procedure
2.1 FEM Procedure
2.2 Derivation of FEM equations by variation principle polynomials
2.3 Concept of shape functions
2.4 Derivation for linear simplex element
2.5 Need for integral forms
2.6 Interpolation polynomials in global and local coordinates
2.7 Weighted residual Methods Concept of weighted residual method
2.8 Derivation of FEM equations by Galerkins method
2.9 Solving cantilever beam problem by Galerkin’s approach
2.10 Derivation of shape functions for CST triangular elements
2.11 Shape functions for rectangular element
2.12 Shape functions for quadrilateral element
Unit - 3 Higher Order Elements
Unit 3
Higher order Elements
3.1 Higher order Elements Concept of isoparametric elements
3.2 Concept of Jacobin Matrix
3.3 Numerical Integration Numerical Integration
3.4 Different problems of numerical integration evaluation of element stiffness matrix
3.5 Automatic mesh generation schemes
Unit - 4 Pascal's Triangle Law For 2D Shape Functions Polynomial
Unit 4
Pascals triangle law for 2D shape functions polynomial
4.1 Pascals triangle law for 2D shape functions polynomial
4.2 Pascals triangle law for 3D shape function polynomials
4.3 Shape function for beam elements
4.4 Hermition shape functions
4.5 Convergence Convergence criteria and Compatibility requirements
4.7 Geometric isotropy invariance
4.8 Shape functions for Isoparametric elements
4.9 Special characteristics of stiffness matrix
4.10 Direct method for deriving shape functions using Langrages formula
4.11 Plane stress problems
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