Dr A.P.J. Abdul Kalam Technical University, UP (AKTU), Civil Engineering Semester 8, Finite Element Method Syllabus

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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

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

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

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

Unit - 5 Analysis of structures

5.1 Analysis of structures Truss elements

5.2 Analysis of truss problems by direct stiffness method

5.3 Analysis of frames and different problems

5.4 Different Axisymmetric truss problems

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