10ME64 Finite Element Methods syllabus for ME


Part A
Unit-1 Introduction 7 hours

Equilibrium equations in elasticity subjected to body force, traction forces, and stress-strain relations for plane stress and plane strains. General description of Finite Element Method, Application and limitations. Types of elements based on geometry. Node numbering, Half band width.

Unit-2 Basic Procedure 7 hours

Euler - Lagrange equation for bar, beam (cantilever / simply supported fixed) Principle of virtual work, principle of minimum potential energy, Raleigh’s Ritz method. Direct approach for stiffness matrix formulation of bar element. Galerkin’s method.

Unit-3 Interpolation Models 7 hours

Interpolation polynomials- Linear, quadratic and cubic. Simplex complex and multiplex elements. 2D PASCAL’s triangle. CST elements-Shape functions and Nodal load vector, Strain displacement matrix and Jacobian for triangular and rectangular element.

Unit-4 Solution of 1-D Bars 6 hours

Solutions of bars and stepped bars for displacements, reactions and stresses by using penalty approach and elimination approach. Guass-elimination technique.

Part B
Unit-5 Higher Order Elements 6 hours

Langrange’s interpolation, Higher order one dimensional elements-Quadratic and cubic element and their shape functions. Shape function of 2-D quadrilateral element-linear, quadric element Iso- parametric, Sub parametric and Super parametric elements. numerical integration : 1, 2 and 3 gauge point for 1D and 2D cases.

Unit-6 Trusses 6 hours

Stiffness matrix of Truss element. Numerical problems.

Unit-7 Beams 6 hours

Hermite shape functions for beam element, Derivation of stiffness matrix. Numerical problems of beams carrying concentrated, UDL and linearly varying loads.

Unit-8 Heat Transfer 7 hours

Steady state heat transfer, 1D heat conduction governing equations. Functional approach for heat conduction. Galerkin’s approach for heat conduction. 1D heat transfer in thin fins.

Last Updated: Tuesday, January 24, 2023