ME 404

FINITE ELEMENT ANALYSIS

UNIT-I

Introduction to Finite Element Method for solving field problems, Stress and Equilibrium, Boundary conditions, Strain, Displacement, Stress-Strain relations.

One dimensional Problems:

Finite Element modeling coordinates and shape functions, Potential Energy approach:  Assembly of Global stiffness matrix and load vector, Finite element equations, Treatment of boundary conditions, Galerkin’s approach, Quadratic shape functions.

UNIT-II

Analysis of trusses and frames:  Element stiffness matrix for a truss member, Analysis of plane truss with two at each node.  Analysis of frames with two translations and a rotational degree of freedom at each node, Analysis of Beams: Element stiffness matrix for two nodes (Two degrees of freedom per node).

UNIT-III

Finite element modeling of two dimensional stress analysis with constant strain triangles and treatment of boundary conditions.  Finite element modeling of axi-symmetric solids subjected to axi-symmetric loading with triangular elements.

UNIT-IV

Two dimensional four nodded iso-parametric elements and numerical integration.  Steady state heat transfer analysis:  One dimensional analysis of a fin and two dimensional analysis of thin plate, analysis of circular shaft subjected to torsion.

UNIT-V

 Dynamic Analysis:  Formulation of finite element model, element matrices, Evaluation of Eigen values and Eigen vectors for a stepped bar and a beam, Time dependent field problems:  Application to one dimensional heat flow in a rod.  Introduction to finite element formulation of three dimensional problems in stress analysis, convergence requirements.  Introduction to Finite Element Analysis Software.

Suggested Reading

1. 1.G. Ramamurthy, Applied Finite Element Analysis, I.K. International Publishing House Pvt. Ltd., New Delhi, 2009.
2. 2.Tirupathi R, Chandraputla and Ashok D Belagundu, ‘Introduction to Finite Elements in Engineering’,  Practice Hall of India, 1997.
3. 3.Rao S.S, ‘The Finite Element Method in Engineering’,  Pergamon Press, 1989.
4. 4.Segerlind L J, ‘Applied Finite Element Analysis’, Wiley Eastern, 1984.
5. 5.Reddy J N, ‘An Introduction to Finite Element Method’, McGraw-Hill,