# MH1003 Finite Element Analysis Syllabus

MH1003 FINITE ELEMENT ANALYSIS 3 0 0 100
(Common to Mechanical, Automobile, Mechatronics (Elective) and Metallurgical Engineering (Elective))

OBJECTIVES
• To understand the principles involved in discretization and finite element approach
• To learn to form stiffness matrices and force vectors for simple elements

1. INTRODUCTION 9
Historical background – Matrix approach – Application to the continuum – Discretisation – Matrix algebra – Gaussian elimination – Governing equations for continuum – Classical Techniques in
FEM – Weighted residual method – Ritz method

2. ONE DIMENSIONAL PROBLEMS 9
Finite element modeling – Coordinates and shape functions- Potential energy approach – Galarkin approach – Assembly of stiffness matrix and load vector – Finite element equations – Quadratic shape functions – Applications to plane trusses

3. TWO DIMENSIONAL CONTINUUM 9
Introduction – Finite element modelling – Scalar valued problem – Poisson equation –Laplace equation – Triangular elements – Element stiffness matrix – Force vector – Galarkin approach - Stress calculation – Temperature effects

4. AXISYMMETRIC CONTINUUM 9
Axisymmetric formulation – Element stiffness matrix and force vector – Galarkin approach – Body forces and temperature effects – Stress calculations – Boundary conditions – Applications to cylinders under internal or external pressures – Rotating discs

5. ISOPARAMETRIC ELEMENTS FOR TWO DIMENSIONAL CONTINUUM 9
The four node quadrilateral – Shape functions – Element stiffness matrix and force vector – Numerical integration - Stiffness integration – Stress calculations – Four node quadrilateral for axisymmetric problems.

TUTORIAL 15
TOTAL : 60

TEXT BOOKS
1. Chandrupatla T.R., and Belegundu A.D., Introduction to Finite Elements in Engineering, Pearson Education 2002, 3rd Edition.
2. David V Hutton “Fundamentals of Finite Element Analysis”2004. McGraw-Hill Int. Ed.

REFERENCES
1. Rao S.S., The Finite Element Method in Engineering, Pergammon Press, 1989
2. Logan D.L., A First course in the Finite Element Method, Third Edition, Thomson Learning, 2002.
3. Robert D.Cook., David.S, Malkucs Michael E Plesha , “Concepts and Applications of Finite Element Analysis”, 2003.
4. Ed. Wiley.Reddy J.N., An Introduction to Finite Element Method, McGraw-Hill International Student Edition, 1985.
5. O.C.Zienkiewicz and R.L.Taylor, The Finite Element Methods, Vol.1. The basic formulation and linear problems, Vol.1, Butterworth Heineman, 5th Edition, 2000.
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