**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.

EmoticonEmoticon