**CE1033 FINITE ELEMENT TECHNIQUES 3 1 0 100**

**OBJECTIVE**

At the end of this course the student shall have a basic knowledge of finite element method and shall be able to analyse linear elastic structures, that he has studied about in core courses, using finite element method.

**1. INTRODUCTION – VARIATIONAL FORMULATION 8**

General field problems in Engineering – Modelling – Discrete and Continuous models –

Characteristics – Difficulties involved in solution – The relevance and place of the finite element method – Historical comments – Basic concept of FEM, Boundary and initial value problems – Gradient and divergence theorems – Functionals – Variational calculus – Variational formulation of VBPS. The method of weighted residuals – The Ritz method.

**2. FINITE ELEMENT ANALYSIS OF ONE DIMENSIONAL PROBLEMS 8**

One dimensional second order equations – discretisation of domain into elements – Generalised coordinates approach – derivation of elements equations – assembly of elements equations – imposition of boundary conditions – solution of equations – Cholesky method – Post processing – Extension of the method to fourth order equations and their solutions – time dependant problems and their solutions – example from heat transfer, fluid flow and solid mechanics.

**3. FINITE ELEMENT ANALYSIS OF TWO DIMENSIONAL PROBLEMS 8**

Second order equation involving a scalar-valued function – model equation – Variational formulation – Finite element formulation through generalised coordinates approach – Triangular elements and quadrilateral elements – convergence criteria for chosen models – Interpolation functions – Elements matrices and vectors – Assembly of element matrices – boundary conditions – solution techniques.

**4. ISOPARAMETRIC ELEMENTS AND FORMULATION 7**

Natural coordinates in 1, 2 and 3 dimensions – use of area coordinates for triangular elements in - 2 dimensional problems – Isoparametric elements in 1,2 and 3 dimensional – Largrangean and serendipity elements – Formulations of elements equations in one and two dimensions - Numerical integration.

**5. APPLICATIONS TO FIELD PROBLEMS IN TWO DIMENSIONALS 7**

Equations of elasticity – plane elasticity problems – axisymmetric problems in elasticity – Bending of elastic plates – Time dependent problems in elasticity – Heat – transfer in two dimensions – incompressible fluid flow.

**6. INTRODUCTION TO ADVANCED TOPICS (NOT FOR EXAMINATION PURPOSE) 7**

Three dimensional problems – Mixed formulation – use of software packages like NISA, ANSYS OR NASTRAN.

**TOTAL : 45**

**TEXT BOOK**

1. Chandrupatla, T.R., and Belegundu, A.D., “Introduction to Finite Element in Engineering”, Third Edition, Prentice Hall, India, 2003

**REFERENCES**

1. J.N.Reddy, “An Introduction to Finite Element Method”, McGraw-Hill, Intl. Student Edition, 1985.

2. Zienkiewics, “The finite element method, Basic formulation and linear problems”, Vol.1, 4/e, McGraw-Hill, Book Co.

3. S.S.Rao, “The Finite Element Method in Engineering”, Pergaman Press, 2003.

4. C.S.Desai and J.F.Abel, “Introduction to the Finite Element Method”, Affiliated East West Press, 1972.

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