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You are here:Open notes-->Anna-University-->CE-2050-FINITE-ELEMENT-TECHNIQUES

# How to study this subject

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.
UNIT I INTRODUCTION � VARIATIONAL FORMULATION 9
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.
UNIT II FINITE ELEMENT ANALYSIS OF ONE DIMENSIONAL PROBLEMS 10
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.
UNIT III FINITE ELEMENT ANALYSIS OF TWO DIMENSIONAL PROBLEMS 10
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.97
UNIT IV ISOPARAMETRIC ELEMENTS AND FORMULATION 8
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.
UNIT V APPLICATIONS TO FIELD PROBLEMS IN TWO DIMENSIONALS 8
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
TOTAL: 45 PERIODS
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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