### CE 2050 FINITE ELEMENT TECHNIQUES B.E. CIVIL ENGINEERING SYLLABUS ELECTIVE – V ANNA UNIVERSITY, CHENNAI AFFILIATED INSTITUTIONS R - 2008

ANNA UNIVERSITY, CHENNAI

AFFILIATED INSTITUTIONS

R -  2008

B.E. CIVIL ENGINEERING

SYLLABUS

ELECTIVE – V

CE 2050                                  FINITE ELEMENT TECHNIQUES                                     L T P C

3  0 0 3

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.

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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