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

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.