ANNA UNIVERSITY, CHENNAI
R - 2008
B.E. CIVIL ENGINEERING
ELECTIVE – V
CE 2050 FINITE ELEMENT TECHNIQUES L T P C
3 0 0 3
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
1. Chandrupatla, T.R., and Belegundu, A.D., "Introduction to Finite Element in
Engineering", Third Edition, Prentice Hall, India, 2003.
1. J.N.Reddy, "An Introduction to Finite Element Method", McGraw-Hill, Intl. Student
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