Friday, 4 January 2013
CE1018 – FINITE ELEMENT TECHNIQUES
L T P C
3 0 0 3
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
UNIT II FINITE ELEMENT ANALYSIS OF ONE DIMENSIONAL
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
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 9
Natural coordinates in 1, 2 and 3 dimensions – Use of area coordinates for triangular
elements in – Two 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
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 TEXT BOOKS
1. Chandrupatla, T.R. and Belegundu, A.D., “Introduction to Finite Element in
Engineering”, 3rd Edition, Prentice Hall, 2003.
2. Rao, S.S., “The Finite Element Method in Engineering”, Pergaman Press, 2003.
1. Reddy, J.N., “An Introduction to Finite Element Method”, McGraw-Hill, 1985.
2. Desai, C.S. and Abel, J.F., “Introduction to the Finite Element Method”,
Affiliated East West Press, 1972.
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