2K6 ME 805(A): FINITE ELEMENT ANALYSIS

Module I (13 hours)
Linear vector spaces – linear transformations and functionals – linear, bilinear and quadratic forms – theory of normed spaces – theory of inner product spaces – concepts from variational calculus – variational methods of approximation – Ritz method – weighted residual method – Galerkin method – subdomain method – collocation method
Module II (11 hours)
Finite element analysis of one dimensional problems – procedure – one dimensional elements and interpolation functions – analysis of one dimensional second and fourth order equations – approximation errors in the finite element method – computer implementation
Module III (15 hours)
Finite element analysis of two dimensional problems – two dimensional elements and interpolation functions – second order equations involving a scalar valued function – comments on mesh generation and composition of boundary conditions – analysis of plane elasticity and incompressible fluid flow problems – time dependent problems (transient heat transfer) – isoparametric elements and numerical integration
Module IV (13 hours)
Alternative formulations – least square formulation – mixed formulation – Eigenvalue problems – nonlinear problems – three dimensional elements and interpolation functions – formulation of three dimensional problems (two and three dimensional Navier-Stokes equations – three dimensional heat transfer equations)

Text books
1 Reddy J.N., An Introduction to the Finite Element Method, McGraw Hill International Edition
2 Reddy J.N., Applied Functional Analysis and Variational Methods in Engineering, McGraw Hill, International Edition 
Reference books
1 Huebner K.H., The Finite Element Method for Engineers, John Wiley
2 Zenkiewicz O., The Finite Element Method, McGraw Hill International Edition