Unit 1

Boundary value problems and the need for numerical discretization: Introduction, examples of continuum problems, history of finite element method.

Weighted residual methods: Approximation by trial functions, weighted residual forms, piecewise trial functions, weak formulation, Galerkin method, examples of one-, two- and three-dimensional problems.

Variational methods: Variational principles, establishment of natural variational principles, approximate solution of differential equations by Rayleigh-Ritz method, the use of Lagrange multipliers, general variational principles, penalty functions, least-square method.

Unit 2

Isoparametric formulation: The concept of mapping, isoparametric formulation, numerical integration, mapping and its use in mesh generation.

Higher order finite element approximation: Degree of polynomial in trial functions and rate of convergence, the patch test, shape functions for C0 and C1 continuity, one-, two- and three-dimensional shape functions.

Unit 3

1. Rao, S. S., “Finite Element Method in Engineering”, Elsevier, 2011.
2. Reddy, J. N., “An Introduction to the Finite Element Method”, Tata McGraw Hill, 2005.

• Bathe K. J., “Finite Element Procedures in Engineering Analysis”, Prentice Hall of India, 1996.
• Cook R. D., Malkus D. S., Plesha M. F., and Witt R. J., “Concepts & Applications of Finite Element Analysis”, Wiley India, 2007.
• Chandrupatla T. R. and Belegundu A. D., “Introduction to Finite Elements in Engineering”, Prentice Hall of India, 2007.
• Zienkiewics O. C., Taylor R. L. and Zhu, J. Z., “The Finite Element Method: Its Basis and Fundamentals”, Butterworth-Heinemann, 2005.