This course focuses on the fundamentals concepts and formulation of the finite element methods for solving differential equations arising in solid and fluid mechanics.
Overview of Engineering systems: Continuous and discrete systems (discussion on differential equations, matrix algebra) – Energy methods: Variational principles and weighted residual techniques (least square method, collocation, sub-domain collocation, Galerkin method) for one-dimensional equation, Rayleigh-Ritz Formulation, development of bar and beam element, application to truss and frames. – Finite elements for two-dimensions: Equivalence between energy formulation and Galerkin approach, discretization concepts, choice of elements, derivation of element shape functions (Lagrangian and Hermite) in physical coordinates, Iso-parameteric mapping, numerical integration, Assembly procedure, solution techniques, introduction to finite element programming. – Applications to problems in engineering: plane elasticity, heat conduction, potential flow and Transient problems. Computer implementation.
 K J Bathe, Finite element procedures, Prentice Hall, Indian edition, 2006.
 J Fish and T Belytschko, A first course in finite elements, Wiley, USA, 2007.
 R D Cook, D A Malkus, M E Plesha, RJ Witt, Concepts and Applications of finite element analysis, John Wiley & Sons, 4th edition, 2002.
 B Szabo and I Babuska, Introduction to finite element analysis, John Wiley & Sons, UK, 2011.
 OC Zienkiewicz and RL Taylor, The finite element method, Volume 1 & 2, 5th edition, Butterworth Heinemann, New Delhi, 2000.