Finite Element Analysis

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Description

This course focuses on the fundamentals concepts and formulation of the finite element methods for solving differential equations arising in solid and fluid mechanics.

Course Contents

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.

Text Books

[1] K J Bathe, Finite element procedures, Prentice Hall, Indian edition, 2006.

[2] J Fish and T Belytschko, A first course in finite elements, Wiley, USA, 2007.

[3] R D Cook, D A Malkus, M E Plesha, RJ Witt, Concepts and Applications of finite element analysis, John Wiley & Sons, 4th edition, 2002.

Reference Books

[1] B Szabo and I Babuska, Introduction to finite element analysis, John Wiley & Sons, UK, 2011.

[2] OC Zienkiewicz and RL Taylor, The finite element method, Volume 1 & 2, 5th edition, Butterworth Heinemann, New Delhi, 2000.