Course

Unit 1

Boundary value problems and the need for numerical discretisation: 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

Coordinate Transformation: Transformation of vectors and tensors, transformation of stiffness matrices, degree of freedom within elements, condensation, condensation and recovery algorithm, substructuring, structural symmetry.

Formulation of stiffness matrix, member approach for truss and beam element, node numbering, assembly of element equations, formation of overall banded matrix equation, boundary conditions and solution for primary unknowns, Equilibrium and compatibility in solution- applications to truss and beam.

Prerequisite(s): 19CIE212 Structural Analysis

Course objectives

• Explain the fundamental concepts of finite element method and solve structural problems by selecting a suitable element, developing stiffness & force matrices and incorporating boundary
• Use mathematical and approximate methods to solve the boundary value problems

Course Outcome

CO1: Solve boundary value problems using various approximate methods

CO2: Develop mathematical formulations for structural systems

CO3: Analyse the structural elements like truss, beam etc by formulating stiffness matrix

CO PO Mapping

Text book(s)

Rao. S.S., “Finite Element Method in Engineering”, Elsevier, 2011.

Reddy, J.N., “An Introduction to the Finite Element Method”, Tata McGraw Hill, 2005.

Reference book(s)

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. & 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.