WITH EFFECT FROM THE ACADEMIC YEAR 2013- 2014

CE 459

FINITE ELEMENT METHODS

(Elective-III)

Instruction                                                                                                                                                                                       4 Periods per week

Duration of University Examination                                                                                                                                                     3 Hours

University Examination                                                                                                                                                                      75 Marks

Sessional                                                                                                                                                                                          25  Marks

UNIT-I

Introduction to finite element method: variational approach, Rayleigh -Ritz, and Galerkin’s methods. Stiffness matrix for two noded bar, truss, and beam elements, problems with 3 degrees of freedom. .

UNIT-II

Stiffness matrix for two noded beam element with 3 degrees of freedom per node. Transformation, generation of stiffness matrix for frames. Strain displacement and stress - strain relationship in an elastic continuum (linear problems). Equations of equilibrium, and boundry conditions. Plane stress and plane strain problems.

UNIT-III

Formulation of finite element method: using principle of virtual displacement. Determination of stiffness matrix for three noded triangular element (constant strain triangle), and 4 noded rectangular element for plane stress and plane strain problems. Convergence criteria for selection of displacement models. Discretisation of continuum.Assembly of global stiffness and load matrices.Displacement boundry conditions.

UNIT-IV

Isoparametric finite elements: Direct construction of shape functions for higher order elements using natural co-ordinate system. Shape functions for eight noded parabolic curved isoparametricelement. Determination of element stiffness matrix for four noded quadrilateral element. Use of Jacobian, and Gauss quadrature techniques. Load matrix for eight noded rectangular isoparametric element (for body forces and surface traction).

UNIT-V

Strain displacement and stress - strain relation for axisymmetric problems. Stiffness matrix for three noded ring element. Volume co-ordinates and stiffness matrix for four noded tetrahedron element.

Suggested Reading :

1. 1.O.C. Zienkiewicz and R.L. Taylor, the Finite Element Method, Vol. I, McGraw Hill, 1989.

1. 2.C.S. Krishna Moorthy, Finite Element Analysis, McGraw Hill, 1991.

1. 3.C.S. Desai and J.E Abel, Introduction to the Finite Method,

VanNostrand, 2902.

1. 4.T.R. Chandrupatla, Finite Element Analysis for Engineering and Technology, Universities Press, 2004.