A Plane Stress Fea Problem For Which Students Can Write A Modest Computer Program

This paper proposes and then describes a modest finite element computer program which a student can write using almost any computer programming language. The types of finite element models which can be handled by this computer program, called PLANESTR, are described. The program steps required for the single element PLANESTR program are described. This program is capable of calculating the tensile stresses and shear stresses, at various locations within the element, based upon the applied forces at the element node points. The finite element stiffness subroutine is presented, since it is crucial to the calculation of stresses for the finite element models. An extension to the single element finite element program is presented which describes the steps involved in the multi-element PLANESTR program. Description of the Symbols Used. Symbol Description a the width of the finite element b the height of the finite element dblkel the finite element stiffness matrix dof degree of freedom E the modulus of elasticity of the material. eta normalized coordinate within the finite element (vertical) { F } column matrix of applied forces [ K ] stiffness matrix of the finite element model. kconst a constant [ L ] lower triangular matrix formed from [ K ] ndofout the number of degrees of freedom which are constrained to u = 0, v = 0, or both. nu the Poisson’s ratio of the material. thick the thickness of the finite element(s) [ U ] represents the inverse of [ L ] { u } column matrix of displacements u displacement in x-direction v displacement in y-direction X,Y global coordinates x,y local coordinates xi normalized coordinate within the finite element (horizontal) P ge 784.1 Proceedings of the 2002 American Society for Engineering Education Annual Conference & Exposition Copyright © 2002, American Society for Engineering Education Symbol Description ( Greek Letters ) b aspect ratio of finite element ( b = b/a ) h normalized coordinate within the finite element (vertical) n the Poisson’s ratio of the material. x normalized coordinate within the finite element (horizontal) {s} column matrix of stresses (sxx, syy, and sxy )