A Plane Stress Fea Problem Which Students Can Solve Using An Inexpensive Calculator

This paper describes a stress analysis problem which can be used to introduce lower division engineering or engineering technology students to the finite element analysis (FEA) method. Step by step the student sets up the matrix equation which represents the system of simultaneous linear equations which is necessary to solve for the unknown displacements at each of the nodes. They then solve this system of equations using a numerical method which is efficient for large systems of simultaneous linear equations. Using these nodal displacements they calculate the normal and shear stresses at several different locations within the finite elements. These stresses are calculated by using the stress-displacement system of equations. This system of equations is also set up by the students. All of this they can do with an inexpensive scientific calculator. Description of the Symbols Used. Symbol Description Aij elements of the matrix [A] a width of the finite element b height of the finite element ci constants Dij elements of the stress-displacement matrix E modulus of elasticity Fi elements of the force matrix kij elements of the stiffness matrix lij elements of lower triangular matrix [L] t thickness of the finite element ui elements of the displacement matrix ux displacement in the x-direction uy displacement in the y-direction vi elements of the matrix [v] x coordinate along the horizontal axis y coordinate along the vertical axis Page 679.1 Proceedings of the 2001 American Society for Engineering Education Annual Conference & Exposition Copyright © 2001, American Society for Engineering Education Description of the Symbols Used ( continued ) Symbol Description ( Greek letters ) β aspect ratio ( i.e. b/a) η dimensionless coordinate ( vertical axis ) ν Poisson’s ratio ξ dimensionless coordinate ( horizontal axis ) σxx normal stress in the x-direction σyy normal stress in the y-direction σxy shear stress in the xy-plane