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Session 3649

A Simple Problem Which Students Can Solve and Check Using an Inexpensive Calculator

Patrick J. Cronin The Pennsylvania State University New Kensington Campus

Abstract

This paper proposes a simple engineering structural analysis problem which can be used to introduce lower division engineering or engineering technology students to the fundamentals of 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 numbers of equations. All of this they do with an inexpensive scientific calculator. As the final step they calculate the stress in each structural member.

1. Introduction

Finite element analysis (FEA) software can produce color stress contour plots representing the stress at thousands of points within a machine part with dozens of forces applied. A student studying stress analysis for the first time can beneficially be exposed to the terminology and progression of calculations used to calculate the stresses in the elements of an FEA model. Terms involved in FEA analysis include: nodes, local and global stiffness matrices, local and global coordinate systems, forward reduction, and backward substitution. A model which I have used is a truss composed of three strut elements which form a triangle. Each strut has a simple 4 x 4 local element stiffness matrix 1. The local x direction of each strut makes a non-zero angle with the global X axis. Therefore, the local stiffness matrix of each strut must be transformed into a global element stiffness matrix. The transformation is done using transformation matrices based upon the angle between the local and global coordinate systems. All of these calculations can be done using an inexpensive scientific calculator. The required data consists of: (1) the

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Cronin, P. J. (2000, June), A Simple Problem Which Students Can Solve And Check Using An Inexpensive Calculator Paper presented at 2000 Annual Conference, St. Louis, Missouri. 10.18260/1-2--8697