New Educational Matlab Tool to Explain Two Dimensional Finite Element Method to Graduate Students

Abstract

In this study a simple code is developed in powerful programming software MATLAB. Graduate engineering students are generally expected to cope with Finite Element Method in two and three dimensions during their Finite Element Courses. However textbooks of that courses, sometimes, do not have enough solved examples for students, because in two and three dimensions calculations are difficult to do manually. At this step a computer program which includes infinite number of examples, as user defines them, and their solution steps, is of crucial importance. The produced MATLAB code has these features as it can display stiffness matrix with or without boundary conditions, deformed shape of the body, displacement, strain and stress distributions over the surface. This code also makes it possible to analyze bodies as it is a plane stress or plane strain body. Besides, this MATLAB code can generate a step by step solution report for students to comprehend the Finite Element procedure. Since this code is a simple and educational tool, only one-piece rectangular bodies can be analyzed. The body to be analyzed can be meshed into various number of rectangular elements. These rectangular elements utilize bilinear Lagrangian shape functions, and Gauss Quadrature technique is used to deal with integrations. In this study four Gauss integration points are used as two in X direction and two in Y direction, which yields the exact integration as approximation functions are bilinear.