A finite element elasticity programming in Mathematica software

Abstract

Modern software's allow computers to perform symbolic calculations in addition to simple numerical computations for which they were originally designed. This fact opens new possibilities in numerical simulation. In this paper a finite element implementation using the commercial software Wolfram Mathematica is used to solve a plane stress elasticity problem. The code adaptability from the provided examples to more challenging problems can easily be performed using the present code. Numerical examples with post‐processing illustrates the new tool and its flexibility. It has been proven in this study the feasibility of Wolfram Mathematica in learning and programming finite element methods for the solution of two‐dimensional problems in elasticity.

FEM education in undergraduate studies: Industry‐informed research

“…Since solving FEM problems by hand is limited to a few simple elements [3], computer programs complement the theoretical part of the coursework [6]. Three schemes can be identified: (a) have the students develop their own FEM solver using Matlab or other programming tools [2,8,31]; (b) provide educational programs that allow the student to understand, and even modify, the operation of a FEM solver [5,11,14,38,40], and (c) use commercial software, either basic FEA modules included in CAD software [21,36,41], or in-depth FEM codes [16,19,39,42].…”

On the solutions of fluid flow problems with a Chebyshev collocation method using Mathematica

“…The use of symbolical software as a tool for the teaching and learning process for engineering students is given, for example, in the work of Cariaga and Nualart [9]; they implemented tools in Matlab and Maple for a numerical analysis course. For example, Jiang and Wang [22] and Cecilio and Dos Santos [11] have used Mathematica to implement the finite element method for the solution of plasticity and elasticity equations, whereas Adair and Jaeger [1] developed a finite volume method to teach the basic steps involved in solving the Navier−Stokes equations. In general, these authors intend to involve students from all mathematical backgrounds in the numerical methodology and motivate them to develop the numerical tools on their own.…”