Teaching Finite Element Method, the controversy between the use of commercial software and the development of mathematical skills

Abstract

Finite Element Method (FEM) course is a good opportunity to develop superior skills in our students; the controversy today is the use of commercial software in order to develop “Computational mechanical skills” which allow to the students to be a very good users and designers. Instead the use of programming skills in order to build codes which solve specific problems. My idea of an adequate course in FEM includes first of all the mathematical foundations like differential equations, matrix algebra, etc. Then the development of the matrix expression for different kinds of elements which includes spring element, bar element, beam element and plate element. With this intention the students can understand the concept of element, assembly of the rigidity matrix, boundary conditions, etc; the evolution of the complexity of the problems can justify the use of the computer code in order to solve big problems. But, what’s going on with complex geometry? The needed of the special code to mesh a complex solid take us in the way to use a commercial one, the most important thing at this moment is the student “have the right to use a commercial software” because already he knows the mathematics secrets of the black box. Obviously the develop of the computer code involves the mathematical aspects such like the weak formulation of the differential equation, the solution of the integrals using numerical procedure. The discussion of this aspect must involve the opinion of the faculty and students in order to clarify the expectative of the curricular plan in which the finite element method is included.