Implementation of an elastoplastic finite element code in Python

Resumo

The use of the finite element method is one of the most efficient approaches to dealing with a problem
with non-linearity. It is common that such problems are taken to commercial engineering programs, whose main
purpose is to obtain the stresses for the user's decision-making, without a deep focus on the methodology that
governs such analyses. In this paper, a finite element code with non-linearity of the material was implemented in
Python, which is a language highlighted for being an Open-Source technology. The work aims to facilitate the
understanding of a practical application of finite elements with perfect elastoplastic behavior and, thus, to serve as
a guide for undergraduate and graduate students interested in the subject. As a practical application, a rectangular
steel plate was modeled and evaluated against a vertical load on one of its edges. To this end, the Von Mises yield
criterion was used to determine the stresses and, after reaching the yield of the material, the Newton-Raphson
iterative method was used to determine the displacements. At the end of the work, there was a good agreement
between stresses obtained with the finite element code and the chosen commercial finite element program.