Modelagem matemática e aplicações do problema da torção elastoplástica para diferentes geometrias

Abstract

A study about the elastoplastic torsion problem for different geometries is presented, regarded as an obstacle type problem by means of the membrane analogy. The problem is to define regions of elasticity and plasticity in the cross section of a bar subjected to torsion. Equivalence with the obstacle problem allows the minimization problem to be formulated as a complementarity problem. Thus, the solution is determined through FDIPA and FDA-MNCP algorithms for minimization and mixed complementarity, respectively, using the finite difference method. Examples for circular, rectangular and L-section bars are developed, as well as comparisons with problems in the literature. The results are satisfactory and show how the shape of the section influences the plasticity regions. Finally, some special cases are presented that do not belong to the elastoplastic torsion problem physically, but they bring interesting discussions.