On the use of a truly–mixed formulation in topology optimization with global stress–constraints

The work refers to the field of topology optimization for bidimensional structures and addresses the case in which global stress–constraints are considered to improve final designs.
Most of the previous research tackles this topic relying on classical displacement–based finite elements where stresses are recovered via post–processing techniques. The work conversely investigates the use of a truly–mixed formulation where stresses are independent variables of the problem while displacements play the secondary role of Lagrangian multiplier. The implemented discretization is based on a composite triangular element whose features may be advantageously exploited in stress–constrained topology optimization. The discretization is checkerboard–free and allows to tackle topology optimization with element–based constraints without introducing any additional filtering technique. The high accuracy in the evaluation of the average stresses is expected to improve the efficiency of the numerical procedure, especially in the case of a single global constraint that has to govern the whole domain. The adopted discretization also passes the robustness condition even in the case of incompressible materials and this allows to menage strength constraints also for rubber–like components.
Basing on these ideas, numerical investigations are carried out to test preliminary applications of the truly–mixed technique coupled with topology optimization and global stress–constraints. To handle the well–known singularity problem, that affects the constraints imposition, an alternative scheme is herein adopted instead of a classical "–relaxation. An example where a homogenous stress distribution is expected is firstly tested, having the aim of pointing out the main features of the proposed procedure. Afterwards, numerical simulations address a classical L–shaped specimen, pointing out pros and cons of the approach.