Solving Topology Optimization Problems with Mixed Finite Elements

We present a novel topology optimization formulation capable to handle in a straightforward fashion the presence of stress constraints. The main idea is to adopt a mixed finite--element discretization scheme wherein not only displacements (as usual) but also stresses are the variables entering the formulation. By so doing, any stress constraint may be directly handled within the optimization procedure. Furthermore, the proposed discretization scheme is capable to handle incompressible materials such as rubber--like materials that are of paramount interest in engineering applications such as base isolation. One should note that incompressible materials cannot be considered within classic displacement--based topology optimization methods that are a#ected by the well--known locking phenomenon