Mixed finite-element approaches for topology optimization

We present a novel topology optimization formulation capable to handle 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. Hellinger-Reissner variational principles are derived in continuous and discrete form that are included in a rather general topology optimization problem in the presence of stress constraints that is solved by the method of moving asymptotes (MMA) [21]. A novel relaxation approach is proposed to handle the non-qualification properties of the stress constraints.