On the Use of Mixed Finite Elements in Topology Optimization

The paper deals with a topology optimization formulation that uses mixed-finite elements. The discretization scheme adopts not only displacements (as usual) but also stresses as primary variables. Two dual variational formulations based on the HellingerReissner variational principle are presented in continuous and discrete form. The use of this technique and the choice of nodal densities as optimization variables are the main features of the topology optimization problem here formulated and solved by the method of moving asymptotes (MMA) [21]. Numerical examples are performed to test the capabilities of the presented method and to introduce the ongoing research concerning the presence of stress constraints and the optimization of incompressible media.