Topology Optimization of Multi-Loaded Structures with Mixed Finite Elements

Abstract

The paper presents a topology optimization formulation that uses mixed-finite elements, here specialized for the design of multi-loaded structures. The discretization scheme adopts stresses as primary variables in addition to displacements which usually are the only variables considered. Two dual variational formulations based on the Hellinger-Reissner variational principle are presented in continuous and discrete form. The use of the mixed approach coupled with the choice of nodal densities as optimization variables of the topology problem lead to 0–1 checkerboard-free solutions even in the case of multi-loaded structures design. The method of moving asymptotes (MMA) by Svanberg (1984) is adopted as minimization algorithm. Numerical examples are provided to show the capabilities of the presented method to generate families of designs responding to different requirements depending on stiffness criteria for common structural multi-load problems. Finally the ongoing research concerning the presence of stress constraints and the optimization of incompressible media is outlined.