Keywords: topology optimization, stress constraints, minimum compliance, singularity problem, strength criteria, unilateral materials.

A formulation for the topology optimization of elastic structures that aims at minimizing the structural weight subject to compliance and a selected set of local strength constraints is investigated. It is especially conceived to exploit a global constraint providing stiffness to the optimal design, whereas active local constraints enforce feasibility with respect to the assigned strength of material. Having the aim of handling materials with either equal or unequal behaviour in tension and compression, the Drucker–Prager failure criterion is implemented. Enforcing the same strength limit in tension and compression, the conventional Von Mises criterion is recovered. Adopting an extreme ratio between them, optimal design involving unilateral materials can be addressed straightforwardly. Numerical issues related to the well–known singularity–problem are recalled. To overcome the related numerical instabilities, the relaxation of the equivalent stress measure called qp–approach herein is adopted. Numerical examples are presented to discuss features of the achieved optimal designs along with performances of the implemented multi–constrained procedure. Comparisons with the conventional compliance–based formulation are shown to investigate differences arising in the optimal design with respect to conventional approaches, depending on the assumed material behaviour.

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