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Abstract This paper explores the application of the Hybrid-Mixed Stress Formulation (HMSF) in the Topology Optimization Method (TOM), a technique for optimizing material distribution in structures. HMSF, a non-conventional Finite Element Method (FEM), places emphasis on direct and independent stress field approximation. Despite recent trends in non-standard FEM methods, hybrid-mixed formulations remain relatively underexplored in TOM problems. The paper also presents the mathematical formulation of HMSF-TOM, crucial for its implementation, and addresses the Minimum Compliance with Weight and Stress Constraints (MCWSC) problem. The potential of the formulation is examined through a stress constraint problem evaluated using a p-mean norm in two examples: the L-Bracket Beam and the Portal Frame. The formulation achieves freely checkboard designs and optimal layouts with no edge fading, consistent with classic FEM results. Concerning the stress constraints problems, the formulation has shown to alleviate the stress concentrations regions, agreeing with the results found on the literature, although not achieving layouts with maximum stress lower than the limit prescribed.
Coutinho et al. (Thu,) studied this question.