The paper deals with the imposition of local stress constraints in topology optimization. The aim of the work is to analyze the performances of an alternative methodology to the ε-relaxation introduced in Cheng and Guo (Struct Optim 13:258–266, 1997), which handles the well-known stress singularity problem. The proposed methodology consists in introducing, in the SIMP law used to apply stress constraints, suitable penalty exponents that are different from those that interpolate stiffness parameters. The approach is similar to the classical one because its main effect is to produce a relaxation of the stress constraints, but it is different in terms of convergence features. The technique is compared with the classical one in the context of stress-constrained minimum-weight topology optimization. Firstly, the problem is studied in a modified truss design framework, where the arising of the singularity phenomenon can be easily shown analytically. Afterwards, the analysis is extended to its\ud natural context of topology bidimensional problems

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We present an alternative topology optimization formulation capable of handling the presence of stress constraints in a straightforward fashion. 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 doing so, any stress constraint may be handled within the optimization procedure without resorting to post-processing operation typical of displacement-based techniques that may also cause a loss in accuracy in stress computation if no smoothing of the stress is performed. Two dual variational principles of Hellinger–Reissner type are presented in continuous and discrete form that, which included in a rather general topology optimization problem in the presence of stress constraints that is solved by the method of moving asymptotes (Int. J. Numer. Meth. Engng. 1984; 24(3):359–373). Extensive numerical simulations are performed and ongoing extensions outlined, including the optimization of elastoplastic and incompressible media

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