A mixed FEM approach to stress-constrained topology optimization

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.