We are concerned with the computational topological optimization of elastic structures, in particular minimization of compliance subject to a constraint on the mass. Through computational experiments, it is discovered that even very simple optimization problems can exhibit complex behavior such as critical points and bifurcation. In the vicinity of critical points, structural topology optimization problems are not well-posed since infinitesimally small perturbations lead to distinct topologies.
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White, D.A., Voronin, A. A computational study of symmetry and well-posedness of structural topology optimization. Struct Multidisc Optim 59, 759–766 (2019). https://doi.org/10.1007/s00158-018-2098-9