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Some convergence results in perimeter-controlled topology optimization. (English) Zbl 0947.74050
Summary: We examine the computation of optimal topologies of elastic continuum structures by using a constraint on the ‘perimeter’. Predicting macroscopic ‘black-white’ topologies without the use of homogenization techniques, this approach is presently one of the most attractive approaches in topology optimization. Mathematical justifications are given for both relaxation of discrete-value constraints on the design variable and for the finite element discretizations. It turns out that for the way in which the perimeter was calculated to date, the numerical results will not approximate the intended original problem, but a problem with a ‘taxi-cab’ perimeter which measures lengths of structural edges after projection onto the coordinate axes.

MSC:
74P15 Topological methods for optimization problems in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
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