Some convergence results in perimeter-controlled topology optimization Original Research Article

The computation of optimal topologies of elastic continuum structures using a constraint on the ‘perimeter’ is investigated. 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 the relaxation of the discrete-value constraint on the design variable and for the finite element discretizations. It turns out that the way in which the perimeter has been calculated to date, the numerical results will not approximate the intended original problem, but one with a ‘taxi-cab’ perimeter which measures lengths of structural edges after projection onto the coordinate axes.