Some convergence results in perimeter-controlled topology optimization

The computation of optimal topologies of elastic continuum structures using a constraint on the 'perimeter' is investigated. Predicting macroscopic 'b lack-white' topologies without the use of homogenization techniques, this a pproach is presently one of the most attractive approaches in topology opti mization. Mathematical justifications are given for both the relaxation of the discre te-value constraint on the design variable and for the finite element discr etizations. It turns out that the way in which the perimeter has been calcu lated to date, the numerical results will not approximate the intended orig inal problem, but one with a 'taxi-cab' perimeter which measures lengths of structural edges after projection onto the coordinate axes. (C) 1999 Elsev ier Science S.A. All rights reserved.