A robust dual algorithm for topology design of structures in discrete variables

摘要

Dual optimization algorithms for the topology optimization of continuum structures in discrete variables are gaining popularity in recent times since, in topology design problems, the number of constrains is small in comparison to the number of design variables. Good topologies can be obtained for the minimum compliance design problem when the perimeter constraint is imposed in addition to the volume constraint. However, when the perimeter constraint is relaxed, the dual algorithm tends to give bad results, even with the use of higher-order finite element models as we demonstrate in this work. Since, a priori, one does not know what a good value of the perimeter to be specified is, it is essential to have an algorithm which generates good topologies even in the absence of the perimeter constraint. We show how the dual algorithm can be made more robust so that it yield good designs consistently in the absence of the perimeter constraint. In particular, we show that the problem of checkerboarding which is frequently observed with the use of lower-order finite elements is eliminated.