Nonlinear filters in topology optimization: existence of solutions and efficient implementation for minimal compliance problems
2016 (English)Report (Other academic)
It is well known that material distribution topology optimization problems often are ill-posed if no restriction or regularization method is used. A drawback with the standard linear density filter is that the resulting designs have large areas of intermediate densities, so-called gray areas, especially when large filter radii are used. To produce final designs with less gray areas, several different methods have been proposed; for example, projecting the densities after the filtering or using a nonlinear filtering procedure. In a recent paper, we presented a framework that encompasses a vast majority of currently available density filters. In this paper, we show that all these nonlinear filters ensure existence of solutions to a continuous version of the minimal compliance problem. In addition, we provide a detailed description on how to efficiently compute sensitivities for the case when multiple of these nonlinear filters are applied in sequence. Finally, we present a numerical experiment that illustrates that these cascaded nonlinear filters can be used to obtain independent size control of both void and material regions in a large-scale setting.
Place, publisher, year, edition, pages
Umeå: Umeå universitet , 2016. , 16 p.
Report / UMINF, ISSN 0348-0542 ; 16.01
IdentifiersURN: urn:nbn:se:umu:diva-115934OAI: oai:DiVA.org:umu-115934DiVA: diva2:901363
FunderSwedish Research Council, 621-3706Swedish Foundation for Strategic Research , AM13-0029