000015081 001__ 15081 000015081 005__ 20161115100211.0 000015081 04107 $$aeng 000015081 046__ $$k2016-08-21 000015081 100__ $$aWadbro, Eddie 000015081 24500 $$aOn nonlinear filters in topology optimization 000015081 24630 $$n24.$$p24th International Congress of Theoretical and Applied Mechanics - Book of Papers 000015081 260__ $$bInternational Union of Theoretical and Applied Mechanics, 2016 000015081 506__ $$arestricted 000015081 520__ $$2eng$$aIt 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 talk, we present that these nonlinear filters ensure existence of solutions to a continuous version of the minimal compliance problem. Moreover, we show numerical experiments that illustrates that cascades of these nonlinear filters can be used to efficiently solve large-scale topology optimization problems. 000015081 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb. 000015081 653__ $$a 000015081 7112_ $$a24th International Congress of Theoretical and Applied Mechanics$$cMontreal (CA)$$d2016-08-21 / 2016-08-26$$gICTAM2016 000015081 720__ $$aWadbro, Eddie 000015081 8560_ $$ffischerc@itam.cas.cz 000015081 8564_ $$s151747$$uhttps://invenio.itam.cas.cz/record/15081/files/TS.MS06-4.04.pdf$$yOriginal version of the author's contribution as presented on CD, page 374, code TS.MS06-4.04 . 000015081 962__ $$r13812 000015081 980__ $$aPAPER