Density filters for topology optimization based on the Pythagorean means

In topology optimization, restriction methods are needed to prohibit mesh dependent solutions and enforce length scale on the optimized structure. This paper presents new restriction methods in the form of density filters. The proposed filters are based on the geometric and harmonic means, respectively, and possess properties that could be of interest in topology optimization, for example the possibility to obtain solutions which are almost completely black and white. The article presents the new filters in detail, and several numerical test examples are used to investigate the properties of the new filters compared to filters existing in the literature. The results show that the new filters in several cases provide solutions with competitive objective function values using few iterations, but also, and perhaps more importantly, in many cases, different filters make the optimization converge to different solutions with close to equal value. A variety of filters to choose from will hence provide the user with several suggested optimized structures, and the new filters proposed in this work may certainly provide interesting alternatives.