Morphology-based black and white filters for topology optimization

Abstract

In order to ensure manufacturability and mesh-independence in density-based topology optimization schemes it is imperative to use restriction methods. This paper introduces a new class of morphology based restriction schemes which work as density filters, i.e. the physical stiffness of an element is based on a function of the design variables of the neighboring elements. The new filters have the advantage that they eliminate grey scale transitions between solid and void regions. Using different test examples, it is shown that the schemes in general provide black and white designs with minimum length-scale constraints on either or both minimum hole sizes and minimum structural feature sizes. The new schemes are compared with methods and modified methods found in the literature.

On the (non-)optimality of Michell structures

“…To achieve a black-and-white solution we extend the filtering with a projection method (Guest et al, 2004;Xu et al, 2010;Sigmund, 2007) in order to introduce a minimum length scale and hence enforce a frame-like solution.…”

Lazy zone bone remodeling theory and its relation to topology optimization

“…To avoid such incorrect solutions, we use the filtering scheme suggested by Sigmund, discussed in [21]. It essentially means using a weighted averaging of e i (ρ k ) over nearby elements.…”

Dynamical systems and topology optimization

“…Note that while ρ is defined on the potential structural domain only, the variable ξ may be defined on the whole space, see [4]. However, a simplified treatment, discussed, e.g., in [21], is to use a ξ-variable that is defined in the structural domain only and that is what is used in the sequel. The discretized version of the relation between the ξ andρ variables is…”

“…Secondly, an averaging of gradients from elements within a radius R of each element needs to be done. An heuristic method which essentially makes only the second of these steps has been suggested by Sigmund, see [21]. In that approach a modification of the gradient is introduced directly without the need for an additional variable ξ.…”