Abstract
Design variables in density-based topology optimization are typically regularized using filtering techniques. In many cases, such as stress optimization, where details at the boundaries are crucially important, the filtering in the vicinity of the design domain boundary needs special attention. One well-known technique, often referred to as “padding,” is to extend the design domain with extra layers of elements to mitigate artificial boundary effects. We discuss an alternative to the padding procedure in the context of PDE filtering. To motivate this augmented PDE filter, we make use of the potential form of the PDE filter which allows us to add penalty terms with a clear physical interpretation. The major advantages of the proposed augmentation compared with the conventional padding is the simplicity of the implementation and the possibility to tune the boundary properties using a scalar parameter. Analytical results in 1D and numerical results in 2D and 3D confirm the suitability of this approach for large-scale topology optimization.
Highlights
Topology optimization is a computational design methodology that is widely used in industry, in particular for aerospace and automotive applications
One of the leading approaches to topology optimization, which is the one followed in this article, is the density-based approach where the topology is described by a density, i.e. volume fraction
In the PDE filter, the filtered density ρis obtained from the nominal design variable density ρ in a competition between (1) the difference between ρand ρ and (2) the spatial variations in ρ
Summary
Topology optimization is a computational design methodology that is widely used in industry, in particular for aerospace and automotive applications. Two techniques have been discussed in the literature: we will refer to both as “padding.” In the first padding method, the filter operation is performed on an extended design domain so that the boundary and interior regions of the original design domain (being solid or void) are filtered in a consistent manner (Zhou et al 2014; Lazarov et al 2016). In the second padding method, both the filter operation and the finite element analysis are performed on the extended design domain (Clausen and Andreassen 2017) The latter method has resolved stress concentrations at re-entrant corners in stress-based topology optimization (Amir and Lazarov 2018; de Troya and Tortorelli 2018).
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