Preprint / Version 1

Introducing a general polygonal primitive for feature mapping-based topology optimization

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DOI:

https://doi.org/10.31224/4026

Keywords:

Feature mapping, Geometrical Projection, Polygons, Topology Optimization, Signed Distance Function

Abstract

In topology optimization, feature mapping approaches allow for maintaining the simplicity of density-based methods while incorporating explicit geometrical parametrization. Existing methods often rely on geometric primitives that have analytical signed distance functions (SDF), which may offer limited design freedom or require costly numerical methods to approximate the SDF. This paper introduces a new type of general polygonal primitive that can be convex or non-convex, with an arbitrary number of vertices, the coordinates of which are assigned with design variables. As a result, the proposed parametrization is geometrically rich and explicit. Specifically, we present a new, differentiable, and efficient way to approximate the signed distance function of arbitrary polygons and develop a scheme that prevents self-intersection of polygons. The optimized designs with the proposed polygonal primitive are similar to classical results obtained with density-based methods, albeit with some minor sacrifice in performance due to the polygonal boundaries. The guaranteed straight lines of the optimized designs, however, are also beneficial in many cases, such as in reinforced concrete structures where curved boundaries are difficult to manufacture. Moreover, the explicit parametrization and the direct shape control facilitate the convenient imposition of a wide range of geometrical constraints that are not trivial with existing primitives.

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Posted

2024-10-21