Pixel-based shape optimization in 2D using constrained density-based topology optimization

Abstract

Shape optimization is an often-used technique in structural, mechanical, and aerospace engineering, to name a few. There are various shape optimization methods, yet many of these require a parametrization of the design geometry into a reduced set of design variables to be later optimized. Moreover, these methods regenerate the finite element mesh (remesh) with every design iteration. The present work proposes a new approach to shape optimization using concepts from density-based topology optimization, where an additional set of constraints are added to the optimization problem to empirically prevent the topology optimization algorithm from introducing new features (holes or members). These constraints can be considered as on-the-fly definitions of passive-solid and passive-void regions, which limit the design evolution to occur only at the solid’s boundary. The method does not require a parametrization of the initial design geometry, nor does it require remeshing the design. The proposed algorithm is later implemented to highlight the method’s capabilities, ease of usage, and associated shortcomings. The method is proven to work with different objective functions, passive-solid and passive-void regions, and has a runtime comparable to a standard density-based topology optimization algorithm. The examples show that the method exhibits relatively good behavior and robustness while requiring little pre-processing and problem setup before running.