Topology Optimization with Geometric Constraints for Visibility Using Fictitious Physical Model

Abstract

This paper proposes a scheme for imposing geometrical constraints in topology optimization to obtain structures considering the visibility of the product user, based on a fictitious physical model. First, a level set-based topology optimization method is concisely introduced, and geometrical requirements for the visibility are clarifid. A fictitious physical model described by a steady-state advection-dffusion equation is then constructed based on the requirements. In this model, virtual heat sources correspond to material domains and the advection direction is aligned with a radial direction around a view point. The visibility is evaluated by the values of the fictitious physical model, and the regions to see, where the value of the fictitious physical field is high, represent blind area. Next, an optimal problem is introduced based on the fictitious physical model. Finally, in the numerical examples, the proposed method yields optimal structure considering the visibility, confirming the validity and the utility of the proposed method.