Topology optimization with accessibility constraint from multiple bi-directions using fictitious anisotropic diffusion equation based on coupled fictitious physical model

In this study, we focus on topology optimization considering the accessibility constraint, which is a constraint that removes inaccessible regions from multiple linear directions. To detect inaccessible regions, we propose a method using a fictitious anisotropic diffusion equation. The proposed equation can simultaneously consider access from a bi-direction, which means one access direction and its 180-degree rotated direction, contributing to computational efficiency improvements. Additionally, we formulate a representative optimization problem with the accessibility constraint from multiple bi-directions and perform sensitivity analysis based on a coupled fictitious physics model. The model can resolve the difficulty in converging to a single optimal shape in the previous formulation method. Furthermore, through various numerical examples, we verify whether the numerical result converges to the optimal structure satisfying the accessibility constraint.