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.

中文翻译：

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基于耦合虚拟物理模型的虚拟各向异性扩散方程的多个双向可达性约束的拓扑优化


在本研究中，我们专注于考虑可访问性约束的拓扑优化，这是从多个线性方向删除不可访问区域的约束。为了检测不可访问的区域，我们提出了一种使用虚构的各向异性扩散方程的方法。所提出的方程可以同时考虑双向访问，即一个访问方向及其 180 度旋转方向，有助于提高计算效率。此外，我们制定了具有多个双向可达性约束的代表性优化问题，并基于耦合的虚拟物理模型进行敏感性分析。该模型可以解决以往公式化方法难以收敛到单一最优形状的问题。此外，通过各种数值例子，我们验证了数值结果是否收敛到满足可达性约束的最优结构。