This article proposes an efficient approach for solving three‐dimensional (3D) topology optimization problem. In this approach, the number of design variables in optimization as well as the number of degrees of freedom in structural response analysis can be reduced significantly. This is accomplished through the use of scaled boundary finite element method (SBFEM) for structural analysis under the moving morphable component (MMC)‐based topology optimization framework. In the proposed method, accurate response analysis in the boundary region dictates the accuracy of the entire analysis. In this regard, an adaptive refinement scheme is developed where the refined mesh is only used in the boundary region while relating coarse mesh is used away from the boundary. Numerical examples demonstrate that the computational efficiency of 3D topology optimization can be improved effectively by the proposed approach.

中文翻译：

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基于比例边界有限元的三维结构显式拓扑优化方法

本文提出了一种解决三维（3D）拓扑优化问题的有效方法。通过这种方法，可以显着减少优化中设计变量的数量以及结构响应分析中的自由度。这是通过在基于可移动分量（MMC）的拓扑优化框架下使用比例边界有限元方法（SBFEM）进行结构分析来实现的。在所提出的方法中，边界区域中的准确响应分析决定了整个分析的准确性。在这方面，开发了一种自适应细化方案，其中细化的网格仅在边界区域中使用，而相关的粗网格在远离边界的地方使用。