In this work, we propose a proportional topology optimization method with a level-set description and evolutionary strategy (PTO-LSES). A level-set function (LSF) evolution scheme based on the nodal compliance proportion is presented and utilized in the new method. Furthermore, a compliance proportion filtering technique, a regularization scheme, and a material interpolation model with penalty are also used in the proposed method. To determine the effectiveness and superiority of the PTO-LSES method, both the 2D (cantilever beam) and 3D (cantilever and half-MBB beams) numerical examples solving the compliance minimization problem, in contrast to the conventional solid isotropic material with penalization (SIMP) and the original proportional topology optimization (PTO) methods, were tested. In addition, we discuss the impact of compliance proportion filtering and regularization schemes on the new method using 2D half-MBB and cantilever beams. The results showed that compared to the SIMP and PTO methods, the PTO-LSES method offered great advantages via the ability to acquire better objective function (compliance) values and more ideal topology structures with smooth and clear boundaries when subjected to specific conditions. Furthermore, applying the compliance pro-portion filtering technique or regularization scheme to the PTO-LSES method enhanced the performance of the new method in many ways.

中文翻译：

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具有水平集描述和进化策略的比例拓扑优化方法


在这项工作中，我们提出了一种具有水平集描述和进化策略的比例拓扑优化方法（PTO-LSES）。提出了一种基于节点柔量比例的水平集函数（LSF）演化方案，并在新方法中使用。此外，该方法还使用了合规比例过滤技术、正则化方案和带有惩罚的材料插值模型。为了确定 PTO-LSES 方法的有效性和优越性，2D（悬臂梁）和 3D（悬臂梁和半 MBB 梁）数值示例均解决了柔度最小化问题，与带有惩罚的传统固体各向同性材料 (SIMP ）和原始比例拓扑优化（PTO）方法进行了测试。此外，我们还讨论了顺应比例滤波和正则化方案对使用 2D 半 MBB 和悬臂梁的新方法的影响。结果表明，与SIMP和PTO方法相比，PTO-LSES方法具有巨大的优势，在特定条件下能够获得更好的目标函数（合规性）值和更理想的边界光滑清晰的拓扑结构。此外，将合规比例滤波技术或正则化方案应用于PTO-LSES方法在很多方面增强了新方法的性能。