栅格结构双尺度并行设计的比例拓扑优化算法

M. Nguyen, D. Vo, T. Bui
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引用次数: 1

摘要

本文将比例拓扑优化(PTO)算法扩展到同时设计结构和材料细胞微结构的双尺度并行拓扑优化中。PTO最初是根据分配给某一要素的材料数量与该要素在目标函数中的贡献成正比这一概念发展起来的。不需要进行敏感性分析。在一个两尺度并行拓扑优化问题中,定义了两组设计变量,一组为宏观结构,一组为微观结构。在这里,目标函数被重新表述,使得每个微尺度设计变量的贡献可以确定,便于PTO的使用。采用基于能量的均匀化方法(EBHM)对宏观有效弹性张量进行了评价,为微观结构和宏观结构之间提供了联系。通过二维和三维结构的基准算例验证了该方法的可行性和有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Proportional Topology Optimization algorithm for two-scale concurrent design of lattice structures
In this paper, the Proportional Topology Optimization (PTO) algorithm is extended for the two-scale concurrent topology optimization, in which both the structure and material cellular micro-structure are subject to design. PTO was originally developed on the concept that the amount of material being distributed to an element would be proportional to the contribution of that element in the objective function. Sensitivity analysis is not required. In a two-scale concurrent topology optimization problem, two sets of design variables are defined, one for macro-structure and one for micro-structure. Here, the objective function is reformulated such that the contribution of each micro-scale design variable can be determined, facilitating the employment of PTO. The macroscopic effective elastic tensor is evaluated by the energy-based homogenization method (EBHM), providing a link between micro-structure and macro-structure. Feasibility and efficiency of the proposed PTO approach are demonstrated via several benchmark examples of both two and three dimensional structures.
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