Scale‐related topology optimization of cellular materials and structures
Scale‐related topology optimization of cellular materials and structures
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DOI：
10.1002/nme.1743
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发表时间：
2006-11
影响因子：
2.9
通讯作者：
Weihong Zhang;Shiping Sun
中科院分区：
文献类型：
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作者：
Weihong Zhang;Shiping Sun
本文对轻质蜂窝材料与结构的集成优化进行了研究。通过分析这样一个双尺度问题的基本特征，表明最优解强烈依赖于材料单胞（MUC）的周期性微结构的尺度效应建模，即所谓的代表性体积元（RVE）。然而，随着渐近均匀化方法广泛应用于实际的拓扑优化过程中，有效的材料性能预测可以产生的极限值只取决于固相的体积分数，性能和微观结构中的组分的空间分布，而不管尺度效应。从这个考虑，我们提出的设计元素（DE）的概念，能够处理传统的设计材料和结构在一个统一的方式。通过改变DE的尺度和长宽比，材料和结构的尺度效应在优化设计模式的最终结果中得到了很好的显示和区分。为了说明所提出的方法，数值设计问题的二维层状结构的蜂窝芯进行了研究。版权所有© 2006约翰威利父子有限公司。
The integrated optimization of lightweight cellular materials and structures are discussed in this paper. By analysing the basic features of such a two‐scale problem, it is shown that the optimal solution strongly depends upon the scale effect modelling of the periodic microstructure of material unit cell (MUC), i.e. the so‐called representative volume element (RVE). However, with the asymptotic homogenization method used widely in actual topology optimization procedure, effective material properties predicted can give rise to limit values depending upon only volume fractions of solid phases, properties and spatial distribution of constituents in the microstructure regardless of scale effect. From this consideration, we propose the design element (DE) concept being able to deal with conventional designs of materials and structures in a unified way. By changing the scale and aspect ratio of the DE, scale‐related effects of materials and structures are well revealed and distinguished in the final results of optimal design patterns. To illustrate the proposed approach, numerical design problems of 2D layered structures with cellular core are investigated. Copyright © 2006 John Wiley & Sons, Ltd.