Topological design of structures and composite materials with multiobjectives
Topological design of structures and composite materials with multiobjectives
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DOI：
10.1016/j.ijsolstr.2007.03.028
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发表时间：
2007-11-01
影响因子：
3.6
通讯作者：
Mai, Yiu-Wing
中科院分区：
文献类型：
--
作者：
de Kruijf, Niek;Zhou, Shiwei;Mai, Yiu-Wing
本文研究了热传导在二维结构和材料设计中的影响。前者试图找到具有最大刚度和最小散热阻力的最佳结构，后者试图定制具有有效热导率和体积模量的复合材料，以达到其上限，如Hashin-Shtrikman和Lurie-Cherkaev边界。在结构拓扑优化部分，本文分别考虑了实体材料和空洞的影响。而在材料设计部分，假设两相无序基础材料（即，一种具有较高的杨氏模量，但较低的热导率，而另一种具有较低的杨氏模量，但较高的电导率），以观察由刚度和传导定义的相分布中的竞争。的有效属性来自均匀化方法与周期性的边界条件内的一个代表性的元素（基本单元）。所有的问题转化为最小化问题的体积和对称性约束的数学和移动渐近线（MMA）的方法，这是指导相对于设计变量的灵敏度。为了正则化问题的SIMP模型探索与非线性扩散技术，以创建边缘保持和棋盘格自由的结果。说明性的例子显示了如何通过线性加权函数生成帕累托前沿，从而深入了解这些目标如何在拓扑结构中竞争。(C)2007爱思唯尔有限公司保留所有权利。
This paper studies the influence of heat conduction in both structural and material designs in two dimensions. The former attempts to find the optimal structures with the maximum stiffness and minimum resistance to heat dissipation and the latter to tailor composite materials with effective thermal conductivity and bulk modulus attaining their upper limits like Hashin-Shtrikman and Lurie-Cherkaev bounds. In the part of structural topology optimization of this paper solid material and void are considered respectively. While in the part of material design, two-phase ill-ordered base materials (i.e. one has a higher Young's modulus, but lower thermal conductivity while another has a lower Young's modulus but higher conductivity) are assumed in order to observe competition in the phase distribution defined by stiffness and conduction. The effective properties are derived from the homogenization method with periodic boundary conditions within a representative element (base cell). All the issues are transformed to the minimization problems subject to volume and symmetry constraints mathematically and solved by the method of moving asymptote (MMA), which is guided by the sensitivities with respect to the design variables. To regularize the problem the SIMP model is explored with the nonlinear diffusion techniques to create edge-preserving and checkerboard-free results. The illustrative examples show how to generate Pareto fronts by means of linear weighting functions, which provide an in-depth understanding how these objectives compete in the topologies. (C) 2007 Elsevier Ltd. All rights reserved.