Optimal design of periodic frame structures with negative thermal expansion via mixed integer programming
Optimal design of periodic frame structures with negative thermal expansion via mixed integer programming
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DOI：
10.1007/s11081-015-9276-z
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发表时间：
2015-12-01
影响因子：
2.1
通讯作者：
Kanno, Yoshihiro
中科院分区：
文献类型：
--
作者：
Hirota, Masayuki;Kanno, Yoshihiro
当由两种或两种以上具有正膨胀的材料组成的结构和微结构具有特定的构型时，它们能够具有负的热膨胀系数，即它们在受热时收缩。针对具有负热膨胀特性的平面周期性结构，提出了一种框架结构的拓扑优化方法。假设每个现有杆件的梁截面是从一组有限多个预先确定的候选对象中选择的，我们证明了这个具有多个材料相的拓扑优化问题可以表示为一个混合整数线性规划问题。因此，可以利用现成的软件包找到全局最优解。由于该方法处理的是框架结构和局部应力约束，所以最优解既不包含薄壁杆件，也不包含铰链区域。为了避免过于复杂的结构设计被实现为许多小部件的组合，本文提出了将两种不同材料的分布分开的约束。数值实验表明，该方法可以得到热膨胀为负或接近于零的结构。
When structures and microstructures consisting of two or more materials with positive thermal expansion have specific configurations, they are able to have negative thermal expansion coefficients, i.e., they contract when heated. This paper proposes a topology optimization methodology of frame structures for designing a planar periodic structure that exhibits negative thermal expansion property. Provided that beam section of each existing member is chosen from a set of finitely many predetermined candidates, we show that this topology optimization problem with multiple material phases can be formulated as a mixed-integer linear programming problem. A global optimal solution can hence be found with a readily available software package. Since the proposed method treats frame structures and addresses local stress constraints, the optimal solution contains neither thin members nor hinge-like regions. To avoid too complicated structural designs realized as assemblage of many small pieces, this paper develops the constraints that separate distributions of two different materials. Numerical experiments are performed to show that structures with negative or near zero thermal expansion can be obtained by the proposed method.