Topology optimization of multiscale elastoviscoplastic structures
Topology optimization of multiscale elastoviscoplastic structures
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DOI：
10.1002/nme.5122
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发表时间：
2016-05-11
影响因子：
2.9
通讯作者：
Breitkopf, Piotr
中科院分区：
文献类型：
--
作者：
Fritzen, Felix;Xia, Liang;Breitkopf, Piotr
本文将拓扑优化的概念推广到非线性微异质材料结构的设计中。目标是在考虑材料的非线性和微观结构的同时，最大限度地提高规定材料体积使用的宏观结构刚度。由此产生的设计问题考虑两个尺度：宏观尺度上进行优化和微观尺度上观察到的材料的异质性和非线性。采用双向渐进结构优化方法进行了宏观尺度的拓扑优化。宏观边值问题的求解需要输入有效的本构响应并充分考虑微观结构。虽然计算均匀化方法，如FE2方法可以用来解决非线性多尺度问题，相关的数值开销（CPU时间和内存）是非常不可接受的。为了重新获得计算规模过渡的计算可行性，最近的模型简化技术的作者：潜在的减少基础模型降阶与图形处理单元加速。数值算例表明了非线性双尺度设计的有效性。研究了不同载荷幅值对设计的影响。版权所有（C）2015约翰威利父子有限公司
This paper extends current concepts of topology optimization to the design of structures made of nonlinear microheterogeneous materials. The objective is to maximize the macroscopic structural stiffness for a prescribed material volume usage while accounting for the nonlinearity and the microstructure of the material. The resulting design problem considers two scales: the macroscopic scale at which the optimization is performed and the microscopic scale at which the material heterogeneities and the nonlinearities are observed. The topology optimization at the macroscopic scale is performed by means of the bi-directional evolutionary structural optimization method. The solution of the macroscopic boundary value problem requires as inputs the effective constitutive response with full consideration of the microstructure. While computational homogenization methods such as the FE2 method could be used to solve the nonlinear multiscale problem, the associated numerical expense (CPU time and memory) is highly unacceptable. In order to regain the computational feasibility of the computational scale transition, a recent model reduction technique of the authors is employed: the potential-based reduced basis model order reduction with graphics processing unit acceleration. Numerical examples show the efficiency of the resulting nonlinear two-scale designs. The impact of different load amplitudes on the design is examined. Copyright (C) 2015 John Wiley & Sons, Ltd.