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Multiscale structural topology optimization with an approximate constitutive model for local material microstructure

机译：具有局部材料微观结构的近似本构模型的多尺度结构拓扑优化

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摘要

This paper builds on our recent work (Xia and Breitkopf, 2014) on multiscale structural topology optimization where at the microscopic scale, local materials are optimized concurrently according to current loading status. The former design framework requires intensive computational cost due to large number of repetitive local material optimizations. To circumvent this limitation, in the present work, we construct a reduced database model viewing the local material optimization process as a generalized constitutive behavior using separated representations. In this model, the database is built from a set of numerical experiments of local material optimizations in the macroscopic strain tensor space. Each value in the database corresponds to the strain energy density evaluated on a material microstructure, optimized according to the imposed macroscopic strain. By tensor decomposition, a continuous representation of the strain energy density is built as a sum of products of one dimensional interpolation functions. As a result of this a priori off-line step, the effective strain-energy and stress-strain relations required for macroscopic structural evaluation and optimization are provided in a numerically explicit manner. The results given by the reduced database model are compared with full-scale results. It is also shown that this explicit constitutive behavior representation can well serve multiscale structural design at a significantly reduced computational cost. (C) 2014 Elsevier B.V. All rights reserved.
机译：本文基于我们最近在多尺度结构拓扑优化上的工作（Xia和Breitkopf，2014），其中在微观尺度上，根据当前的加载状态同时优化了局部材料。由于大量重复的局部材料优化，前一种设计框架需要大量的计算成本。为了避免这种局限性，在本工作中，我们构造了一个简化的数据库模型，将局部材料优化过程视为使用单独表示形式的广义本构行为。在此模型中，数据库是根据宏观应变张量空间中局部材料优化的一组数值实验建立的。数据库中的每个值都对应于在材料微观结构上评估的应变能密度，并根据施加的宏观应变进行了优化。通过张量分解，应变能密度的连续表示被构建为一维插值函数的乘积之和。由于该先验的离线步骤，以数值明确的方式提供了宏观结构评估和优化所需的有效应变能和应力应变关系。将精简数据库模型给出的结果与全面结果进行比较。还表明，这种显式的本构行为表示可以很好地为多尺度结构设计服务，而其计算成本却大大降低。 （C）2014 Elsevier B.V.保留所有权利。

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