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A reduced multiscale model for nonlinear structural topology optimization

机译：非线性结构拓扑优化的简化多尺度模型

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摘要

This paper presents a reduced multiscale model for macroscopic structural design considering microscopic material nonlinear microstructures. This work introduces Reduced Order Model (ROM) to alleviate the heavy computational demand of nonlinear nested multiscale procedures, particularly in an optimization framework which requires multiple loops involving similar computations. The surrogate model constructed using Proper Orthogonal Decomposition (POD) and Diffuse Approximation reduces the computational effort for solving the microscopic boundary value problems. Multiscale analysis model (FE~2 ) is applied to link structure and microstructures in the two scales. Maximum stiffness design of the macroscopic structure is realized using a discrete level-set topology optimization model. It is shown by means of numerical tests that the reduced multiscale model provides reasonable designs as compared to those obtained by the unreduced model while with a significantly reduced computational effort.
机译：本文提出了一种考虑微观材料非线性微观结构的宏观结构设计的简化多尺度模型。这项工作引入了降阶模型（ROM），以减轻非线性嵌套多尺度过程的繁重计算需求，尤其是在需要多个涉及相似计算的循环的优化框架中。使用适当的正交分解（POD）和扩散近似构造的替代模型减少了解决微观边界值问题的计算量。将多尺度分析模型（FE〜2）应用于两个尺度的链接结构和微观结构。使用离散的水平集拓扑优化模型可实现宏观结构的最大刚度设计。通过数值测试表明，与未缩减模型相比，简化多尺度模型提供了合理的设计，同时大大减少了计算量。

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