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首页> 外文期刊>Composite Structures >Topology optimization of nonlinear periodically microstructured materials for tailored homogenized constitutive properties
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Topology optimization of nonlinear periodically microstructured materials for tailored homogenized constitutive properties

机译：非线性周期性微观结构材料的拓扑优化，用于量身定制的均化构成特性

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摘要

A topology optimization method is presented for the design of periodic microstructured materials with prescribed homogenized nonlinear constitutive properties over finite strain ranges. Building upon an existing computational homogenization method for periodic materials undergoing finite strain, generalized sensitivity equations are derived for the gradient-based topology optimization of periodic unit cells that account for the nonlinear homogenized response of the unit cell. The mechanical model assumes linear elastic isotropic materials, geometric nonlinearity at finite strain, and a quasi-static response. The optimization problem is solved by a nonlinear programming method and the sensitivities computed via the adjoint method. Several topology optimization examples are presented to evaluate the performance of the developed method. Furthermore, two-dimensional structures identified using this optimization method are additively manufactured and their uniaxial tensile strain response compared with the numerically predicted behavior. The optimization approach herein enables the design and development of lattice-like materials with prescribed nonlinear effective properties, for use in myriad potential applications, ranging from stress wave and vibration mitigation to soft robotics.
机译：提出了一种拓扑优化方法，用于设计周期性微结构化材料，其在有限菌株范围内具有规定的均质非线性本构性能。基于经历有限菌株的周期性材料的现有计算均化方法，推导出用于定期单元电池的梯度基拓扑优化，其考虑了单位细胞的非线性均质响应的周期性单元细胞的梯度的拓扑优化。机械模型假设线性弹性各向同性材料，有限菌株的几何非线性，以及准静态响应。通过非线性编程方法解决优化问题，并且通过伴随方法计算的灵敏度。提出了几种拓扑优化示例以评估开发方法的性能。此外，使用该优化方法识别的二维结构是加容量制造的及其单轴拉伸应变响应，与数值预测的行为相比。这里的优化方法能够设计和开发具有规定的非线性有效性能的晶格状材料，用于无数潜在应用，从应力波和减轻软机器人的减轻。

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