非线性周期性微结构材料的拓扑优化以定制均匀化本构特性
Topology optimization of nonlinear periodically microstructured materials for tailored homogenized constitutive properties
摘要：
提出了一种拓扑优化方法，用于设计具有均匀化非线性本构特性的周期性微结构材料。力学模型假设线性弹性各向同性材料，在有限应变的几何非线性，和准静态响应。最优化问题的解决，通过非线性规划方法和灵敏度计算通过伴随方法。使用这种优化方法识别的二维结构被增材制造，并且它们的单轴拉伸应变响应与数值预测的行为进行比较。本文的优化方法使得能够设计和开发具有规定的非线性有效特性的格子状材料，用于无数潜在的应用，从应力波和振动缓解到软机器人。
英文摘要：
A topology optimization method is presented for the design of periodic microstructured materials with prescribed homogenized nonlinear constitutive properties over finite strain ranges. 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. 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.
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