Topology optimization of nonlinear periodically microstructured materials for tailored homogenized constitutive properties
Topology optimization of nonlinear periodically microstructured materials for tailored homogenized constitutive properties
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DOI：
10.1016/j.compstruct.2021.113729
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发表时间：
2021-03-29
影响因子：
6.3
通讯作者：
Boechler, Nicholas
中科院分区：
文献类型：
--
作者：
Behrou, Reza;Ghanem, Maroun Abi;Boechler, Nicholas
提出了一种拓扑优化方法，用于设计在有限应变范围内具有指定均匀非线性本构特性的周期性微结构材料。基于承受有限应变的周期性材料的现有计算均质化方法，导出了广义灵敏度方程，用于周期性晶胞的基于梯度的拓扑优化，该优化解释了晶胞的非线性均质化响应。力学模型假设线性弹性各向同性材料、有限应变下的几何非线性以及准静态响应。优化问题通过非线性规划方法求解，灵敏度通过伴随方法计算。提出了几个拓扑优化示例来评估所开发方法的性能。此外，使用这种优化方法识别的二维结构是增材制造的，并且它们的单轴拉伸应变响应与数值预测的行为进行了比较。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类晶格材料，用于从应力波和振动缓解到软机器人的无数潜在应用。
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.