Stress-constrained optimization using graded lattice microstructures
Stress-constrained optimization using graded lattice microstructures
复制标题
DOI：
10.1007/s00158-020-02723-z
复制
发表时间：
2020-10
影响因子：
3.9
通讯作者：
Dilaksan Thillaithevan;P. Bruce;M. Santer
中科院分区：
文献类型：
--
作者：
Dilaksan Thillaithevan;P. Bruce;M. Santer
在这项工作中，我们提出了一种新的方法来预测应力在多尺度晶格优化框架。在微观尺度上，在大型全析因实验设计中为每个微结构捕获可扩展的应力。采用多元多项式响应面模型来表征微结构材料的性能。不同于传统的固体各向同性材料与惩罚为基础的应力方法或使用均匀化的应力，我们提出了使用真实的微观应力分量与宏观应变通过线性叠加。为了检验多尺度应力方法的准确性，进行了具有非周期性边界条件的全尺寸有限元模拟。使用一系列微观结构分级，确定需要6层微观结构来实现全尺寸模型内的周期性。多尺度应力模型的有效性，然后检查。使用不同的梯度结构和两个负载情况下，我们的方法被证明是复制的von Mises应力在中心的单位晶格细胞内的10%，在大多数的测试情况。最后，通过对3个应力约束优化问题的求解，验证了该方法的有效性。两个应力约束的重量最小化的问题进行了演示，旁边的应力约束的目标变形问题。在所有情况下，优化器都能够充分地减少目标，同时考虑所施加的应力约束。
In this work, we propose a novel method for predicting stress within a multiscale lattice optimization framework. On the microscale, a scalable stress is captured for each microstructure within a large, full factorial design of experiments. A multivariate polynomial response surface model is used to represent the microstructure material properties. Unlike the traditional solid isotropic material with a penalization-based stress approach or using the homogenized stress, we propose the use of real microscale stress components with macroscale strains through linear superposition. To examine the accuracy of the multiscale stress method, full-scale finite element simulations with non-periodic boundary conditions were performed. Using a range of microstructure gradings, it was determined that 6 layers of microstructures were required to achieve periodicity within the full-scale model. The effectiveness of the multiscale stress model was then examined. Using various graded structures and two load cases, our methodology was shown to replicate the von Mises stress in the center of the unit lattice cells to within 10% in the majority of the test cases. Finally, three stress-constrained optimization problems were solved to demonstrate the effectiveness of the method. Two stress-constrained weight minimization problems were demonstrated, alongside a stress-constrained target deformation problem. In all cases, the optimizer was able to sufficiently reduce the objective while respecting the imposed stress constraint.