Microstructural Stress Shape Optimization Using the Level Set Method
Microstructural Stress Shape Optimization Using the Level Set Method
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DOI：
10.1115/1.4047152
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发表时间：
2020-06
影响因子：
3.3
通讯作者：
R. Picelli;S. Townsend;H. Kim
中科院分区：
文献类型：
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作者：
R. Picelli;S. Townsend;H. Kim
本文将基于应力的形状优化应用于微结构，这是一个文献中很少探讨的话题。由于在宏观结构上产生的实际应力是尺度分离的，这里将微观结构应力视为施加测试单位应变载荷情况后的代表性体积单元(RVE)的状态，而与宏观载荷无关。二维三种应力状态通过p范数函数进行聚合，p范数函数用于应力最小化。采用基于应力的水平集方法。该方法将目标函数和约束函数线性化，并在每一次迭代中求解一个优化问题以获得边界速度。用拟物质法计算被边界分割单元的刚度。为了验证该方法，对单孔夹杂微结构进行了最小应力优化。
This paper applies stress-based shape optimization to microstructures, a scarcely explored topic in the literature. As the actual stresses arising at the macroscopic structure are scale separated, the microstrucural stress is considered herein as the state of a representative volume element (RVE) after applying test unit strain load cases, not related to the macroscale loads. The three stress states in 2D are aggregated via p-norm functions, which are used for stress minimization. A stress-based level set method is applied. The method linearizes the objective and constraint functions and solves an optimization problem at every iteration to obtain the boundary velocities. The Ersatz material approach is used to compute the stiffness of the elements sliced by the boundary. A single hole inclusion microstructure is optimized for minimum stress in order to verify the methodology.