A level set shape metamorphosis with mechanical constraints for geometrically graded microstructures
A level set shape metamorphosis with mechanical constraints for geometrically graded microstructures
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DOI：
10.1007/s00158-019-02293-9
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发表时间：
2019-05
影响因子：
3.9
通讯作者：
Xiao-Yi Zhou;Zongliang Du;H. Kim
中科院分区：
文献类型：
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作者：
Xiao-Yi Zhou;Zongliang Du;H. Kim
分级材料或微结构变化带来的功能性能优势已经确立。然而，连接相邻微观结构的挑战仍然是开放的。没有连接的微观结构，设计只是理论上的，无法在实践中实现。本文提出了一种形状变形方法来解决这一挑战。该方法制定了一个优化问题，以最小化两种形状之间的差异，其中优化迭代过程中生成的形状形成渐变的微结构。提出了一种基于刚度的约束，以消除在生成中间形状时可能出现的断裂或收缩，并利用中间形状建立两个形状连接的过渡区。这也确保了最优功能不会受到显著影响。一系列的数值研究表明，该方法能够产生多尺度优化的光滑连接微结构。
Functional performance benefits brought by graded materials or a variation of microstructures have been established. However, the challenge of connecting the adjacent microstructures remains open. Without connected microstructures, the design is only theoretical and cannot be realized in practice. This paper presents a shape metamorphosis approach to address this challenge. The approach formulates an optimization problem to minimize the difference between two shapes, where the shapes generated during the optimization iterations form the graded microstructures. A stiffness-based constraint is proposed to eliminate potential breakage or shrinkages in generating the intermediate shapes, which are used to build a transition zone for the two shapes to be connected. This also ensures that the optimal functionality is not compromised significantly. A series of numerical studies demonstrate that the proposed approach is capable of producing smoothly connected microstructures for multiscale optimization.