水平集方法及其在柔顺机构拓扑优化中的应用(英文)

Level Set Method and Its Applications to Topology Optimization of Compliant Mechanisms

由于具有跟踪拓扑结构变化、优化边界清晰光滑等优点,水平集方法作为一种新颖的机构拓扑优化方法近来受到了重视.文中首先讨论了水平集方法中Hamilton-Jacobi方程的求解、水平集函数的重新初始化、速度场扩展等出现的问题.在此基础上,给出了应用逆风差分格式求解Hamilton-Jacobi方程的数值方法,并采用改进的符号函数有效解决了数值的不稳定问题,提出的快速扫描法可以对速度场进行有效扩展.最后,建立了基于水平集方法的柔顺机构拓扑优化模型,利用水平集法对反位移柔顺机构进行了拓扑优化设计.

The level set method has recently been proposed and studied as a novel structural topology optimization method, which is flexible in handling complex topological changes and concise in describing the boundary shape of the structure. In this paper, first, some numerical issues are discussed, such as the solution of Hamil- ton-Jacobi equations, the re-initialization of the level set function and the extension of velocity fields. Then, several robust and effective numerical technologies, which are important to the implementation of the level set method, are proposed. For example, the upwind difference scheme is used to solve Hamilton-Jacobi equations, the signature function is modified to ensure the numerical stability, and the fast scanning method is developed to construct extension velocities. Moreover, based on the level set method, a topology optimization model for compliant mechanisms is presented. Finally, the proposed level set method is illustrated by the topology optimization of a displacement inverter.