Peridynamics (PD) is a meshless approach that addresses some of the difficulties and limitations associated with mesh-based topology optimization (TO) methods. This study investigates topology optimization of structures with and without embedded cracks using peridynamics (PD-TO). To this end, PD is coupled with two different continuous density-based topology optimization methods, namely the optimality criteria and the proportional optimization. The optimization results are compared for a continuous definition of the design variables, which are the relative densities defined for PD particles. The checkerboard issue has been removed using filtering schemes. The accuracy of the proposed PD-TO approach is validated by solving benchmark problems and comparing the optimal topologies with those obtained using a FEM-based topology optimization. Various problems are solved with and without defects (cracks) under different loading and constraint boundary conditions. Topology optimization for an unstructured discretization problem has also been investigated applied to a complex geometry. The optimal topology of a cracked structure may change for different optimization methods. The numerical results demonstrate the accuracy, high efficiency, and robustness of the PD-TO approach.

Peridynamics（PD）是一种无网格方法，可解决与基于网格的拓扑优化（TO）方法相关的一些困难和局限性。这项研究使用绕动力学（PD-TO）研究具有和不具有嵌入式裂纹的结构的拓扑优化。为此，PD结合了两种不同的基于连续密度的拓扑优化方法，即最优性准则和比例优化。比较优化结果以连续定义设计变量，这是为PD粒子定义的相对密度。棋盘格问题已使用过滤方案消除。通过解决基准问题并将最佳拓扑与使用基于FEM的拓扑优化获得的拓扑进行比较，可以验证所提出的PD-TO方法的准确性。解决了在不同的载荷和约束边界条件下有无缺陷（裂纹）的各种问题。还研究了将非结构化离散化问题的拓扑优化应用于复杂的几何体。裂纹结构的最佳拓扑可能会因不同的优化方法而改变。数值结果证明了PD-TO方法的准确性，高效率和鲁棒性。