This study proposes a generalized coordinates based smoothed particle hydrodynamics (GSPH) method with overset methods using a Total Lagrangian (TL) formulation for large deformation and crack propagation problems. In the proposed GSPH, the physical space is decomposed into multiple domains, each of which is mapped to a local coordinate space (generalized space) to avoid coordinate singularities as well as to flexibly change the spatial resolution. The smoothed particle hydrodynamics (SPH) particles are then non-uniformly, e.g., typically in the boundary-conforming way, distributed in the physical space while they are defined uniformly in each generalized space similarly to the normal SPH method, which are numerically related by a coordinate transformation matrix. By solving a governing equation in each generalized space, the shape and size of the SPH kernel can be spatially changed in the physical space so that a spatial resolution is adaptively varied a priori depending on the deformation characteristics, and thus, a low-cost calculation with the less number of particles is achieved in complex shape structures.

中文翻译：

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在总拉格朗日公式中使用覆盖方法的广义平滑粒子流体动力学

这项研究提出了一种基于总坐标的平滑粒子流体动力学（GSPH）方法，该方法采用了采用总拉格朗日（TL）公式的超调方法来解决大变形和裂纹扩展问题。在提出的GSPH中，物理空间被分解为多个域，每个域都映射到局部坐标空间（广义空间），以避免坐标奇异性以及灵活地更改空间分辨率。然后，将平滑的粒子流体动力学（SPH）粒子非均匀地（例如通常以边界一致的方式）分布在物理空间中，而类似于常规的SPH方法，它们在每个广义空间中被统一定义，其数值关系如下：坐标变换矩阵。通过求解每个广义空间中的控制方程，