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.

翻译：这项研究提出了一种基于光滑粒子流体动力学(GSPH)的通用坐标法,该坐标法采用全拉格朗江(TL)配方法,对大型变形和裂变扩散问题采用超常方法。在拟议的普惠制H型中,物理空间被分解成多个领域,每个领域都绘制到地方坐标空间(通用空间),以避免协调特性,并灵活改变空间分辨率。光滑粒子流体动力学(SPH)颗粒不统一,例如,通常以边界相容方式分布在物理空间,同时在与普通的SPH法相似的每个通用空间统一定义,而普通的平面法则与正常的SGH型变形矩阵在数字上相关。通过在每一个通用空间中确定一个支配方程式,SPH内核的形状和大小可以在物理空间中进行空间空间空间空间的改变,以便空间分辨率根据变形特性而先变,因此在复杂的形状结构中以较少的微粒子数量进行低成本的计算。