The Fragile Points Method (FPM) is an elementarily simple Galerkin meshless method, employing Point-based discontinuous trial and test functions only, without using element-based trial and test functions. In this study, the algorithmic formulations of FPM for linear elasticity are given in detail, by exploring the concepts of point stiffness matrices and numerical flux corrections. Advantages of FPM for simulating the deformations of complex structures, and for simulating complex crack propagations and rupture developments, are also thoroughly discussed. Numerical examples of deformation and stress analyses of benchmark problems, as well as of realistic structures with complex geometries, demonstrate the accuracy, efficiency and robustness of the proposed FPM. Simulations of crack initiation and propagations are also given in this study, demonstrating the advantages of the present FPM in modeling complex rupture and fracture phenomena. The crack and rupture propagation modeling in FPM is achieved without remeshing or augmenting the trial functions as in standard, extended or generalized FEM. The simulation of impact, penetration and other extreme problems by FPM will be discussed in our future papers.

中文翻译：

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一种简单的 Galerkin 无网格方法，脆弱点方法 (FPM) 使用点刚度矩阵，用于复杂域中具有裂纹和破裂传播的二维线弹性问题

脆弱点法 (FPM) 是一种基本简单的 Galerkin 无网格方法，仅使用基于点的不连续试验和测试函数，不使用基于单元的试验和测试函数。在这项研究中，通过探索点刚度矩阵和数值通量校正的概念，详细给出了线性弹性 FPM 的算法公式。FPM 在模拟复杂结构变形以及模拟复杂裂纹扩展和破裂发展方面的优势也进行了深入讨论。基准问题的变形和应力分析以及具有复杂几何形状的真实结构的数值示例证明了所提出的 FPM 的准确性、效率和鲁棒性。本研究还给出了裂纹萌生和扩展的模拟，展示了当前 FPM 在模拟复杂破裂和断裂现象方面的优势。FPM 中的裂纹和破裂扩展建模是在没有像标准、扩展或广义 FEM 中那样重新划分网格或增加试验函数的情况下实现的。FPM 对撞击、穿透和其他极端问题的模拟将在我们以后的论文中讨论。