论文标题
一个新的无网状脆弱点方法（FPM）在每个点上具有最低未知数，用于在具有裂纹传播的两种理论下进行挠性分析。第一部分：理论和实施
A New Meshless Fragile Points Method (FPM) With Minimum Unknowns at Each Point, For Flexoelectric Analysis Under Two Theories with Crack Propagation. Part I: Theory and Implementation
论文作者
论文摘要
挠性电信是指涉及机械应变梯度和电化极化的现象。在这项研究中，提出了一种无网状易碎点方法（FPM），用于分析介电固体中的挠性效应。局部，简单，多项式和不连续的试验和测试功能是借助局部无网状差分差异的衍生物近似。基于有或没有电梯度效应和麦克斯韦应力的两种替代柔性理论，开发了原始FPM和混合FPM。在目前的原始和混合FPM中，只有位移和电势被保留为最终代数方程中每个内部脆弱点的显式未知变量。因此，代数方程最终系统中未知数的数量绝对是最小的。提出了一种用于使用当前FPM模拟裂纹启动和传播的算法，具有经典的基于压力的标准以及基于键合的键合（BER）基于裂纹的标准。与当前的计算挠性分析方法相比，目前的原始和混合FPM方法具有明显的优势，使用原始和混合有限元方法，无元素galerkin（EFG）方法，无网状的本地Petrov Galerkin（MLPG）方法（MLPG）方法，以及无效的方法（Iga Galer），因为新功能是新功能。多项式试验和测试功能；每点最小的DOF使其非常易于用户友好；任意的多边形亚域使其可以灵活地建模复杂的几何形状。原始和混合FPM弱形式的数值整合在琐碎的情况下很简单。 FPM可以轻松地用于裂纹开发模拟中，而无需重新提高或试验功能增强。
Flexoelectricity refers to a phenomenon which involves a coupling of the mechanical strain gradient and electric polarization. In this study, a meshless Fragile Points Method (FPM), is presented for analyzing flexoelectric effects in dielectric solids. Local, simple, polynomial and discontinuous trial and test functions are generated with the help of a local meshless Differential Quadrature approximation of derivatives. Both primal and mixed FPM are developed, based on two alternate flexoelectric theories, with or without the electric gradient effect and Maxwell stress. In the present primal as well as mixed FPM, only the displacements and electric potential are retained as explicit unknown variables at each internal Fragile Point in the final algebraic equations. Thus the number of unknowns in the final system of algebraic equations is kept to be absolutely minimal. An algorithm for simulating crack initiation and propagation using the present FPM is presented, with classic stress-based criterion as well as a Bonding-Energy-Rate(BER)-based criterion for crack development. The present primal and mixed FPM approaches represent clear advantages as compared to the current methods for computational flexoelectric analyses, using primal as well as mixed Finite Element Methods, Element Free Galerkin (EFG) Methods, Meshless Local Petrov Galerkin (MLPG) Methods, and Isogeometric Analysis (IGA) Methods, because of the following new features: they are simpler Galerkin meshless methods using polynomial trial and test functions; minimal DoFs per Point make it very user-friendly; arbitrary polygonal subdomains make it flexible for modeling complex geometries; the numerical integration of the primal as well as mixed FPM weak forms is trivially simple; and FPM can be easily employed in crack development simulations without remeshing or trial function enhancement.
