论文标题
新的无网格“脆弱点法（FPM）”，基于盖尔金弱形式用于2D挠性分析
A New Meshless "Fragile Points Method (FPM)" Based on A Galerkin Weak-Form for 2D Flexoelectric Analysis
论文作者
论文摘要
提出了一种无网状脆弱点方法（FPM），用于分析2D挠性问题。局部，简单，多项式和不连续的试验和测试功能是在前三个衍生物的局部无网差正交近似近似的帮助下生成的。使用内部惩罚数值通量来确保该方法的一致性。基于Galerkin弱形式的配方，当前的FPM导致对称和稀疏的矩阵，并避免了先前无网状方法中数值集成的困难。提供了一些具有挠性和压电效应的各向同性和各向异性材料的数值示例作为验证。目前的方法比有限元方法，或无元素的Galerkin（EFG）和无网状局部Petrov-Galerkin（MLPG）方法，而弱形式的数值集成在微不足道上很简单。
A meshless Fragile Points Method (FPM) is presented for analyzing 2D flexoelectric problems. Local, simple, polynomial and discontinuous trial and test functions are generated with the help of a local meshless differential quadrature approximation of the first three derivatives. Interior Penalty Numerical Fluxes are employed to ensure the consistency of the method. Based on a Galerkin weak-form formulation, the present FPM leads to symmetric and sparse matrices, and avoids the difficulties of numerical integration in the previous meshfree methods. Numerical examples including isotropic and anisotropic materials with flexoelectric and piezoelectric effects are provided as validations. The present method is much simpler than the Finite Element Method, or the Element-Free Galerkin (EFG) and Meshless Local Petrov-Galerkin (MLPG) methods, and the numerical integration of the weak form is trivially simple.
