薄板弯曲分析的节点积分高阶无网格法

High order meshfree method with nodal integration for thin plate bending analysis

采用高阶无网格法求解薄板弯曲问题,在已发展的线性曲率光顺方案的基础上,通过引入泰勒展开技术,建立了能够精确再现纯弯曲和线性弯曲模式的节点积分方法。与之相比,目前无网格薄板分析主要采用的节点积分方法仅能精确再现纯弯曲模式。数值结果表明,本文方法可精确通过纯弯曲和线性弯曲试验,且能得到光滑、无振荡的弯矩场。与标准的高斯积分方法和目前已存在的节点积分方法相比,本文方法在计算精度、效率以及弯矩分布等方面均展现出显著优势。

In this paper,high order meshfree method is employed to solve thin plate bending problems.Based on the developed linear curvature smoothing scheme,a nodal integration method is established by introducing the Taylor’s expansion technique.The proposed nodal integration method is able to exactly reproduce the pure bending and linear bending modes.In contrast,the existing nodal integration method which dominates meshfree analysis of thin plate bending problems is only able to reproduce the pure bending mode.Numerical results show that the proposed method is able to exactly pass the pure bending and linear bending tests and obtain smooth,oscillation-free distribution of bending moments.In comparison with the standard Gauss integration method and the existing nodal integration method,the presented method shows remarkable advantages in computational accuracy,efficiency and bending moment distributions.