摘要
自然单元法是一种新兴的无网格数值计算方法,基于Reissner-Mindlin板弯曲理论,将自然单元法应用于平板弯曲问题的计算中,给出了相关的公式,推导了总体刚度矩阵和荷载列阵的计算列式.算例分析表明,自然单元法应用于中厚板的弯曲问题具有较高的计算精度,并可用于Winkler地基上基础板的计算.同时指出,对于厚跨比较小的薄板,由于对挠度和中面法线转角采用相同的插值形式,当板厚变薄时夸大了虚假的剪切变形影响,因而表现出剪切自锁现象.对进一步开发厚薄板通用的计算程序作了初步探讨.
The natural element method （NEM） is a recently developed meshless method. Based on Reissner-Mindlin＇s plate theory,NEM is applied in analyzing the bending problem of elastic plate,and the corresponding formulas of global stiffness matrix and external nodal force being developed. Numerical simulations illustrate that the accuracy of this method for moderately thick plate is satisfactory, and the proposed technique can also be applied in plates on Winkler foundation. The paper points out that the shear locking happens since the same approximation function for transverse displacement and normal rotational angle to the middle plane is adopted, thus the effect of null transversal shear deformations is exaggerated when the plate becomes thin. Some questions related to construction of a universal NEM program for thin and thick plates are discussed.
出处
《固体力学学报》
CAS
CSCD
北大核心
2009年第4期424-431,共8页
Chinese Journal of Solid Mechanics
基金
国家自然科学基金(50539090)资助
关键词
自然单元法
平板弯曲
变分原理
剪切自锁
natural element method, bending of plate, variational principle, shear locking
