小波加权残值法在斜板后屈曲上的应用  

Wavelet Weighted Residuals with Application to Post-Buckling Analysis of Skew Plates

作　　者：纪冬梅[1,2] 胡毓仁[1] 

机构地区：[1]上海交通大学,上海200090 [2]上海电力学院,上海200030

出　　处：《应用力学学报》2008年第4期673-677,739,共5页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(50279020)

摘　　要：将斜板在大挠度理论下的平衡方程和变形协调方程转化为斜坐标系下的表达式,并无量纲化,对于四边固支斜板,选用尺度小于1的二维bior3.1重构尺度函数与小波作试函数,满足板在平面外的几何与自然边界条件,利用小波-Galerkin法将板的无量纲平衡控制方程与变形协调方程转化为两个非线性方程组,从而将后屈曲路径的求解转化为两非线性方程组的求解问题。以载荷作为迭代步长,采用Newton-Raphson迭代算法求得承受单向压缩四边固支斜板在不同边长比、不同斜角下的后屈曲平衡路径及四级渐近解。Based on the theory of large deflection, the non-dimensional expressions of the equilibrium equation and compatibility equations in skew coordinates are established. For the clamped skew plates, the 2D reconstruction scalling functions and wavelet functions of bior3. 1 wavelet with scalling less than 1 are chosen as the trial functions, which satisfy the out of plane geometrical and natural boundary conditions. The non-dimensional equilibrium equations and the compatibility equations are transformed to two systems of non-linear equations. The post-buckling behavior can be obtained by solving the two systems of non-linear equations, where Newton-Raphson method is employed and the load is taken as iterative step. The post-buckling behavior and four terms approximate solution for the clamped skew plates with different aspect ratios and different skew angles subjected to uniaxial compressive loads are obtained.

关 键 词：小波 加权残值法 斜板 固支 后屈曲 

分 类 号：U661.4[交通运输工程—船舶及航道工程]