考虑横向剪切变形简支矩形中厚板的屈曲分析  

Study on buckling of simply supported rectangular medium plate considering the transverse shearing deformation

作　　者：黄会荣[1,2] 郝际平[2] 张海霞[3] 郭家元[1] 

机构地区：[1]西安建筑科技大学机电工程学院 [2]西安建筑科技大学土木工程学院 [3]山东省泰安市建筑设计院,山东泰安271000

出　　处：《西安建筑科技大学学报（自然科学版）》2011年第5期638-643,共6页Journal of Xi'an University of Architecture & Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(50878181);陕西省教育厅专项基金资助项目(11JK0958)

摘　　要：基于考虑横向剪切变形中厚板的几何方程、物理方程及平衡方程,建立关于一个中面挠度和两个中面转角为独立变量的中厚板大挠度弯曲的位移型控制微分方程,从而获得中厚板小挠度屈曲的位移型控制微分方程.该方程退化为薄板屈曲的控制微分方程的正确性说明推导过程的正确性及一般性.文中中厚板小挠度屈曲的位移型控制微分方程是一个六阶耦合微分方程,对其使用双重三角级数并作为广义坐标,将两个中面转角解耦为中面挠度的函数,进一步建立中厚板小挠度屈曲的特征方程,从而借助MATLAB工具得到简支矩形中厚板小挠度屈曲的临界荷载表达式,最后应用MATLAB工具通过临界荷载表达式获得临界荷载系数的曲线,整个求解过程简便,且其曲线退化后符合经典的薄板临界荷载曲线.Based on the theory of geometric equation, physical equation and equilibrium equation of medium plate considered transverse shearing deformation, the displacement governing differential equation for the large-deflection bending of medium plate is established, concerning three independent variables including one middle surface displacement and two middle surface angles of rotation. So the displacement governing differential equation for the small-deflection buckling of medium plate is obtained. Furthermore, the equation could degenerate into the governing differential equation for the buckling of thin plate, which demonstrates the validity and generality of the solving process. The displacement governing the differential equation for the small-deflection buckling of medium plate is a sixth-order differential equation by applying double trigonometric series as generalized coordinates. The characteristic equation for the small-deflection buckling of medium plate is obtained through decoupling of two middle surface angles of rotation into middle surface deflection function. Thus, the critical load formula for the small-deflection buckling of simply supported rectangular medium plate is gained through MATLAB. Finally, the curves of critical load coefficient through the critical load formula by MATLAB are ob- tained. Generally, it＇s a simplified and convenient solving process, and the degenerative curve is in line with the classical critical load curve of thin plate.

关 键 词：横向剪切变形 位移型控制微分方程 小挠度屈曲 简支矩形中厚板 双重三角级数 临界荷载 

分 类 号：TU33[建筑科学—结构工程]