弹性地基上四边自由的各向异性矩形板  

Bending of anisotropic rectangle plates with four free edges on elastic foundation

作　　者：刘俊聊[1] 王克林[1] 

机构地区：[1]西安建筑科技大学,西安710055

出　　处：《应用力学学报》2003年第3期103-106,共4页Chinese Journal of Applied Mechanics

摘　　要：通过叠加法得到了弹性地基上的各向异性矩形板的一般解。每个叠加解被展成重傅立叶级数 ,其自身或其一阶导数在边界上的值被展成单傅立叶级数。利用控制微分方程和一些边界条件 ,每个叠加解被简化成用边界值的级数的系数表示的傅立叶级数。文后给出了弹性地基上的方板的挠曲面图。In this paper the general solutions of anisotropic rectangle plate with four free edges on elastic foundation have been obtained by means of the method of superposition. Each component of superposition is expanded to double Fourier series and some of its differential coefficients on boundaries are expanded to single Fourier series. Using governing equation and some boundary conditions, each component of superposition is reduced to Fourier series for coefficients in the series of its self or its differential coefficients on boundaries. The deflections of rectangle plate on elastic foundation are presented. This represents, to the author's knowledge, the first accurate comprehensive treatment of this set of problems.

关 键 词：弹性地基 各向异性 矩形板 叠加法 傅立叶级数 挠曲面图 控制微分方程 边界条件 

分 类 号：TU348[建筑科学—结构工程] TU311