双参数弹性地基上的正交异性矩形板的弯曲  

BENDING OF ORTHOTROPIC RECTANGULAR PLATES ON DOUBLE-PARAMETRIC ELASTIC FOUNDATION

作　　者：杨端生[1] 黄炎[2] 

机构地区：[1]长沙理工大学土木与建筑学院,长沙410004 [2]国防科技大学航天技术与工程系,长沙410073

出　　处：《工程力学》2009年第3期26-30,共5页Engineering Mechanics

基　　金：国家自然科学基金项目(19872072)

摘　　要：建筑物底层支柱下面的钢筋混凝土底板可视为弹性地基上的四边自由中点受集中力的正交异性板的弯曲问题。为了求得板中心的弯矩,应将集中力改为支柱横截面承受的分布力。该文建立了双参数弹性地基上的正交异性矩形薄板弯曲问题的一般解析解。可用以精确地求解矩形板在任意载荷作用下和任意边界的弯曲问题。以四边自由在中点附近承受局部均布载荷的方板为例进行了计算,并求得了板的最大弯矩。该文的一般解同样适用于单参数弹性地基以及各向同性板的情形。计算过程简单、便于应用。A reinforced concrete base plate supporting the column of the lowest basement of buildings is studied as an orthotropic plate on elastic foundation with four edges free and subjected to a concentrated load at the center. To obtain the bending moment at the center of the plate, the concentrated load must be transformed into distributed load acting on an area equal to the cross sectional area of the column. A general analytical solution for bending problem of orthotropic rectangular thin plates on double-parametric elastic foundation is established in this paper, which can be used to solve precisely bending problems of rectangular plates subjected to arbitrary loads and arbitrary boundaries. For the purpose of illustration, a square plate with four edges free and uniformly loaded on a small area near the center is analyzed and the maximum bending moment is obtained. This general solution can also be applied in the analysis of single-parametric elastic foundation and isotropic plates.

关 键 词：正交异性板 弹性地基 解析法 弯曲 挠度 

分 类 号：O343.8[理学—固体力学]