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用三维弹性力学方法研究圆板的稳定问题
引用本文:侯宇,何福保.用三维弹性力学方法研究圆板的稳定问题[J].上海力学,1995,16(1):13-19.
作者姓名:侯宇  何福保
作者单位:中国计量学院 (侯宇),上海工业大学(何福保)
摘    要:用三维弹性力学方法研究任意边界条件圆板的轴对称稳定问题,利用H变换和Stockes变换,导出位移函数及其偏导数的一种新型双重极数式,并由数学弹性定理论的基本方程和边界条件建立的特征方程,求得最小临界载荷的精确解,文末以简支圆板为例进行数字计算,结果表明:在弹性失稳范围内,三维弹性力学方法求得的临界载荷略低于经典理论的结果,对于薄板的弹性稳定问题,经典板理论有足够的精度。

关 键 词:圆板  弹性力学  三维问题  稳定性

A STUDY OF THE STABILITY PROBLEM OF CIRCULAR PLATES BY THE THREE-DIMENSIONAL THEORY OF ELASTICITY
Hou Yu He Fubao.A STUDY OF THE STABILITY PROBLEM OF CIRCULAR PLATES BY THE THREE-DIMENSIONAL THEORY OF ELASTICITY[J].Chinese Quarterly Mechanics,1995,16(1):13-19.
Authors:Hou Yu He Fubao
Institution:Hou Yu He Fubao (China Institute of Metrology) (Shanghai University of Technoloey)
Abstract:In this paper, the axisymmetric stability problem of circular plates with arbitrary axisymmetric boundary condition is investigated by the use of the three-dimensional theory of elasticity. By means of the H-transformation and Stockes' transformation, a new kind of displacement function in the form of double series is obtained together with its partial derivatives. Hence the characteristic equation may be established by the use of the fundamental equation an'd boundary conditions of the mathematical theory of elastic stability and the exact solution may be obtained. A numerical example to find the critical radial load of a circular plate with simple supported edge is presented. It is found that the critical load from the three-dimensional theory of elasticity is slightly lower than that from the classical theory. It is also manifested that the classical theory is quite accurate.
Keywords:Circular plates  Elastic stability  H- transformation  Stockes' transformation  
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