四边弹性梁支承的矩形板非线性弯曲

本文给出四边弹性梁支承的矩形板在横向荷载作用下的非线性弯曲的重级数解。通过把板内的横向位移展成重傅里哀级数,在边界上的位移展成单傅里哀级数以及把应力函数展成广义傅里哀级数,使边界条件转化成了无穷线性代数方程,控制微分方程转化成了无穷非线性代数方程。文后给出了四边弹性梁支承和对边简支对边弹性梁支承的矩彤板非线性弯曲的计算结果。

NONLINEAR BENDING OF RECTANGULAR PLATES SUPPORTED BY FOUR BEAMS

This paper presents a series solution to Von Kaman nonlinear equations of a rectangular plates supported be four beams under the action of lateral load.Using ordinary Fourier series for the edge displacement,double Fourier series for the deflection,and generalized Fourier se- ries for the stress function,governing equations are reduced to an infinite set of nonlinear algebraic equations,boundary conditions to an infinite set of linear algebraic equations for coefficients in these series.Numerical results for deflections of the plates,which are supported by four beams,are graphically presented.