球壳轴对称弯曲问题共轭二阶挠度微分方程

提出球壳轴对称弯曲问题共轭二阶挠度微分方程并给出了初等函数解. 球壳微分方程是薄壳理论三大壳之一旋转壳的典型方程. 共轭二阶挠度微分方程是球 壳中微分方程形式最简单的, 是人们最喜爱的挠度微分方程. 挠度微分方程满足边 界条件非常简单, 使球壳的计算得到很大的简化.     

REFINED DIFFERENTIAL EQUATIONS OF DEFLECTIONS IN AXIAL SYMMETRICAL BENDING PROBLEMS OF SPHERICAL SHELL AND THEIR SINGULAR PERTURBATION SOLUTIONS

This paper deals with the research of accuracy of differential equations of deflections.The basic idea is as follows.Firstly,considering the boundary effect the meridianmidsurface displacement u=0,thus we derive the deflection differential equations;secondly we accurately prove that by use of the deflection differential equations or theoriginal differential equations the same inner forces solutions are obtained;finally,weaccurately prove that considering the boundary effect the meridian surface displacementu=0 is an exact solution.In this paper we give the singular perturbation solution of thedeflection differential equations.Finally we check the equilibrium condition and prove theinner forces solved by perturbation method and the outer load are fully equilibrated.Itshows that perturbation solution is accurate.On the other hand,it shows again that thedeflection differential equation is an exact equation.The features of the new differential equations are as follows:1.The accuracies of the new differentia     

圆锥壳轴对称弯曲问题精确的四阶挠度微分方程和贝塞尔函数解

本文提出了轴对称圆锥壳精确的四阶挠度微分方程。和现行薄壳理论中常用的四阶剪力Q_1微分方程相比,挠度微分方程与其精度相同,阶数相同,而且满足边界条件简单,使圆锥壳的计算得到很大的简化。     

圆锥壳轴对对称弯曲问题精确的四阶挠度微分方程和贝塞尔函数解

本文提出了轴对称圆锥壳精确的四阶挠度微分方程。和现行薄壳理论中常用的四阶剪力Ｑ１微分方程相比，挠度微分方程与其精度相同，阶数相同，而且满足边界条件简单，使圆锥壳的计算得到很大的简化。     

球壳轴对称弯曲问题精确的挠度微分方程及其奇异摄动解

本文提出了球壳轴对称弯曲问题精确的挠度(ω)微分方程和精确的转角(dω/da)微分方程. 本文重点研究了挠度微分方程的精度,基本思路是:首先假设边缘效应时经线中面位移u=0,从而建立挠度微分方程,然后再精确地证明挠度微分方程与原来微分方程内力解答完全相同.再精确地证明边缘效应时经线中面位移u=0是精确解. 本文给出了挠度微分方程的奇异摄动解,最后验算了平衡条件,证明摄动解求出的内力和外荷载是完全平衡的.这一方面表明摄动解的计算是正确的;另一方面也再二次表明挠度微分方程是精确的微分方程. 新微分方程的优点是:1.新微分方程和原来微分方程精度完全相同;2.新微分方程满足的边界条件非常简单;3.新微分方程便于使用摄动解;4.新微分方程可以得到挠度(ω)和转角(dω/da)的表达式. 新微分方程使球壳的计算得到很大的简化.本文采用的符号与徐芝纶《弹性力学》第二版下册相同.