多外载联合作用下圆板的非线性弯曲

Nonlinear Bending of Circular Plates under Combined Loadings

分析了多外载联合作用下圆板的轴对称非线性弯曲问题。分析从极坐标系下圆板弯曲的Ｖｏｎ－Ｋａｒｍａｎ方程出发，运用微分求积方法（ＤＱ法）导出了控制方程的ＤＱ形式；边缘径向位移和边缘力矩由两个统一的方程来表示，通过改变方程中的约束刚度和边缘载荷系数，实现了对任意边界条件的模拟；对最终得到的非线性方程组，用Ｎｅｗｔｏｎ－Ｒａｐｈｓｏｎ方法进行了迭代求解。文中给出了圆板受横向均布力、板心横向集中力、边缘均布径向力、边缘均布弯矩等四种载荷两两联合作用下的计算结果曲线，讨论了不同联合载荷对回板非线性弯曲的影响。与文献结果比较表明，该方法能满足各种边界条件，具有较高的求解精度。

The nonlinear axisymmetrical bending of circular plates subjected to various combined loadings has been analyzed by the differential quadrature (DQ) method. The radial displacement and the moment at the edge are expressed with two simple equations,from whichvarious boundary conditions are given by different supporting stiffness and loading coefficients.Four types of loads under consideration are a uniform transverse load,a concentrated load acting at the center, a uniform edge moment,and uniform edge radial force. Numerical results areobtained for circular plates with several different boundary constraints and subjected to a variety of combined loadings. Results are compared well with the existing data in the open literature. It is shown that the numerical results presented herein are reliable and that the Domethod is a useful tool for routine engineering analysis.