Von-Karman板方程的摄动—复变函数解法

发布时间：2018-06-13 19:41

本文选题：Von-Karman方程 + 大挠度　；参考：《四川建筑科学研究》2015年06期

【摘要】：板的大挠度方程由Von-Karman于1909年推导出来,这便是著名的Von-Karman大挠度方程组。但是,由于Von-Karman方程为八阶非线性耦合方程,求解十分困难,至今尚无精确解。为求解Von-Karman方程,一般采用瑞利-李兹法、能量法、迦辽金法及摄动法以求得近似解。复变函数最初由原苏联科学家柯索洛夫引入解弹性平面问题,而后由穆什维海尔院士集大成,解决弹性平面问题及一系列孔洞及复杂边界问题,后由萨文、卢尔瓦兹等一批原苏联科学家引入到求解板的小挠度方程问题中。本文进一步将复变函数推广到板的大挠度方程中,得出VonKarman方程在复变函数下的表达式;另外,给出了求解大挠度板复变函数方法的一般步骤,并求解出固支边界圆板的渐近解。
[Abstract]:The equation of large deflection of plate is derived by Von-Karman in 1909, which is the famous equations of large deflection of Von-Karman. However, since the Von-Karman equation is an eighth-order nonlinear coupled equation, it is very difficult to solve it. In order to solve the Von-Karman equation, the Rayleigh-Leeds method, the energy method, the Galerkin method and the perturbation method are generally used to obtain the approximate solution. The complex variable function was first introduced by the former Soviet scientist Kozolov to solve the elastic plane problem, and then by academician Mushvihaer to solve the elastic plane problem and a series of holes and complex boundary problems. A group of former Soviet scientists, such as Luervaz, were introduced to solve the small deflection equations of plates. In this paper, the complex variable function is extended to the large deflection equation of the plate, and the expression of the Von Karman equation under the complex variable function is obtained. In addition, the general steps for solving the complex variable function of the large deflection plate are given, and the asymptotic solution of the fixed boundary circular plate is obtained.
【作者单位】：江苏科技大学;上海交通大学;
【基金】：国家高分辨率对地观测系统(GFZX04020602)
【分类号】：TU311

【共引文献】