弹性薄圆板混合边界问题的解析解法──分区联合解法

Analytic Solution of Compound Boundary Problem of Elastic Thin Circular Plates──Regional-United Method

板的混合边界问题的解析解法长期未能满意解决，对这方面所做的工作很少。近年来我国力学工作者做出了不少成绩，但都是有效的近似解法［１－３］。设弹性薄圆板周边支承与板内受载周期性地改变，可将板假想地分成若干以圆心为顶点的扇形，每一块扇形内只有一种支承方式，再设载荷对称于各该扇形的中线，在以上条件下，根据天津大学严宗达教授首先系统地提出的“加补充项的广义Ｆｏｕｒｉｅｒ－Ｂｅｓｓｅｌ双重级数会［４－６］提出了“分区联合解法”，即分区列出方程，全板联合求解，最后得到了二重级数形式的解析解。

The compund boundary problem of plates hasn't satisfactorily resolved by analytic method for a long time and the works concerned are very rare. In recent years some of the Chinese scholars in mechanics have made some contributions, which are all effective and approximate methods. Assume that the supports of the edges and the loads of elastic thin circular plates are varying periodically. The plates may be ideally divided into some circular sectors and the form of support in each sector is fixed. Furthermore, assume that the load in each sector varies symmetrically about its centre line. In this case,based on the method of general Fourier-Bessel double-series with additional terms systematically suggested first by Prof Yan Zongda of Tianjin University, this paper gives a regional-united method,which means that the equstions must be established in each sector and solved for the whole plate. Finally,gives an analytic solution in a double-series form.