弹性地基上的自由边矩形板

A Free Rectangular Plate on Elastic Foundation

摘要: 本文讨论了在弹性地基上的自由边矩形板的弯曲问题.我们讨论了两种情形,诸如在板的中心受到一集中力作用和在板的四个角点上各受到一相等的集中力作用.文中选择了一个挠曲函数,它不但能满足所有自由边上的全部几何边界条件,而且也满足所有的内力边界条件.同时,我们应用了变分法,从而得到了较好的近似解答.
- 矩形薄板 /
- 弯曲 /
- Галёркин变分法 /
- 挠曲函数
Abstract: This article will discuss the bending problems of the rectangular plates with free boundaries on elastic foundations.We talk over the two cases,that is,the plate acted on its center by a concentrated force and the plate subjected to by a concentrated force equally at four corner points respectively.We select a flexural function which satisfies not only all the geometric boundary conditions on free edges wholly but also the boundary conditions of the total internal forces.We apply the variational method meanwhile and then obtain better approximate solutions.
- rectangular thin plate /
- bending problem /
- Galerkin’s variational method /
- flexural function

[1]	Власов В.З.и Н.Н.Леоитъев,Балкц,Ллцмы ц Оболочкц на Упруом Оскоoahuu.Гостехиздат(1960).
[2]	Кононелко Е.С.,О приближенном расчетапрямоуголъных пянт на упругомоснонании,Исслебованца по Теорця Сооруженцц,Сборнцк Смамец(1960).(in Russian).
[3]	张福范,《弹性薄板》,第二版,科学出版社(1984),237-249.
[4]	陈叔陶,弹性地基上自由边矩形板,力学学报 (1960).
[5]	范家参、黎家佑,对弹性地基上的自由边矩形板的探讨,应用数学和力学,2,4(1981),499-504.
[6]	生跃、黄义,双参数弹性地基上自由边矩形板.应用数学和力学,8,4(1987),325-338.
[7]	王克林、黄义.弹性地基上四边自由矩形板,计算结构力学及其应用,2(1985).
[8]	成祥生,弹性地基上自由边矩形板的弯曲、稳定和振动,应用数学和力学,9,6 (1988),573-578.
[9]	Timoshenko,S.and S.Woinowsky-Krieger,Theory of Plates and Shells,Second.Edition,McGraw-Hill Book Comp.,Inc.(1959).
[10]	Лехникий C.Г.,Анцзомролные Пласмцкка,Гостехиздат,М.(1957).