任意分布横向载荷下圆板混合边值问题的一种解析方法
An Analytical Method for a Mixed Boundary Value Problem of Circular Plates under Arbitrary Lateral Loads
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摘要: 通过引入边界混合函数的概念,选用极坐标下双调和方程的特解序列为试函数,本文提出了一种求解圆板混合边值问题的解析方法.最后通过三个实例计算说明了该方法具有较好的收敛性和稳定性.Abstract: In this paper by using the concept of mixed boundary funetions,an analytical method is proposed for a mixed boundary value problem of circular plates.The trial functions are constructed by using the series of particular solutions of the biharmonic equations in the polar coordinate system.Three examples are presented to show the stability and high convergence rate of the method.
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Key words:
- circular plate /
- mixed boundary value problem /
- mixed boundary functions /
- analytical method /
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[1] Timoshenko,S.and S.Woinowsky-Krieger,Theory of Plate and Shells,McGraw-Hill Book Company,Inc.(1959). [2] 林鸿荪,任意横向载荷下弹性圆形及圆环形薄板的弯曲,物理学报,12(1956), 360-375. [3] 叶开元、许剑云.任意分布横向载荷下的环形薄板弯曲的一般解及若干应用问题,兰州大学学报.力学专号,1(1979),202-225. [4] 钱伟长,《变分法及有限元》(上册),科学出版社(1980). -
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