k个内点支承圆板的对称弯曲
The Symmetrical Bending of an Elastic Circular Plate Supported at k Internal Points
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摘要: 本文研究在均布载荷作用下,表面上有k个等距离内点支承的弹性圆板的对称弯曲.将自由边界位移和转角展开成Fourier级数,应用文献[6]的方法,使平衡方程和边界条件同时得到精确满足,从而获得了挠曲面方程的解析表达式.这是一种简便、有效的算法.Abstract: This paper treats the symmetrical bending of a uniformly loaded circular plate supported at k internal points. The boundary displacement and slope are expanded in Fourier seriesr. The method proposed by [6] is applied. As both the governing differential equation and boundary conditions are satisfied exactly, we therefore obtain the analytic expression of the transverse deflectionul equation of the circular plate. This is an easy and effective methed.
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Key words:
- internal point support /
- symmetrical bending /
- deflectional equation
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[1] Bassali,W.A.,The transverse flexure of thin elastic plates supported at several points.Proc.Cambridge Phil.Soc.53(1957) 728-743. [2] Yu.J.C.L.,and H.H.Pan,Uniformly loaded circular plate supported at discrete points.Int.J.Mech.Sci.,8(1966) 333-340. [3] Leissa,W.and L.T.Wells,On a direct Fourier solution for circular plates loaded bysingularities,The Journal of the Industrial Mathematics Society.20,part 1,(1970). [4] Timoshenk,S and S.Woinowsky-Krieger,Theory of Plates and Shells,2nd edition(1959). [5] 付宝连,应用功的互等定理求解具有复杂边界条件的矩形板的挠曲面方程,应用数学和力学,3(3) (1982). [6] 李农、付宝连,应用功的互等定理计算弹性圆薄板挠曲面方程,应用数学和力学.9(9)1988. -
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