关于集中载荷下圆板非线性弯曲问题的解析电算求解*
On Analytical-Computerized Method to Solve Nonlinear Bending Problem of Circular Plate under a Concentrated Load
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摘要: 本文获得了求解中心承受集中载荷的圆板大挠度问题迭代解析解的递推公式的计算程序,使之能便于计算执行。同时,通过对此方法收敛性的研究,得到了关于载荷值P收敛的一个上界值。这为解析电算法的应用提供了一个有用的判据。Abstract: In this paper, we have got a procedure of the recurrence formulas of analytical solution of iteration on solving the large deflection problem of circular plate under a concentrated load by computer. By researching convergence of the method, we have got a convergent upper bound value about load p, which is a useful criterion for analytical-computerized method.
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[1] 叶开沅、顾淑贤,均布载荷作用下圆底扁球壳的非线性稳定性,《1980年全国计算力学会议文集梦,北京大学出版社(1980), 280-287. [2] Keller,H.B.and E.L.Reiss,lterative solutions for the nonlinear bending of circular plates,Comm.Pure Appl.Math.11(1958),273-292. [3] Yeh Kai-yuan,Zheng Xiao-jing and Zhou You-he,An analytical formula of exact solution to Kármán's equations of circular plate under a concentrated load,Proc.ICNM.Shanghai,Science Press,Beijing,China (1985),386-391. [4] 钱伟长、叶开沅,圆薄板大挠度问题,物理学报,10,3 (1954), 209-238 -
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