环形和圆形薄板在各种支承条件下的非对称非线性弯曲问题(Ⅰ)
Unsymmetrical Bending Problems for the Annular and Circular Thin Plates under Various Supports (I)
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摘要: 本文研究环形和圆形薄板在各种支承条件下的非对称非线性弯曲问题.应用[7]中提出的摄动方法导出一致有效的渐近解.Abstract: In this paper we consider the nonlinear and unsymmetrical bendings of annular and circular thin plates under various supports. The uniformly valid asymptotic solutions have been derived by means of the perturbation method presented in [7].
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[1] Chien,W.Z.(钱伟长〕,Asgmptotic behavior of a thin clanmped circular plate under uniforn norml pressure at verg large deflection.Sci.Rep.Nat.Tsing Hua Univ.,Ser.A,5,(1948),71-94. [2] Chien Wei-zang(钱伟长) and Yeh Kai-yuan(叶开沅),On the large deflection of circular plate.Acta Scientia Sinica,3,4,(1954),403-436. [3] Bromberg,E.,Nonlinear bending of a ciruclar plate under normal pressure.Comm;Pure and Appl.Math.,9,(1956),633-659. [4] Fife,P.,Nonlinear deflection of thin elastic plates under tension.Comm.Pure and Appl.Math.,14,(1961),81-112. [5] Срубщик Л.С..Об асимптотыческоы иятегрироваыии сиссемы нелияейыых уравяеяий теории пластиы.ПММ.28.2(1964).335-349.. [6] 江福汝,关于椭圆型方程的奇摄动,复旦学报(自然科学报),2 (1978). 29-37. [7] 江福汝,摄动方法在薄板弯曲问题中的某些应用,应用数学和力学,1,1(1980),37-53. [8] S.铁摩辛柯,S.沃诺斯基,《板壳理论》,科学出版社,(1977). [9] A.C.沃耳密尔,《柔勒板与柔勒壳》,科学出版社,(1959), 198-202. -
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