椭圆板的大挠度问题

Large Deflection Problem of a Clamped Elliptical Plate Subjected to Uniform Pressure

Shanghai University of Technology, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai

摘要: 本文在圆薄板大挠度问题摄动解法(1948)^[1].(1954)^[2]的基础上,求得了椭圆板大挠度问题的摄动解.本文的公式推导是1957年以前完成的,由于某些原因,长期未得发表.1959年见到Nash-Cooley^[3]以摘要形式发表的类似工作,但只有λ=a/b=2的数值结果.这里将原先推导的正确至二级近似的分析公式以及计算结果发表.其中包括泊桑比v=0.25,0.30,0.35,椭圆半径比λ=1,2,3.4.5的全部计算结果,以备工程设计计算之用.
- 椭圆板 /
- 大挠度 /
- 摄动
Abstract: In this paper,the perturbation solution of large deflection problem of clampedelliptical plate subjected to uniform pressure is given on the basis of the perturbationsolution of large deflection problem of similar clamped circular plate (1948)^[1],(1954)^[2].The analytical solution of this problem was obtained in 1957.However,due to social difficulties,these results have never been published.Nash and Cooley (1959)^[3] published a brief note of similar nature,in which only the case λ=a/b=2 is given.In this paper,the analytical solution is given in detail up to the 2nd approximation.The numerical solutions are given for various Poisson ratios ν =0.25,0.30,0.35 and for various eccentricities λ=1,2,3,4,5,which can be used in the calculation of engineering designs.
- elliptical plate /
- large deflection /
- perturbation method

[1]	Chien Wei-zang,Large deflection of a circular damped plate under uniform pressure,Chinese Journal of Physics,7(1948),107-113.
[2]	钱伟长、叶开沉,圆薄板大挠度问题,中国物理学报,10,3(1954),209-238.
[3]	Nash,W.A.and I.D.Cooley,Large deflections of a clamped eiliptical plate subjected to uniform pressure,Journal of,4pplied Mechanics,26(1959),291-293.
[4]	Th.von Karman,Festigkeits Problem in Maschinenbau,Enzyklopadie der Mathema-tischen Wissenschaften,4,27(1910).
[5]	Th.yon Karmán,The engineer grapples iwth non-linear problem,Ball.Amer.Math.Soc.,46(1940),615-683.
[6]	Way,S.,Bending of circular plates with large deflection,A.S.M.E.Transactions,Applied Mechanics,56(1934),627-636.
[7]	Levy,S.,Bending of rectangular plate with large deflections,N.A.C.A.Reports,737(1924).
[8]	McPherson,A.E.,W.Ramburg and S.Levy,Normal pressure tests of circular plates with clamped edges,N.A.C.A.Reports,744 (1942).
[9]	Chien Wei-zang and Yeh Kal-yuan,On the large deflection of rectangular plate,Proceedings of Ⅸ Congress of Applied Mechanics,Bruxelles (1956).
[10]	Weil,N.A.and N.M.Newmark,Large deflections of elliptical plates,Journal of Applied Mechanics,28(1956),21-26．