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椭圆板的大挠度问题

钱伟长 潘立宙 刘晓明

钱伟长, 潘立宙, 刘晓明. 椭圆板的大挠度问题[J]. 应用数学和力学, 1992, 13(10): 857-871.
引用本文: 钱伟长, 潘立宙, 刘晓明. 椭圆板的大挠度问题[J]. 应用数学和力学, 1992, 13(10): 857-871.
Chien Wei-zang, Pan Li-zhou, Liu Xiao-ming. Large Deflection Problem of a Clamped Elliptical Plate Subjected to Uniform Pressure[J]. Applied Mathematics and Mechanics, 1992, 13(10): 857-871.
Citation: Chien Wei-zang, Pan Li-zhou, Liu Xiao-ming. Large Deflection Problem of a Clamped Elliptical Plate Subjected to Uniform Pressure[J]. Applied Mathematics and Mechanics, 1992, 13(10): 857-871.

椭圆板的大挠度问题

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

  • 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.
  • [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.
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出版历程
  • 收稿日期:  1991-12-01
  • 刊出日期:  1992-10-15

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