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.
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.
Large Deflection Problem of a Clamped Elliptical Plate Subjected to Uniform Pressure
Received Date: 1991-12-01Publish Date:
1992-10-15
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.
References
[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.
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Th.von Karman,Festigkeits Problem in Maschinenbau,Enzyklopadie der Mathema-tischen Wissenschaften,4,27(1910).
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Th.yon Karmán,The engineer grapples iwth non-linear problem,Ball.Amer.Math.Soc.,46(1940),615-683.
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Way,S.,Bending of circular plates with large deflection,A.S.M.E.Transactions,Applied Mechanics,56(1934),627-636.
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Levy,S.,Bending of rectangular plate with large deflections,N.A.C.A.Reports,737(1924).
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McPherson,A.E.,W.Ramburg and S.Levy,Normal pressure tests of circular plates with clamped edges,N.A.C.A.Reports,744 (1942).
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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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