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均布载荷下矩形板大挠度问题的摄动变分解

潘立宙 王蜀

潘立宙, 王蜀. 均布载荷下矩形板大挠度问题的摄动变分解[J]. 应用数学和力学, 1986, 7(8): 675-688.
引用本文: 潘立宙, 王蜀. 均布载荷下矩形板大挠度问题的摄动变分解[J]. 应用数学和力学, 1986, 7(8): 675-688.
Pan Li-zhou, Wang Shu. A Perturbation-Variational Solution of the Large Deflection of Rectangular Plates under Uniform Load[J]. Applied Mathematics and Mechanics, 1986, 7(8): 675-688.
Citation: Pan Li-zhou, Wang Shu. A Perturbation-Variational Solution of the Large Deflection of Rectangular Plates under Uniform Load[J]. Applied Mathematics and Mechanics, 1986, 7(8): 675-688.

均布载荷下矩形板大挠度问题的摄动变分解

A Perturbation-Variational Solution of the Large Deflection of Rectangular Plates under Uniform Load

  • 摘要: 本文以中心挠度为摄动参数,将矩形板大挠度问题的非线性偏微分方程组转化成几个线性偏微分方程,然后用变分法求解,得出了具有任意长宽比的板的解答,给出了位移、挠度及各内力的解析表达式;并给出中心点和边界中心的应力数值计算公式。本文还以长宽比λ为参数,作出了最大挠度——载荷曲线及最大应力曲线。其结果与实验进行了比较,表明二者是一致的。
  • [1] Way, S.,Uniformly loaded, clamped, rectangular plates with large deflection,Proc, Fifth Int, Cong, Appl, Mech.(Cambridge, Mass, U, S.A.1938),(1939),123-128.
    [2] Levp, S,Bending of rectangular plates with large deflections, NACA, TR,737(1942).Square plate with clamped edges under normal pressure producing large deflection,NACA, TR, 740 (1942).
    [3] Wang, C, T,Nonlinear large deflection boundary value problems of rectangular plates, NACA, TN,1425 (1948).
    [4] Wang, C, T,Bending of rectangular plates with large deflection,NACA, TN, 1462(1948).
    [5] Chien, W, Z,Large deflection of a circular clamped plate under uniform pressure,Chinese J.of Physics, 7 (1947),102-113.
    [6] Yeh, K, Y,Large deflection of a circular plate with a circular hole at the centre,Acta Scientia Sinico, 2 (1953),127-144.
    [7] Chien, W, Z, and K, Y.Yeh, On the large deflection of circular plate, Acfa Scientia Sinica, 3 (1954),405-436.
    [8] Chien, W, Z, Prohlem of large deflection of circular plate, Nodbitko Z.Archiwum Meehonki Stosowanej,Warszawa, 8 (1956),1-2
    [9] Chien, W, Z, and K, Y.Yeh, On the large deflection of rectangular plate, Proc.Ninth Intern, Congr, Appl, Mech.,Brussels, 6 (1957),403.
    [10] 叶开沉、房居贤、王云,在法向均布载荷下四边固定的矩形板大挠度问题的摄动解,《第六届全国弹性元件会议论文集》(厦门)(1981).
    [11] Ramberg, W.,A, B, Mepherson and S, Levp, Normal-pressure tests of rectangular plates, NACA, Report No,748.(1942).
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出版历程
  • 收稿日期:  1985-06-01
  • 刊出日期:  1986-08-15

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