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极正交各向异性圆板非线性弯曲的定性分析及单调迭代解

尚新春 程昌钧

尚新春, 程昌钧. 极正交各向异性圆板非线性弯曲的定性分析及单调迭代解[J]. 应用数学和力学, 1990, 11(12): 1067-1081.
引用本文: 尚新春, 程昌钧. 极正交各向异性圆板非线性弯曲的定性分析及单调迭代解[J]. 应用数学和力学, 1990, 11(12): 1067-1081.
Shang Xin-chun, Cheng Chang-jun. Qualitative Investigation and Monotonic Iterative Solutions for Nonlinear Bending of Polar Orthotropic Circular Plates[J]. Applied Mathematics and Mechanics, 1990, 11(12): 1067-1081.
Citation: Shang Xin-chun, Cheng Chang-jun. Qualitative Investigation and Monotonic Iterative Solutions for Nonlinear Bending of Polar Orthotropic Circular Plates[J]. Applied Mathematics and Mechanics, 1990, 11(12): 1067-1081.

极正交各向异性圆板非线性弯曲的定性分析及单调迭代解

Qualitative Investigation and Monotonic Iterative Solutions for Nonlinear Bending of Polar Orthotropic Circular Plates

  • 摘要: 本文对极正交各向异性圆板在任意轴对称载荷和边界条件下的非线性弯曲问题进行了较为系统的研究.首先,将边值问题归结为等价的积分方程,并且借助于广义函数得到了线性问题的一般解答.其次,对导出的非线性积分方程解的性质作了较为细致的讨论,例如边缘皱褶,非负性和奇性等.然后,构造了解的双边单调迭代格式,并给出了迭代格式的收敛性判据和误差估计,同时还讨论了解的全局存在唯一性.最后,给出了一个数值例子来说明本文方法和结论的应用.本文某些结果是由作者新得到的.
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    [9] Weinitschke,H.J.,On uniqueness of axisymmetric deformations of elastic plates and shells,SIAM J.Math.Anal.,19(1988),580-592.
    [10] 尚新春、程昌钧,圆板非线性轴对称弯曲的定性分析(待发表).
    [11] Keller,H.B.and E.L.Reiss,Iterative solutions for the nonlinear bending of circular plates,Comm.Pure Appl.Math.,11(1958),273-298.
    [12] Lekhnitskii,S.G.,Theory of Elasticity of an Anisotropic Elastic Body,Holden-Bay Sense in Mathematical Physics,Julius J.Brandstaffer,Ed.(1963),85.
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出版历程
  • 收稿日期:  1990-04-26
  • 刊出日期:  1990-12-15

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