均布载荷作用下变厚度圆球扁薄壳的非线性轴对称弯曲和稳定性

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基金项目: 中国科学院科学基金

Nonlinear Axisymmetric Bending and Stability of Thin Spherical Shallow Shell with Variable Thickness under Uniformly Distributed Loads

摘要: 本文应用叶开沅教授与作者在文[1]中提出的修正迭代法,研究了在均布载荷作用下变厚度圆球扁薄壳的非线性轴对称弯曲和稳定性.求得了挠度曲线与临界载荷值,所获得的数值结果以图表形式给出.另外关于确定壳体中心挠度与载荷的方程式对应于尖点突变流形.

Abstract: In this paper, the nonlinear bending and stability of thin spherical shallow shell with variable thickness under uniformly distributed loads are investigated by a new modified iteration method proposed by Prof. Yeh Kai-yuan and the author^[1]. Deflections and critical loads have been calculated and the numerical results obtained have been given in figures and tabular forms. It is shown that the final equation determining the central deflection and the load obtained coincides with the cusp catastrophe manifold.

[1]	叶开沅、叶志明、王新志,对“变厚度圆薄板在均布载荷下大浇度问题”解法的讨论,应用数学和力学,6, 3 (1985), 285-287.
[2]	Ye Zhi-ming, The nonlinear bending and stability of thin circular plates and thin conical and spherical shallow shells with variable thickness, Proc. Int. Conf. Non-Linear Mech., Shanghai, Oct. (1985), 28-31.
[3]	叶开沅、宋卫平,在均布压力作用下圆锥扁壳的非线性稳定性,兰州大学学报(自然科学版)力学专号,19 (1983).
[4]	叶开沅,柔韧构件的研究在中国的进展,力学进展,13, 2 (1983).
[5]	铁木辛柯,S., S.沃诺斯基著,《板壳理论》,科学出版社(1977).
[6]	Huang, N.C., Unsymmetrical buckling of thin shallow spherical shells, J. Appl. Mech., 1 (1964).
[7]	Banerjee, B., Large deflections of circular plates of variable thickness, J. Appl. Mech., 49, 1 (1982).
[8]	Banerjee, B., Large deflections of circular plates of variable thickness, Int. J. Solids and Structures, 19, 2 (1983).
[9]	Poston, T., and I. Stewart, Catastrophe Theory and Its Applications, Pitman, London (1978).
[10]	叶开沅、顾淑贤,在均布压力作用下圆球扁壳的非线性稳定性,《中国力学学会全国计算力学会议论文集》,北京大学出版社(1981).
[11]	Stumpf, H., On the nonlinear buckling and post-buckling analysis of thin elastic shell, Int. J. Nonlinear Mechanics, 19, 3 (1984).