在复合载荷作用下变厚度圆薄板大挠度问题
Large Deflection Problem of Circular Plates with Variable Thickness under the Action of Combined Loads
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摘要: 本文用变厚度板壳大挠度理论的修正迭代法[1],对周边固定,在复合载荷下的变厚度圆薄板进行了求解,从而得到了精确度较高的二次近似解析解.将本文的结果退化到特殊情况就可以得到和文[1、2]完全一致的结果.本文还绘出特征曲线进行比较,其结果是理想的.Abstract: By using the modified iteration method of large deflection theory of plates with variable thichness[1], we solve the problem of circular plates with variable thickness subjected to combined loads under the boundary conditions of the clamped edges and get comparatively more accurate second-order approximate analytical solution.If the results of this paper are degraded into the special cases, the results coinciding with those of papers [1,2] can be obtained.In this paper, the characteristic curves are plotted and some comparisons are made.The results of this paper are satisfactory.
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[1] 叶开沅、王新志,变厚度圆薄板大挠度理论的修正迭代法,《国际非线性力学论文集》,科学出版社(1985), 398-403. [2] 王晋莹,变厚度圆薄板在集中荷载作用下的非线性问题.应用数学和力学,8, 3 (1987), 247-252. [3] Turvey,G, J,,Proceedings of the American Scciety of Civil Engineers, Journal of the Engineering Mechanics Division(1978),351-365. [4] 王新志,变厚度圆薄板在均布载荷下的大挠度问题,应用数学和力学,4, 1 (1983),103-112. [5] 叶志明,变厚度圆底扁薄球壳的非线性稳定问题,力学学报,16, 6 (1984)634-638. [6] 杨嘉实、谢志诚,变厚度圆板大挠度理论的摄动法,应用数学和力学.5, 2 (1984),255-261. [7] 王铎,在均布载荷作用下圆锥形扁壳丧失稳定的问题,哈尔滨工业大学学报,3(1958),135-143. [8] 王新志、王林祥,边缘荷载下变厚度环形板大挠度问题,应用力学学报,3, 1 (1986), 91-94. -
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