【作者】 李其中；

【导师】 陈山林；

【作者基本信息】 重庆大学 ， 工程力学， 2003， 硕士

【摘要】 正则摄动法是一种在力学领域求解非线性微分方程的方法。尤其在求解板和壳体的大挠度问题上，正则摄动法得到了广泛的使用，并取得了比较理想的计算结果。但选择摄动参数却是正则摄动法求解过程中的一个比较困难的问题，现在对于这一问题仍然没有一个一般的原则，而主要是利用经验对该问题进行处理。 本文的主要目的是介绍一种求解轴对称板壳大挠度问题的新的正则摄动方法——自由参数摄动法。采用该方法求解板以及壳体的大挠度问题，研究者无须具体选择摄动解的摄动参数就能够得出问题的全部弹性特征，减少了在摄动过程中的先验因素，使得求解结果更趋于合理。 本文首先介绍了采用自由参数摄动法求解轴对称板壳大挠度问题的一般步骤及计算公式，然后采用该方法求解了均布和集中载荷单独及联合作用下圆板的大挠度问题，并在求解中通过与传统正则摄动法的计算结果以及计算原理的比较，证明了本方法的合理性。而后本文将自由参数摄动法与样条函数拟和法结合起来，研究了圆底扁球壳在均布载荷作用下的失稳问题。通过编制计算程序计算具体算例，并将其结果与半解析法与数值方法计算结果的比较，进一步验证了本方法的实用性以及准确性，同时也得出了一些具有理论意义和工程应用价值的结果。更多还原

【Abstract】 Perturbation method of analysis is a prevalent method to solve nonlinear differential equation in mechanics field. Especially in the theory of plates and shells in large deflections, perturbation method of analysis was widely applied and gave relatively precise results. However, it is difficult to choose proper perturbation parameter in the process of applying this method. Even in present day, there have not a dependable norm to confirm certain parameter and researcher often search it through engineering experience.This paper presents a new perturbation method of analysis to solve large deflections problems of plates and shells-Free-Parameter Perturbation Method (FPPM). By this method of analysis, researcher can get all of elastic characters without choosing proper perturbation parameter to create perturbation solution. Since this method of analysis reduce the experience factors in the process of analysis, the results of it can be more reasonable.This paper firstly presents the general steps and formulas of FPPM to analysis the large-deflection problems of plate and shallow shell. After that, FPPM is applied to analysis large-deflection problems of circular plate under uniform pressure, concentrate load and compound load. The analysis process and results are compared to those of previous perturbation method and the applicability and rationality of FPPM are proved as well, In the following part, FPPM together with Spline-Method are applied to analysis the nonlinear stability problem of thin shallow spherical shell. Programmes are made to calculate specific example and the results are compared to other research’s results. Through comparison, the advantages of FPPM are presented again. Besides that, some results of this paper are theoretically valuable and useful for engineering.更多还原