【作者】 李彬；

【导师】 陈山林；

【作者基本信息】 重庆大学 ， 工程力学， 2005， 硕士

【摘要】 扁薄壳结构在工程中占有非常重要的地位，其非线性稳定问题是一个长期以来被中外学者关注和研究的经典问题。由于其基本微分方程的非线性特征，使其求解比较困难，而自由参数摄动法作为求解轴对称扁壳非线性局部稳定问题一种改进的摄动方法，使研究者无须具体选择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。但是，已有的研究成果没有讨论壳体局部稳定问题，本文的主要目的是采用自由参数摄动法研究碟形扁壳的非线性局部稳定问题。 文中首先介绍了采用自由参数摄动法求解碟形扁壳大挠度问题的计算原理及过程，而后本文将自由参数摄动法与样条函数拟合法结合起来，求解在均布和线布载荷分别作用下碟形扁壳的非线性局部稳定问题，通过编制计算程序计算具体算例，研究了壳体的失稳起始区域，以及该区域与载荷形式、几何参数的关系等问题。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】 Shallow thin shells play a very important role in engineering field and nonlinear stability related these components have long been a classical problem, which has been studied by numerous investigators in the world. Because of the nonlinear character of basic differential equation, it is difficult to obtain solution. As a ameliorative perturbation method which can solve the nonlinear local stability of axisymetrical shallow thin shells, the free-parameter perturbation method (FPPM) make researchers obtain the all elastic characters without choosing proper perturbation parameter to create perturbation solution, eliminate the empirical factors during the perturbation process and get more reasonable results. The existing results, however, involve no local stability of shells. The fundamental objective in this dissertation lies in applying FPPM to solve the nonlinear local stability of dished flat shells.This paper firstly presents the calculating principles and process of FPPM applied in the large-deflection problems of dished shallow shells. FPPM together with Spline-method are applied to study the nonlinear local stability of dished shallow shells under uniformly distributed loads and line distributed loads, respectively. Programmes are made to calculate specific examples. The first buckling area of shells and the correlations among the area, the loads’pattem and geometrical parameters et al are discussed. Some valuable results in theory and practice are also obtained.更多还原