Apply Free-Parameter Perturbation Method To Analyze The Large Deflection Problems Of Plates And Shells

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.