Nonlinear Local Stability Of Dished Shallow Shells

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.