Nonlinear Instability Modes Analysis Of Dished Shallow Shells

The shallow-thin-shell structure, because of its beautiful appearance, reasonable load, economy and practicality, has been widely applied in the fields of construction, machinery, chemical industry etc. The main form of its destruction is buckling, which often happens suddenly and causes irresistable loss of life and property. There are lots of factors which affect the shallow thin shells'destabilizing critical loads and instability modes, such as geometric parameters, loads'pattern and acting position of the external loads. So the nonlinear stability problem of the structure has been long focused and studied by Chinese scholars and those from all over the world.The shallow thin shell's basic governing differential equations are difficult to reach a solution. As a ameliorative perturbation method which can solve the nonlinear local stability of axisymetrical shallow thin shells, the free-parameter perturbation method (FPPM) helps researchers get all elastic characters without determining the specific physical meaning of perturbation parameter, eliminate the empirical factors during the perturbation process and make the solving proces more reasonable.In previous studies of nonlinear stability problem of shells, researchers mainly focus on the characteristic equation of the load with respect to the center deflection. Assuming instable sighs firstly appear at the center, they discuss the shells'overall stability according to the characteristic equation; This dissertation is to apply FPPM in solving the nonlinear stability problem of the dished shallow shells, establish the characteristic equations of the load with respect to the deflection at any point, find the area where the dished shallow shell under loads firstly started to lose stability, obtain the deflection at any point of dished shallow shells under loads according to the characteristic equations and gain further the modes of nonlinear instability, then analyse the modes of nonlinear instability for dished shallow shells, explore further the certain relationship between the first buckling areas and the first instability mode.This paper firstly introduces the calculating principles and process of FPPM applied in the large-deflection problems of dished shallow shells, and then, by combing FPPM with Spline-method, study the nonlinear stability of dished shallow shells under uniformly distributed loads and line distributed loads, respectively. Through calculating the computational examples, we can obtain the rule about how the deflection curves change with the loads before the first instability, obtain the rule how the first instability modes changes with geometric parameters, loads'pattern and acting position, investigates further the internal relationship between the first buckling area and the first instability mode. These conclusions have a certain engineering value and theoretical significance, which can provide theoretical basis for the engineering design and instability prediction.