The Perturbation Method Of The Large Deflection Problem Of Circular Corrugated Plate With Sine-shape Shallow Waves

Based on the nonlinear theory of large deflection of shallow conical shells,this paper gives approximate solution of the large deflection equations of circular corrugated plate with sine-shape shallow waves having a central platform under different load.The elastic characteristics of circular corrugated plate are obtained by using the perturbation and power series method.In Chapter 1,the history of development of geometrical nonlinear theory of thin shells is reviewed at first.The characteristics of the corrugated diaphragm are summarized,and the theory for large deflection of cylindrically anisotropic circular plates for solving problems of corrugated diaphragms is compared with the theory for deflection of thin shells.Finally,the content and investigating methods of this paper are presented.In Chapter 2,by using the equilibrium method of differential elements of shells, the equilibrium equations of axisymmetric shells of revolution are given.Then, based on the geometric and the stress-strain relationships,the Nonlinear coupled ordinary differential equations regarding radial angleβand stress function F are derived.The basic non-linear differential equations are obtained for the theory of medium rotation and the theory of shallow shells.Chapter 3 gives approximate solution of the large deflection equations of circular corrugated plate by utilizing the perturbation and power series method. Selecting deflection at the center as parameter of perturbation,a series of linear differential equations are obtained.For the central platform,the linear differential equations describing the perturbation of different orders are reduced to Euler equations which can be solved accurately.For the corrugated parts,the accurate answers of perturbation can not be obtained,power series method is used to solve the problem.Finally,according to boundary conditions,continuous conditions and conditions of perturbation,the perturbation problems are reduced to linear algebraic equations. In Chapter 4,by numerical calculation of the circular corrugated plate with sine-shape shallow waves,the characteristics of the central deflection of the second item are obtained,and the relevant characteristic curves are also obtained.In Chapter 5,the whole paper is summarized,and some useful conclusions which are helpful to the design of the corrugated diaphragm are obtained.Then, some further investigations fields on nonlinear mechanics of the corrugated diaphragm are presented.