Static And Dynamic Analysis On Geometric Nonlinear Of Deep Spherical Shell

Shell structures, because of its beautiful shape and excellent mechanical properties,are widely used in engineering. However, the theoretical studies on the mechanical properties of shell structures of are not perfect. The current studies focus on shallow shells and cylindrical shells, and the studies on the non-linear static and dynamic problems of deep shell structures are seldom. The thesis has studied linear and non-linear problems of deep thin spherical shell subjected static transverse load, and based on the previous studies, the dynamic problem of deep thin spherical shell subjected static transverse load is studied in the thesis.Main contents of this thesis are as follows:1.Starting with the analysis of the general shell, the fundamental equations and the governing equations of deep thin spherical shell are obtained after derivation. At the same time, the boundary conditions about different boundary constraints of deep thin spherical shell are given.2. The fundamental equations of linear problem are obtained by the simplification of the fundamental equations of deep thin spherical shell. Through the introduction of dimensionless quantities,the fundamental equations of linear problem are transformed into the dimensionless equations.Combined with the corresponding boundary conditions, the dimensionless equations are solved by Shooting Method. The relationship between the center deflection of shell W0 and dimensionless load Q,spread angleα0,as well as shell thickness is discussed through the obtained figures.And the configuration charts of deep thin spherical shell are drawn.3.The fundamental equations of non-linear problem are obtained by the simplification of the fundamental equations of deep thin spherical shell.The dimensionless equations are solved by the same numerical method in the second item. The relationship between the center deflection of shell W0 and dimensionless load Q,spread angleα0,as well as shell thickness upon the non-linear deformation of shell is discussed through the analysis of charts,and the conclusions of non-linear analysis are compared with its of linear analysis.4.Considering the deformation of geometric non-linearity, the governing equations of non-linear problem of deep thin spherical shell are obtained after derivation. Displacements are separated into static and dynamic items, and according to Hamilton principle, dimensionless partial differential equations are transformed into ordinary differential equations.Using the same numerical method in the second item, the relationship between the former three order vibration frequencies and various parameters of deep thin spherical shell is discussed through the obtained figures.The vibration model charts of the former three order vibration of deep thin spherical shell are drawn.