Nonlinear Dynamic Analysis Of Laminated Shallow Spherical Thick Shells Under Impact

By considering the nonlinear theory of the shallow spherical thick shells and the elastic contact mechanics and taking the laminated shallow spherical thick shells under impact as the research objects, the essential characters nonlinear mechanical dynamic behavior are analysed in the thesis and some achievements are obtained. The main researches of the thesis are as follows.Based on the nonlinear theory of shallow shells, a set of nonlinear equations of motion for transversely isotropic shallow spherical shells subjected to a central impact force are founded. According to Hertzian law and considering the effect of the contact between the striking object and the shallow spherical shell, the contact force applied to the shells is determined. By using the orthogonal point collocation method and the time increment procedure, the nonlinear equations are resolved. In the numerical calculation, the effects of striking object's initial velocity and the shells'geometrical parameters on the dynamic response of shells are discussed.On the basis of the nonlinear theory of shallow spherical shells and considering the shear deformation , a set of nonlinear equations of motion for the laminated shallow spherical thick shells subjected to an eccentric normal impact force are founded. By using the finite difference method and the time increment procedure, the nonlinear equations are resolved. In the numerical calculation, the effects of striking object's initial velocity, and the shells'geometrical parameters and the point of contact on the dynamic response of shells are discussed.Based on the the Talreja's damage model with tensor valued internal state variables, a set of constitutive relations with damage for the fibre-reinforced composite laminated shallow spherical thick shells containing matrix cracks which are vertical or parallel to the fibers are derived by using invariant theory. Applied Kachanov damage evolution equation to constitutive relations with damage as above, a dynamic model considering damage and damage evolution for the fibre-reinforced composite laminated shallow spherical thick shells is found. By using finite difference method , Newmark method and integration method synthetically, the nonlinear dynamic analyses of fiber-reinforced composite laminated shallow spherical thick shells with damage are investigated. The main researching contents include the dynamic response and dynamic buckling for laminated shallow spherical thick shells with damage under impact of a mass. In summary, the present study shows that the emergence and evolution of the damage will reduce the stiffness of structures and influence the structures'dynamic behaviors remarkably.