Dynamic stability of a hemispherical shell with shape imperfections

Abstract

The nonlinear dynamic analysis of imperfect hemispherical shell under pressure was executed. The finite element model of hemisphere in the software NASTRAN was built. The shell wall in the form of the three-cornered and four-cornered finite element net was presented. Shape imperfection as a lower buckling form (Buckling) of perfect hemispherical shell under action of static pressure was modelled. Value of imperfection amplitude was set proportionally to a shell wall thickness. Two boundary conditions in the form rigid and hinged supports on the nodes of lower edge of the shell were considered. Excitation as external pressure, which linearly depended on time and uniform distributed on elements of hemispherical shell was presented. The modal analysis of perfect hemisphere with different wall thicknesses and shell with modelled shape imperfections by the Lanczos method using computational procedure of task on natural vibrations (Normal Modes) was executed. The nonlinear dynamic analysis (Nonlinear Direct Transient) of imperfect hemispherical shell under pressure by N’yumark method was executed. Influence of modelled shape imperfections amplitude on the critical values of dynamic loading and appropriate deformation forms of shell with different boundary conditions were investigated. It was discovered that a modelled imperfection in the form of a lower buckling form of perfect shell under static pressure in the modal and the dynamic analysis of hemisphere under the same type of the loading was effective. A significant influence of the amplitude of the shape imperfection on the critical values of the dynamic load (55 %) was observed. Also, in our opinion, the presented model of shape imperfection can be used to assess design reliability of the hemisphere under the action of dynamic loads using Bolotin probabilistic approach.