Abstract
In the present paper, a new method for the dynamic buckling analysis of rotational shells with initial imperfections is formulated based on the finite element method and mode superposition method. This method avoids the direct finite element method of nonlinear effects and also takes advantage of the important feature that structural response is fundamentally due to several basic vibration modes. The two in-plane displacements u and v are explicitly obtained compatible with the assumed lateral displacement w and initial imperfection w^I, both of which are expanded by free vibration modes. The governing equation is composed of a set of algebraic cubic polynominal equations in terms of the generalized modal displacements. The coefficients in the equations for a shell with an initial imperfection are obtained through a simple matrix manipulation of those for the perfect shell and the coefficients in Fourier expansion of the imperfection. This formulation can treat with a nonlinear dynamic stability problem subjected to time dependent axial and lateral loads also a problem with nonlinear inertial forces. The pressent method is applied to solve the axisymmetric dynamic buckling of clamped spherical caps under a uniform step load, whose shell parameter λ ranges from 5 to 10. Imperfection sensitivity of the dynamic buckling load is investigated as well as both of the static and astatic buckling loads. The dynamic buckling load, determined in numerical responses, is found to lie between the static and astatic buckling load. This tendency is valid in case of shells with initial imperfections. Then, the astatic buckling load can be considered as a lower limit for the axisymmetric dynamic buckling.
