Abstract
In the present paper, the initial imperfecton sensitivity of the axisymmetric dynamic buckling loads for clamped spherical caps, from λ=5 to 10, under a uniform step load is discussed. And the imperfection sensitivity of static, and astatic buckling loads are treated as well as dynamic buckling loads. The analysis is based on the finite element method and mode superposition method. This method avoids the direct finite element method of nonlinear effects and also takes an advantage of the important feature that a structural response is fundamentally due to several basic vibration modes. The governing equation is composed of a set of algebraic cubic polynominal equations in terms of the generalized modal displacements. The coeffcients 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. The result is confirmed by the present numerical analysis of buckling behaviour that an initial imperfection proportional to a buckling mode of a perfect caps is major for a static buckling load, and other nonproportional initial imperfections are minor. When the maximum value of any initial imperfection is about from 20 to 30 percents of the shell thickness, the static buckling load reduces severely, and accordingly the static buckling mode changes. Dynamic and astatic buckling loads are insensitive to any initial imperfection mode. The astatic buckling load can be considered as a lower limit not only for the theoretical value but also by a numerical response of the axisymmetric dynamic buckling of a calmped spherical cap with initial imperfectial under a uniform step load.
