抄録
The present paper follows the author's preceding two papers on axisymmetric static, dynamic and astatic buckling of clamped spherical caps due to a uniform step load. The analysis is based on the finite element method and mode superposition method. This method avoids the direct finite element methods of nonlinear effects and also takes an advantage of the importance that a structural response is fundamentally due to several basic vibration modes. The in-plane displacements which satisfy the tangential equilibrium equations are obtained compatible with the normal displacements which are, alone, assumed by eigen vectors. The governing equation is composed of a set of algebraic cubic polynominal equations in terms of the generalized displacements. The coefficients in the equations for a shell with an initial imperfection are obtained through a simple manupilation of those for the perfect shell and the coefficient in Fourier expansion of the imperfection. The conclusions from the present analysis are as follows. (a) The dynamic buckling load is severely reduced by asymmetric imperfections, reaching to one-fifth of the classical static buckling load in case of λ=7 and ω_i/t=0.30. (b) Asymmetric imperfections have the same effects as the symmetric imperfections if the magnitude ω_i/t is greater than around 0.2. (c) The dynamic buckling mechanism is classified approximately into three types. (1) Direct snap through buckling. (2) Bifurcating dynamic buckling into asymmetric deformation, with a complete snap through to a reversed shape. (3) Bifurcating dynamic buckling into asymmetric deformation without snapping to a reversed shape.
