Abstract
The efficient and practical system to analyse the dynamic nonlinear problems of rotational shells is developed. The system consists of the finite element and the mode superposition methods, and is effectively applied to solve the dynamic buckling of spherical shells under the simultaneous action of a uniform load and a concentrated force on the apex. The critical step loads reguired to produce snapping are numerically determined for shell parameterλfrom 10 to 18. The axisymmetrical snapping is found to be localized around the apex. The axisymmetric dynamic buckling loads, composed of a uniform lateral pressure and a concentrated force, being 2.42% of the total load, are compared with the static buckling loads obtained from the experiments by many authers and are revealed to be in exact agreement with the lower bound of the experiments. (Part 3) Asymmetric dynamic buckling loads of shallow caps with parameterλ=5, 6, 7 and 7.5 are numerically obtained. The asymmetric buckling is found to begin with the Mathieu typed oscillation between the symmetric and asymmetric deformations, however, the magnitude of the asymmetric displacements is too small to compare with the symmetric ones. The critical uniform step load, p/p_<cl>=0.40 in caseλ=7.5, gives a good agreement with the experimental results investigated by M.H. Lock et. al., which are ranging from p/p_<cl>=0.364 to 0.438. (Part 4)
