Dynamic Instability Analysis of Thin Shell Structures subjected to Follower Forces

Abstract

The general governing equations of equilibrium and dynamic stability for thin shells subjected to follower loads and undergoing large deformations have already been detailed in the previous reports for the general shell defined in a monoclinically convected coordinate system. Various numerical results were obtained to show the feasibility and applicability of the present approach. The existance of a threshold point of dynamic stability for a particular shell was illustrated to prove the effect of disturbances on the behaviour of shells near the point of critical static stability.The present report expands on this approach elaborately for a wide curvature range from shallow to deep shells and obtained the characteristic curves of dynamic stability threshold for partial cylindrical shells and partial spherical shells. It is found that while the spherical shells generally fail dynamically before the static critical limit, cylindrical shells retain their dynamically stable behaviour a little more beyond. The backgrounds of geometrical and strength aspects during the deformation process are also analyzed. The existance of a post-critical stability phase for shallow shells, which had been hypothesized in the previous report is investigated here and conclusive numerical evidence to this effect is obtained. The practical aspects of a shell design for the elastically feasible range of ultralarge deformations can be visualized here, for which there may be a need arising in the futuristic constructions in the sea with dynamically deflecting outer shells that may be allowed to flex safely like the tarpaulin tent in the wind.