Nonlinear Dynamic Responses of a Corrugated Shell Structure under Uniform Load

Corrugated shell structures are widely used in civil, naval, automotive, and aerospace engineering because of their superior properties. In this paper, the nonlinear dynamic deformation of a class of longitudinally corrugated shell with a second-order differentiable wave under a uniform load was investigated. On the basis of their previous research result—that the corrugated shell undergoes large deformation but small strains—the authors proposed an assumption that the dynamic configuration of the corrugated shell is the same as the static configuration with a different load. Then the governing equations of the dynamic deformation of the corrugated shell were derived using Lagrange’s equation, and an efficient numerical method without element discretization to solve those nonlinear differential equations was formulated. The accuracy of the present simplification was proved by comparing it with results obtained from a widely used nonlinear finite-element program, and the assumption on the dynamic configuration was shown to be applicable for most engineering applications. Furthermore, the developed method was adopted to perform parametric studies and it is found that the loading rates, the depth of wave, and the number of wave can greatly change the expansion velocity of the corrugated ring. And most importantly, the authors revealed that different corrugation types with the same ratio of the radius of the median surface to the depth of wave $R_0/L_w$, the number of waves $N$, and the circumference $C_T$ can yield similar dynamic expansion responses, which should be useful for future design of corrugated shell.