Nonlinear deformation of a longitudinally corrugated shell structure with uniform load

Abstract

In this paper, we study the nonlinear deformation of a longitudinally corrugated shell (a type of morphing structure) with a uniform load. We derived the governing equations of the deformations of that corrugated shell with Nayfeh and Pai's [1] initial curvature of shell geometries and developed numerical solutions for that nonlinear mechanics problem. This numerical method is extremely efficient since no element discretization is implemented. The obtained solutions can be verified by comparing with the analytical solution for the same structure with infinitesimal strains. Furthermore, we apply the present method to study a cylindrical shell under the uniform internal pressure, and find that the displacements and internal forces of the cylindrical shell agree well with results obtained from von Kármán nonlinear shell theory. Finally, from parametric studies, we can figure out that the increment of the percentage of the arc part and the total length of the corrugated ring can increase the expansion and internal forces of the corrugated ring. And the configuration of the corrugated ring are more sensitive to the change of geometry and material parameters than internal forces, which indicate that the morphing function can be realized through the change of geometry and material parameters of the structure without great change in the maximum internal forces of the ring. By comparing the results from present nonlinear theory with those from linear theory, we can also find that the displacements and internal forces obtained from linear shell theory can either be exaggerated or disguised for the different configurations of the ring.