Wrinkling analysis of circular membranes by a Fourier based reduced model

Abstract

As a material with an almost negligible bending stiffness, membranes may easily lose their mechanical stability. Generally, the wave lengths of the wrinkles are quite small, leading to the intensive computation in numerical simulations. To deal with the issue, a Fourier based reduced model is recently developed by Huang et al. (2019) showing good performance in both accuracy and efficiency for the simulation of circular membrane wrinkling. The objective of this paper is to improve the reduced model by accounting for several Fourier harmonics, then employ it to study the wrinkling phenomenon in the circular domain. By accounting for several Fourier harmonics, the reduced model can automatically distinguish the lowest instability pattern, which facilitates the study of the cases of unknown wrinkling patterns. The instability mechanism of an annular membrane under in-plane stretching is also investigated. The results show that the appearance of the wrinkles in circular membranes does not rely on the Poisson’s effect, although the value of Poisson’s ratio and the geometric dimensions have great influence on the wrinkling patterns. Finally, the instability problem of a circular thin plate under the in-plane compression is studied. The effects of the boundary condition and the wrinkling pattern on the crest position and the critical load are investigated.