Abstract
As a soft material with an almost negligible bending stiffness, a membrane may easily lose its mechanical stability. To capture its entire instability process, intensive computation is required, especially in the case of short wave length. The objective of this paper is to construct an efficient model to simulate and study the instability phenomena of circular membranes. By using the method of Fourier series with slowly variable coefficients in the circumferential direction, a new family of one-dimensional reduced finite elements are developed to study the three-dimensional problems. The nonlinear system is solved by the Asymptotic Numerical Method(ANM), which is reliable and efficient for tracing the bifurcation points and post-buckling equilibrium path compared with other classical non-linear solution algorithms. The accuracy and efficiency of the reduced model is verified by simulating the instability phenomena in stretched annular membranes and a compressed circular plate. The relation between critical loads and bifurcation patterns and the evolution of stress components in the entire wrinkling process are discussed. This study provides new simulation schemes to explore the instability in circular membranes under complex loadings and boundary conditions.
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