Wrinkle Prediction of Membrane Structures under Uniform Normal Tensions

Abstract

Wrinkles always produce to counteract the compressive stress in the thin membrane structures, which has become a popular topic. In this paper, for the inhomogeneous membrane structure with depth-dependent Young’s modulus, a power-law index is introduced. The effect of inhomogeneity on the displacement and stress fields is analyzed. On this foundation, the membrane structures with uniform normal tension loadings are studied to be accorded with practical cases of engineering application. The stress fields are derived by the superposition of the concentrated tension solution based on the Airy stress superposition theory. Compressive stress generally leads to wrinkling, then the wrinkle regions under different tension conditions are predicted accurately. The proposed stress model is simple, and the computation complexity is reduced without using a finite element solution.