Global shape optimization of fixtures to suppress wrinkles in large-displacement membrane structures

Membrane fixtures provide external tensile forces and boundary conditions for thin membranes; thus, they play an important role in the minor principal stress distribution and wrinkling patterns. Here, we propose a global optimization approach for designing the shape of membrane fixtures to suppress stress-related wrinkles under large membrane deformations. The objective of the optimization model is to maximize the minimal value of the in-plane minor principal stress over the entire membrane. This model incorporates the Kriging surrogate method, which is a robust optimization technique, to make the membrane in a taut state and to find out the global optimal solution. Several examples with different stretching displacements are presented to demonstrate the effectiveness of this proposed optimization method. Moreover, the method provides an efficient way to obtain wrinkle-free membrane structures without reducing the membrane area.