Wrinkle-free membranes with optimized holes

Membranes are easy to buckle and wrinkle due to their extreme flexibilities, leading to the performance degradation and hampering the engineering applications. Here we propose a wrinkle-free approach through optimizing the shape and distribution of interior irregular holes in the membrane. A theoretical model with Marguerre function and complex analysis is performed to accurately estimate the stress distribution and wrinkling capability of the non-uniform membrane. The non-gradient particle swarm optimization (PSO) algorithm is implemented to determine the optimized holes to achieve wrinkle-free performance with ignorable area loss, the computational efficiency has been significantly enhanced through the superposition method. Both post-buckling analyses and physical experiments are carried out to verify wrinkle-free performance of membranes with optimized holes. In addition, an easy-to-implement empirical method is provided to guide the design of wrinkle-free membranes with arbitrary aspect ratio.