Wrinkling And Wrinkling-suppression Design Optimization Of Stretched Membrane

For two-dimension thin membrane materials like polyimide membranes in aerospace and graphene membranes in nanoelectronics,the high surface accuracy requirement is the key issue for application.The ignorable bending stiffness makes the two-dimensional membrane structure tend to have the out-of-plane buckling and wrinkling.This affects the surface smoothness,electrical and mechanical properties and restricts the wide application of the membrane structure.Therefore,it is necessary to explore the wrinkling and the wrinkling-suppression mechanism.The related work in this thesis are as follows:1.The topology optimization was performed for the rectangular membrane under tension.The optimization objective is to maximize the structural stiffness,the design domain is the whole membrane structure,the design variables are the element densities.We propose the optimized structure under the positive minimum principal stress constraint.Based on the topology optimization result,we give the pre-necking strategy by adopting the elliptical free edges to suppress the stretch-induced wrinkling,which will be helpful for the realization of digital CAD.At the same time,the configuration of pre-necking strategy can meet the requirement of thin film shape accuracy while keeping smaller area loss.Pre-necking strategy only modifies the shape of membrane structure,which is easy to implement,and it doesn't need any auxiliary structure or extra control,it has low cost and strong manipuility,which can satisfy the demand for thin film surface smoothness.2.Through a series of finite element analysis,this thesis discusses the wrinkling and wrinkling-suppression mechanisms of the stretch-induced wrinkling in membranes with frozen zone are qualitatively and quantitatively elucidated with finite element analyses.For graphene membranes with frozen zones,the Possion effect and the overall effect of clamped edges restraint on wrinkling amplitude yields an increasing-and-decreasing tendency of A_maxax with the increase of the tensile strain.The wrinkle of the interior region occurs at small deformation and the vanishing under large deformation.In this thesis,the optimal design solution for wrinkling-suppression and achieving wrinkle-free performances in rectangular membrane with frozen zone will be presented and the wrinkle-free rectangle membrane with frozen zone will be obtained.As for this solution,the voids around frozen zone and at clamped edges,isolating stress and hampering the influence of frozen zone and the impact of clamped edges,are responsible for preventing the frozen zone wrinkles and clamped edge wrinkles,respectively.3.We performed finite element analysis and physical experiment to quantitatively analyze the mechanism of four-corner tensioned membranes structures and explain it.Four-corner tensioned membrane structures is built and analyzed in the Python language.With the minimum of four-corner tensioned membrane structures developed within in-plane principal stress as the optimization goal and using B-Spline curve fitting of edges as the initial contour position,as well as the fitting point coordinates as the optimization variables,a constraint function is established on the relationship between the configuration area of optimal wrinkle-free four-corner membrane under tension and the configuration area of initial four-corner membrane under tension.A shape optimization methodology with Genetic algorithm is performed to seek the optimal wrinkle-free design of four-corner tensioned membranes structures with symmetric loading.The wrinkling-suppression capability of optimal design is verified by finite element analyses and physical experiments,and we achieve wrinkle-free performances in four-corner tensioned membranes structures.The shape optimization methodology with Genetic algorithm will be helpful for the realization of digital CAD and be beneficial to the application of practical engineering.