An analytical approach based on the bifurcation theory is presented,in which the wrinkles are treated as the local buckling phenomena of the elastic thin plate with little bending stiffness.The average wrinkling wavelength was determined by incorporating the stress field and the out-of-plane force equilibrium condition of the wrinkled membrane.The wrinkling amplitude was then obtained by associating the characteristics of wrinkling texture with the obtained wrinkling wavelength.Results reveal that the wrinkled pattern exhibits a noticeable difference when the tension load is changed gradually,and two wrinkling styles are identified.The first style occurs for symmetric and moderately asymmetric loading,and it is characterized by small,radial corner wrinkles;the second style occurs for strongly asymmetric loading and is characterized by a deep,large diagonal wrinkle.The analytical predictions on the wrinkling characteristics and the developed rules are validated against wrinkling experimental observations.
The axisymmetric deformation of a paraboloidal membrane inflatable structure subjected to a concentrated load at its apex and a uniform internal pressure was analyzed. The wrinkle angle was obtained according to the membrane theory when wrinkles appeared and determined the wrinkle region. The wrinkled deformation was obtained based on the relaxed energy function. The effects of inflation pressure and concentrated loads on the wrinkle angle were analyzed and the deformation was obtained at the apex of structure. According to the numerical analysis, the shape of deformed meridians with wrinkles was obtained.
