Behavior of doubly curved partly wrinkled membrane structures formed from an initially flat membrane

Abstract

A theory is presented for the elastic analysis of deep doubly curved, axisymmetric, partly wrinkled membranes which are formed from an initially flat sheet. The doubly curved membrane surface is analyzed separately in the wrinkled and unwrinkled regions and then properly matched together. The wrinkled region is considered as a zero hoop stress linear membrane, while in the unwrinkled region where stretching of the membrane surface is important, small strain nonlinear membrane theory is used. In addition, meridional and circumferential stiffening cords which are closely spaced so that their effects may be "smeared out" or averaged over the surface are included. In order to demonstrate the application of the proposed theory, three illustrative wrinkled membrane problems are solved. The first problem is an initially flat circular membrane which has been pleated around its outer circumference to form a deep doubly curved axisymmetric surface which is then attached to a rigid boundary and pressurized. The second problem solved is the stretching of an initially flat circular membrane over a doubly curved, axisymmetric mandrel and the last problem solved is the very large deformation behavior of a pressurized membrane cylinder subjected to a radial line load. In order to assess the validity of the theory presented, an experimental investigation of the first problem was conducted. In the experiments circular sheets of 1/2-mil Mylar were pleated around the circumference, attached to a rigid circular boundary, and then pressurized. Measurements were made for different levels of internal pressure of the depth and extent of the resulting unwrinkled region at the crown. The results were compared with theoretical predictions and the correlation between experiment and theory was very good until yielding of the Mylar occurred.