Improved Procedures for Static and Dynamic Analyses of Wrinkled Membranes

Abstract

An analysis of large deformations of flexible membrane structures within the tension field theory is considered. A modification of the finite element procedure by Roddeman et al. (, , , , 1987, ASME J. Appl. Mech.54, pp. 884–892) is proposed to study the wrinkling behavior of a membrane element. The state of stress in the element is determined through a modified deformation gradient corresponding to a fictive nonwrinkled surface. The new model uses a continuously modified deformation gradient to capture the location orientation of wrinkles more precisely. It is argued that the fictive nonwrinkled surface may be looked upon as an everywhere-taut surface in the limit as the minor (tensile) principal stresses over the wrinkled portions go to zero. Accordingly, the modified deformation gradient is thought of as the limit of a sequence of everywhere-differentiable tensors. Under dynamic excitations, the governing equations are weakly projected to arrive at a system of nonlinear ordinary differential equations that is solved using different integration schemes. It is concluded that implicit integrators work much better than explicit ones in the present context.