Numerical Analysis of Wind-Induced Response of a Wrinkled Membrane

Membranes have been popularly used in the fields of civil engineering and aerospace engineering. When wrinkled, a membrane loses its stiffness in the direction perpendicular to wrinkles and is more sensitive to wind loads. This paper numerically studied the wind-induced responses of a wrinkled membrane and their variations with respect to wind speed, wind direction and wrinkling deformation. Based on the stability theory of plates and shells, the wrinkling deformation of a rectangular membrane under shear was obtained by post-buckling analysis. Then, by using the wind load derived from a wind tunnel test, the dynamic responses of the wrinkled membrane were numerically analyzed for different wind speeds, wind directions and wrinkling deformations. The results indicate the following: (1) the displacement and extreme stresses of a membrane are gradually intensified with an increase in the wind speed; (2) the wind direction plays an important role in the displacement, but it has little effect on the stresses and (3) the displacement increases with the wrinkling deformation, and the extreme stresses are intensified with an increase in the pre-tension. This study on the wind-induced responses of a wrinkled membrane is helpful to the understanding of the complex behavior of a wrinkled membrane under wind loads while reducing the adverse effects of wrinkling deformation and ensuring the dynamic stability of membrane structures.

Numerical analysis of dynamic properties of wrinkled thin membranes

Purpose This paper aims to numerically study the effects of boundary conditions, pre-stress, material constants and thickness on the dynamic performance of a wrinkled thin membrane. Design/methodology/approach Based on the stability theory of plates and shells, the dynamic equations of a wrinkled thin membrane were developed, and they were solved with the Lanczos method Findings The effects of wrinkle-influencing factors on the dynamic performance of a wrinkled membrane are determined by the wrinkling stage. The effects are prominent when wrinkling deformation is evolving, but they are very small and can hardly be observed when wrinkling deformation is stable. Mode shapes of a wrinkled membrane are sensitive to boundary conditions, pre-stress and Poisson’s ratio, but its natural frequencies are sensitive to all these five factors. Practical implications The research work in this paper is expected to help understand the dynamic behavior of a wrinkled membrane and present access to ensuring its dynamic stability by controlling the wrinkle-influencing factors. Originality/value Very few documents investigated the dynamic properties of wrinkled membranes. No attention has yet been paid by the present literature to the global dynamic performance of a wrinkled membrane under the influences of the factors that play a pivotal role in the wrinkling deformation. In view of this, this paper numerically studied the global modes and corresponding frequencies of a wrinkled membrane and their variation with the wrinkle-influencing factors. The results indicate that the global dynamic properties of a wrinkled membrane are sensitive to these factors at the stage of wrinkling evolution.

Approximated Solutions for Axisymmetric Wrinkled Inflated Membranes

The axisymmetric inflation problem for a wrinkled membrane is solved by means of a simple nonlinear ordinary differential equation. The solution is illustrated in full details. Both the free and constrained cases are addressed, in the limit case where the membrane is fully wrinkled. In the constrained inflation problem, no slippage is allowed between the membrane and the constraining surfaces. It is shown that an actual membrane can in no way reach the fully wrinkled configuration during free inflation, regardless of the membrane's initial configuration and constituent material. The fully wrinkled solution is compared to some finite element results obtained by means of an expressly developed iterative–incremental procedure. When the values of the inflating pressure and length of the meridian lie within a suitable applicability range, the fully wrinkled solution may represent a reasonable approximation of the actual solution. A comparison with some numerical and experimental results available in the literature is illustrated.