Analysis On Development Of Membrane Wrinkles And Dynamic Characteristics Based On Stability Theory

With a large number of membrane structures used in the fields of building structures and spacecrafts, negative effects of wrinkles have aroused wide concern. The existences of wrinkles not only affect the surface accuracy of a structure, but also change its stress distributions and vibration performance and further affect the aerodynamic characteristics under wind load. Therefore, it is required that further researches be performed on the formation characteristics and the transition of wrinkles. Practical membranes are more complex and diverse in geometry than planar ones, and planar tension membrane is just one of the simplest structures, analysis on a simple planar membrane will contribute a lot to the attention on the common problems abstracted from membrane structures by excluding secondary factors and reveal the variation of mechanical properties following transition of wrinkles. Therefore, in this paper a planar membrane is mainly concerned to study the wrinkles and their influences on structures.The content of this paper can be divided into two aspects of theory and numerical calculation:(1) One part is on the theoretical analysis. Based on the stability theory, a new method of calculating critical compressive stress was proposed, in which the effect of tension stress along the wrinkling direction is considered. Afterwards, the formulas of wavelength and amplitude were easily obtained. Comparisons with the experiment results and the numerical results in the literatures show that the formulas given in this paper are valid, and have good accuracy.(2) The other part is on the numerical analyses as the following:a. A new method which divided the transition of the membrane wrinkles into three states was proposed. Generation and development of wrinkles were studied. The results show that:wrinkles appear first in the positions where compressive stress occurs earliest, and then expand to the middle part gradually until they are stable. The whole wrinkling process can be characterized by three typical stages:The Initial-Stage, The Expansion-Stage and The Stable-Stage. And the characteristics of each stage were studied. Through this part of study, the mechanism of wrinkles can be cognized. And the influence laws of mechanical properties affected by wrinkles can be mastered. And also, through this division, the degree of transition can be effectively measured; the wrinkles characters in a particular state can easily be studied and described.b. Proposes and confirms a critical value to control wrinkles, in order to provide the quantitative basis to prevent the structural failure caused by the deformation and the wrinkles increases. The simulation researches on the shear rectangular tensile membrane show that:Wrinkles should be restricted to such an extent that the ratio between the out-plane displacement and the membrane thickness is less than1%. Otherwise, the out-plane deformation would increase rapidly, and cause the structure’s failure.c. The influence of thickness, initial prestress and initial imperfections on the wrinkles are studied. The results show that:with the increase of thickness, wrinkles decrease in number, but increase in wavelength and amplitude. However, the ratio of out-plane displacement to thickness decreases. Therefore, the smaller the thickness is, the larger the wrinkling impact is. Increase of the prestress can enhance the structure’s out-plane stability and delay the appearance of wrinkles, but decrease the safety margin of structures. Therefore, the tension prestress should also be confined to a reasonable range. The initial imperfections mainly affect the location of wrinkles, especially the location where wrinkles appears first. But their influence on the wrinkling number, wavelength and amplitude is not obvious.d. Dynamic characteristics of the structure at the different wrinkling stages are studied. The results show that:The frequency variation with shear displacement angle can also be characterized by three stages:The Initial-Stage in which the frequency is declining, The Expansion-Stage in which the frequency is raising fluctuates, and The Stable-Stage in which the frequency is declining again. In The Stable-Stage, because of the second-buckling of the membrane structure, the frequency appears to fluctuate. The change of the mode shape is much more complex than that of frequency. The mode shapes tend to increase along the wrinkles.