# Performance and Measurement Devices for Membrane Buildings in Civil Engineering: A Review
## 3 Performance
### Air-Supported Membrane Structure
#### 3.1.5 Wrinkle  
Membranes are prone to wrinkling when subjected to compressive or shear stresses due to their low bending stiffness. The local wrinkling occurs when the maximum compressive or shear stress exceeds the uniform critical value [88]. Wrinkles in membranes are a localized buckling phenomenon that decreases the performance and stability of the structure, so it is an important task to minimize or avoid wrinkles in membrane structures. The complex wrinkling effect plays a significant role in the deformation process, making it difficult to predict the buckling properties of the structure through theoretical methods. Therefore, experiments and numerical simulations are the main approaches to investigating membrane wrinkling, especially for inflatable structures [89].  
The local buckling of existing wrinkles, along with changes in local modes, is the causal factor leading to the creation of new wrinkles [90]. The initial imperfections in membrane thickness can significantly affect the distribution of wrinkles, and the shapes of the wrinkles are not unique when the membranes are repeatedly deformed under the same conditions [90; 91]. Moreover, the wrinkles' shapes influence the membrane's vibration modes, and the stresses in the wave peaks of the wrinkles are larger than those in other parts of the membrane [92]. The critical wrinkle strain of the membrane can be calculated from the out-of-plane displacement and the in-plane stress, where the mean principal stress of the membrane increases as the shear displacement increases [93].  
Inflatable beams and arches as load-bearing components gradually decrease in flexural load capacity with the occurrence and propagation of wrinkles [94]. The development of inflatable structural wrinkles with increasing load is shown in Figure 16. The critical wrinkle load is sensitive to the load location, internal pressure, and material properties, where the magnitude of the critical load increases when the load location moves away from the middle of the inflatable beam [89; 95; 96]. [PERSON] et al. [89] found that the bending wrinkle characteristics of the structure are poorly related to the boundary conditions and the shape of the structure based on the pseudo curved beam (PCB) model. However, [PERSON] et al. [88] reported a contradictory conclusion based on the Fourier model, finding that the boundary conditions strongly influence the wrinkling behavior of the structure.  
The minimization or avoidance of wrinkles is a precondition to ensure that the structure maintains its performance given the adverse effects of wrinkles on membrane struc  
Figure 16: Development of wrinkles [94].  
tures. [PERSON] and [PERSON] [97] installed shape memory alloy (SMA) wires on the stretching side of an inflatable beam corresponding to a wrinkled area, which effectively controlled the number of wrinkles. Similar results were obtained by [PERSON] et al. [98], where structures designed based on the mesh reinforced membrane (MRM) concept restricted the evolution of wrinkles. For tensioned structures, [PERSON] et al. [99] found that wrinkles are effectively reduced by trimming the edges of rectangular membranes into curved lines.