Study On Aerodynamic Stability Of Umbrella-shaped Membrane Structure Under Wind Load

Umbrella-shaped membrane structure is widely used,with the characteristics of light weight,small damping,small stiffness,beautiful shape,artistic durable and so on.The light and flexible characteristics of umbrella-shaped membrane structure are easily affected by external loads,especially the response of wind load to umbrella-shaped membrane structure is very obvious.At present,some experts and scholars have carried out field measurement,wind tunnel test,numerical simulation and other research,but the theoretical research on the aerodynamic stability of umbrella-shaped membrane structure is still relatively small.By analyzing the damage of umbrella-shaped membrane structure under wind load at home and abroad,it can be seen that the design of umbrella-shaped membrane structure based on the results of measurement,wind tunnel test and numerical simulation is not completely reliable,so it is urgent to carry out theoretical research on the aerodynamic stability of umbrella-shaped membrane structure under wind load.The purpose of this paper is to study the aerodynamic stability of umbrella-shaped membrane structure under horizontal,incompressible,inviscid and steady wind.The relationship between wind speed and structural stability is obtained by analytical method.Based on elastic mechanics and shell theory,the geometric equation,physical equation and equilibrium equation of umbrella-shaped membrane structure are constructed,and the displacement expression is obtained without considering geometric nonlinearity.Considering the interaction between the wind load and the umbrella-shaped membrane structure,the aerodynamic forces acting on the umbrella-shaped membrane structure are obtained according to the theory of symmetrical thin airfoil in hydrodynamics.Considering the geometric nonlinearity,the nonlinear governing equations about the stress function and structural displacement are established.Combined with the nonlinear governing equations,the aerodynamic coupling governing equations of the dynamic response between the umbrella-shaped membrane structure and the wind load are established.Bubnov Galerkin method is used to approximate the nonlinear equations of aerodynamic coupling,and Routh Hurwitz stability criterion is used to express the structural instability with critical wind speed.The analytical expression of critical wind speed of umbrella-shaped membrane structure under wind load is derived.The effects of pretension,span,ratio of height to span and elastic modulus on the aerodynamic stability of the umbrella-shaped membrane structure are analyzed.The critical wind speed increases with the increase of pretension,and the overall trend is approximately linear.Reasonable increase of pretension plays a positive role in improving the aerodynamic stability of the structure.The critical wind speed decreases with the increase of span,and the overall trend shows an approximately inverse proportional change.When the height span ratio is less than 0.3,the critical wind speed increases with the increase of height span ratio;when the height span ratio is greater than 0.3,the critical wind speed decreases with the increase of height span ratio.The critical wind speed increases with the increase of elastic modulus,and the overall trend is approximately linear.