Experiment And Simulation Researches On Form-Inflating Of ETFE Cushions Based On Material Nonlinearity And Flat Patterning

The first ETFE(Ethylene-Tetra-Fluoro-Ethylene)cushion structure was built in the Netherlands in 1982.After the ETFE cushion structure was introduced into China in 2008,it has become the highlight point and industrialization growth point in development of the novel membrane structure in the world.According to the model used for the cutting analysis,the forming design method of ETFE cushion can be divided into two kinds,including three-dimensional patterning method and flat patterning method.The three-dimensional patterning method,based on the form finding analysis,is the typical design method of membrane structure.The forming design method through flat patterning,making full use of nonlinear characteristics of ETFE foils,is a new design method and still is the key research problems in the fields of academic and engineering in the world.Therefore,this paper performed the systematic researches on the mechanical test and constitutive model of ETFE foils,as well as the forming test and numerical simulation of ETFE cushions.The main work and corresponding conclusions are thus as follows:Firstly,the uniaxial tensile test of ETFE foils under a wide range of strain rates(0.1~1000 %/min)was carried out to obtain the stress-strain curves.After proposing the energy method to determine the equivalent elasticity modulus of strain energy,the mechanical properties of ETFE foils related to the strain rate has been well revealed.On the basis of the generalized Maxwell model from the viscoelastic-plastic theory of polymer materials,the stress-strain constitutive model of ETFE foils under uniaxial tension was deduced.The presented constitutive model was used to fit the stress-strain curves of ETFE foils under different tensile strain rates in order to obtain the model parameters.By establishing the functional relationships between the model parameters and strain rates,the rate-dependent continuous constitutive model considering the strain rate as the variable was well presented.The three-element model and five-element model of the generalized Maxwell model can be utilized to effectively simulate the uniaxial tensile mechanical properties of ETFE foils before the second yield point and the strain of 30%,respectively.The uniaxial tensile test of ETFE foils,experiencing the loading,creep,unloading and creep-recovery four stages,was performed by using the testing machine following the automatic controlling flows.Test conditions included that the stress condition was divided into 10 groups(2,4,6,8,10,12,14,16,18,20 MPa)and the loading time condition was divided into 8 groups(0.5,1,2,3,6,12,18,24 h).The different strain-time curves under different conditions could be acquired from the uniaxial tensile test.The maximum strains and residual strains under different creep stresses and times were analyzed to reveal the nonlinear and time-dependent characteristics of ETFE foils.Based on the generalized Kelvin-Voigt model from the viscoelastic-plastic theory of polymer materials,the basic time-dependent equation of ETFE foils under the uniaxial tensile loading-unloading process was established after defining the recoverable viscoelastic strain and residual viscoplastic strain in the creep process.According to the experimental result,after determining the time-dependent equation form and the relevant model parameters of the residual viscoplastic strain,the model parameters of the viscoelastic strain under the creep time of 24 h could be further identified.Then,the time-dependent continuous model with the variable of creep time was proposed by introducing the ratio of the viscoelastic strain values between the arbitrary creep time and the creep time of 24 h.Finally,through establishing the functional relationships between the model parameters and creep stresses,the stress-time-dependent continuous model was presented for the mechanical properties of ETFE foils under uniaxial loading-unloading tension.The long-term uniaxial tensile creep test of ETFE foils under the time of 30 days and different creep stresses(2,4,6,8,10,12,14,16,18,20MPa)was carried out by using the self-developed loading and measuring devices.The creep curves under different creep stresses were obtained from the test to reveal the creep characteristics of ETFE foils.Based on the modified generalized Kelvin-Voigt model,the long-term creep model was deduced.According to the experimental results,the parameters of the time-dependent model were identified,and the stress-dependent continuous creep model with the variable of creep stress was further well established according to the functional relationships between the model parameters and creep stresses.Then,in order to study the ETFE cushion,the high accurate control method of internal pressure with high pressure and small disturbance and the three-dimensional shape measurement method with non-contact and real-time dynamic were proposed,with developing the pressure control system and three-dimensional photogrammetry system.The analysis methods for measurement of stress and strain combining the non-contact photogrammetry and analysis were presented.The stress analysis method was found based on the equilibrium of inflated pressure and film internal force.The strain analysis method was presented based on the changes of three-dimensional coordinates of measured points before and after the deformation.An ETFE cushion model was developed and performed with inflated forming test to validate the proposed methods.Finally,the inflated forming test was performed on two triangular ETFE cushion models based on the flat patterning method,experiencing the inflating,creep,deflating and creep-recovery four stages.By using the proposed measurement and analysis method,the internal pressure,membrane shape,stress and strain of the cushion models were obtained and analyzed.The comparison of ETFE cushion models experiencing different creep stresses and creep times was performed to reveal the time-dependent characteristics of ETFE cushion related to the creep time.The material nonlinearities of the rate-dependent continuous constitutive model with the variable of the strain rate and the stress-time-dependent continuous model with the variable of the creep stress was considered in compiling the UMAT user material subroutine for the numerical simulation on the total forming process of ETFE cushion.The comparison of the rises,shapes,stress and strain distributions on the membrane surfaces between the simulations and experimental results was performed to verify the applicability and accuracy of the numerical simulation method.