Study On The Stochastic Response And Reliability Of Construction Membrane Structure Induced By Dynamic Load

Along with the progress of science and technology,the membrane structure has been applied in different fields including civil engineering,mechanical engineering,biological engineering,astronaut and aerospace engineering.Since the membrane structure is both relatively lightweight and highly flexible,it has been applied in large-scale stadium and art museum.However,the dynamic loads such as downburst wind,heavy rainfall and hailstorm apply the structure repeatedly during its serving period.Consequently,the large deformation caused by serious vibration will exceed the structural ultimate deformation in probability,which will lead to the tearing of membrane and failure of structure.In present literature,the determined vibration problem of membrane structure has been studied mostly,neglecting the random characteristics of load and structure response.Thus,it is hard to predict the probability and reliability of membrane structure during the process of design and utilizations,which will bring out the risk during its longtime serving.Therefore,this dissertation aimed to study the stochastic vibration and reliability problem of membrane structure induced by dynamic load theoretically and experimentally as well as to provide some suggestion for the structural design based on reliability theory.The objectives of the paper are:(1)The theoretical model of stochastic vibration of membrane structure induced by dynamic load is proposed.Firstly,the differential equation of vibration of membrane structure is established by combining the principle of minimum potential energy with the Von Karman’s large deflection theory.The mode function satisfying the boundary condition of arbitrary shape can be pursued based on the Fourier expansion method.Then,the governing equation of vibration can be derived after simplifying the differential equation by the Galerkin method,and solved by the perturbation method and FPK method,respectively.Consequently,the analytical solution and statistical characters of dynamic response of membrane structures can be obtained.(2)The stochastic vibration problem of orthotropic rectangular and circular membrane structure is studied by applying the stochastic vibration model proposed above.Firstly,the governing equations of forced vibration of rectangular and circular membrane structure induced by dynamic load are established.Then,the governing equations can be solved by the perturbation method and FPK method,respectively.The corresponding approximate analytical solution of maximal displacement can be identified during the forced vibration,and their statistical results can be obtained further.In addition,the governing equations of free vibration of membrane structure are solved by multi-scale method.Consequently,the analytical solution of frequency and maximal amplitude can be obtained.It is shown that the nonlinearity is becoming larger with random load increasing,along with the phenomena that the distribution type of response turns from Gaussian distribution to Non-Gaussian distribution,which indicates that membrane structure is becoming the nonlinear system from linear one.(3)Based on the theoretical model of stochastic vibration of membrane structure proposed above,the reliability problem can be studied further.By introducing the lever-crossing process theory,the reliability function can be established based on the analytical solution of displacement response of rectangular and circular membrane structures.Then,the failure probability and reliability index of rectangular and circular membrane structure can be obtained by means of advanced first order and second moment method.The parameters discussions show that the key parameters affecting membrane structural reliability are load and pretension force,and the effect of orthotropic characters of material is limited.(4)The stochastic vibration and reliability problems of rectangular and circular membrane structures are studied experimentally.First,the statistical results of experimental data are analyzed by the Monte Carlo method.Then,the theoretical model can be validated by comparing the analytical solution with experimental results.Finally,the rule of stochastic vibration and reliability can be obtained,and their relationship with different parameters including pretension force,dynamic load and material characters can be revealed further.Both the theoretical algorithm and the experimental studies are expected to be proposed and summarized.