Research On The Random Stability Of Single-layer Reticulated Shells Considering The Random Field Of Initial Geometric Defects

Since the 21st century,the single-layer spherical reticulated shell structure has been extensively built in practical engineering due to its characteristics such as reasonable stress,large span,and light weight.However,the single-layer spherical reticulated shell is a defect-sensitive structure,of which the bearing capacity can be greatly impacted by the initial geometric imperfections caused by the deviation of nodes.Because of the randomness existed in initial geometric imperfections,analyzing the stability of the defective initial geometric imperfections reticulated shell structure has important theoretical significance and application value.By comparing the classic consistent mode imperfection method,stochastic imperfection modal method and stochastic imperfection mode superposition method,this thesis summarizes the disadvantages of these imperfection simulation methods.To avoid these disadvantages,an improved random field imperfection simulation method is proposed.This method uses field measured data of the newly-built real reticulated shell structure as reference,so as to generate the correlated random initial geometric imperfection distribution.In this regard,the randomness of imperfection distribution and the correlation between node imperfections are both considered in this method.In addition,this method can provide the reliability guarantee for the obtained bearing capacity.The stability bearing capacity calculation of the single-layer spherical reticulated shell structure considering stochastic imperfection is a high-dimensional problem,which requires huge computational costs.To solve this problem,this thesis employs a fractional moments-based maximum entropy method to construct the probability density function of the stability bearing capacity,which significantly reduces the number of calculations for structural stable bearing capacity under a specified reliability index and maintains high calculation accuracy.In this regard,it is possible to analysis the stability of the single-layer latticed dome with initial imperfections in engineering application.The steps to implement the reliability-based proposed method are as follows: First,by using the Latinized partial stratified sampling method to simulate the random field of initial geometric imperfections,the relevant representative points of initial geometric imperfections are generated;then,implement the deterministic calculations of stability analyses of the single-layer spherical reticulated shell to obtain the fractional moments of stability bearing capacity.Finally,the fractional moment constrained maximum entropy method is utilized to reconstruct the entire distribution of stable bearing capacity of the single-layer spherical reticulated shell,so as to obtain the structural stable bearing capacity under a specified reliability index.By comparing the stability bearing capacity of the same single-layer spherical reticulated shell calculated by the consistent mode imperfection method,stochastic imperfection modal method,stochastic imperfection mode superposition method and the proposed method,this thesis summarizes the variation rules of stability bearing capacity under different methods and validates the rationality of the proposed method.Besides,this thesis suggests a superposition degree for balancing the efficiency and accuracy by using the proposed method.In order to further study the influence of various factors on the stability of single-layer spherical reticulated shell under stochastic imperfections,this thesis also studies and parametrically analyzes the effects of the imperfection amplitude,the rise-span ratio,the load distribution form and other factors.In addition,by comparing with the results of the consistent mode imperfection method,the correctness of the proposed method is testified.Some conclusions with reference value are summarized:The imperfection size is the major factor of impacting the bearing stable capacity of reticulated shell;the imperfection amplitude is suggested to choose;the bearing stable capacity is positively associated with rise-span ratio,and is negatively associated with the proportion of live load.