Stochastic Seismic Response And Reliability Analysis Of Single-layer Spherical Reticulated Shell

The single-layer spherical reticulated shell is widely used in many practical projects due to its beautiful shape and good performance.However,with the continuous improvement of people's demand and construction technology,the span of reticulated shell is increasing and the mechanical properties become more complicated.In addition,China is a country with frequent earthquake disasters,thus leading to much attention attracted on the seismic performance of large-span reticulated shell.On the one hand,the current research on seismic performance of reticulated shells mainly focuses on revealing its failure mechanisms under strong earthquakes,and a complete theoretical framework from two perspectives of dynamic instability and strength failure has been set up.How to make use of these achievements has become one of the tasks in the future.On the other hand,the seismic excitations have remarkable randomness and non-stationarity.Especially when the randomness and non-stationarity are coupled with the nonlinearity of reticulated shells,the response behavior of the shells will be more difficult to characterize.In other words,the traditional deterministic dynamic response analysis cannot give a reasonable judgment on the safety of reticulated shell,that we must consider the non-stationarity and randomness of seismic excitations both,so as to make the results more objective and credible.This thesis intends to investigate the seismic performance of single-layer spherical reticulated shell from the perspective of randomness.The spectral representation-random function model is employed to generate a controllable number of stochastic ground motions.In conjunction with the probability density evolution method(PDEM),one can carry out stochastic seismic response and reliability analysis of reticulated shells.The main research works are as follows:(1)The spectral representation-random function model is applied to generate a class of stochastic ground motions with assigned probabilities and quantities.First,the basic principle of evolutionary power spectrum theory is briefly described,and two kinds of spectral representation methods for non-stationary stochastic processes are derived.Then,based on the classical spectral representation theory,the idea of random function is introduced to reduce the degree of randomness for stochastic processes to 1 or 2.Further,the basic point set describing the randomness of ground motions is determined,and the probability space of which is subdivided based on Voronoi domain to obtain the assigned probability of each point.Finally,the mean value of seismic response spectrum is fitted by iteration.The results show that,the first and second order statistical values obtained by the method in this thesis fit better with the target values compared with the classical spectral representation method;(2)A stochastic seismic response and reliability analysis scheme for single-layer spherical reticulated shell is proposed.The principle of preservation of probability is briefly described.Based on this,the generalized probability density evolution equation(GPDEE)is derived and specific numerical solution steps are given.Taking the K8 reticulated shell with a span of 60 m as an example,the instantaneous probability density evolution process of the maximum displacement of the shell is investigated from the perspective of PDEM.The mean and standard deviation accords well with the results by 10000 Monte Carlo simulations.A method for calculating the global dynamic reliability of reticulated shell based on the equivalent extreme event and PDEM is presented.Further,two indices,selected from macro and micro levels,are introduced to evaluate the dynamic reliability of K8 reticulated shell.The results show that the extreme value distribution obtained by stochastic ground motions can cover the results obtained from natural ground motions in its distribution range;(3)On the basis of reliability analysis,a systematic seismic performance research framework for single-layer spherical reticulated shell is established.From two perspectives of ground motions and structural models,the parametric analysis scheme based on reliability of K8 reticulated shell is set up.The dynamic characteristic analysis is carried out,so as to study spectral characteristics of the reticulated shells under different parameters.Taking the maximum nodal displacement and 1P plastic rod ratio as the indices,the systematic parameter analysis is carried out for K8 reticulated shell considering different site types,span ratios,roof loads and initial defects.Referring to above ideas,the reliability-based seismic fragility analysis for K8 reticulated shells is established with the comprehensive response,i.e.damage factor,as the index,which provides theoretical support for performance-based multi-levels seismic design.