Solution Of Static Response Of Structures With Random Parameters Based On Homotopy Stochastic Residual Error Method

Throughout the process of constructing,use and operation and maintenance of engineering structures,there are various uncertainties in their construction materials,boundary conditions and loads applied,etc.For reliability analysis and safety evaluation of structures,random parameters can be used to represent these uncertainties and determine the random response of structures and their statistical properties.This thesis presents a proposed approach for solving the stochastic static response of large civil engineering structures,called homotopy stochastic residual error method(HSREM),considering the variety and large variability of the probability distribution of building material parameters and static loads.By defining and minimizing the residual error of the stochastic static equilibrium equation,HSREM calculates the values of the coefficients of each order in the homotopy series,and then obtains the explicit function of the structural response(including displacement,stress and internal force)with respect to the stochastic parameters.Compared with the regressive stochastic finite element method and the spectral stochastic finite element method,HSREM is more flexible in dealing with random variables with arbitrary distribution,and it can also obtain the first fourth order statistical moments of the random response with high accuracy when the variability of the random variables is large.After establishing the explicit connection of the random response with regard to the structural parameters,this explicit expression may be simply used to the global sensitivity analysis of the structure.This thesis proposes a novel approach to rapidly solve the random response and global sensitivity analysis of complex civil engineering structures.In this thesis,the main research and findings are as follows:1.The status and outcomes of the study on random field discretization at home and abroad are summarized.In view of the diversity of probability distributions of random parameters in complex engineering systems,the particular approaches to implement arbitrary distribution random field discretization via Karhunen-Loève(K-L)series expansion and Polynomial Chaos(PC)expansion are highlighted.2.The perturbation stochastic finite element method and the spectral stochastic finite element method,which are widely used at present,as well as the homotopy stochastic finite element method,are analyzed in detail.The characteristics and limitations of these methods for solving the stochastic static response control equations are also summarized.3.A novel intrusive stochastic finite element approach for addressing the static response of stochastic parametric structures,called homotopy stochastic residual error method,is presented by merging the principles of stochastic residual error minimization.The approach is paired with the finite element method to describe the nodal displacement vector of the structure in the form of a homogeneous series.Then,by defining the residual error of the static control equation on the random parametric probability space and minimizing this residual error to determine the value of the convergence function in the homotopy series expression of the random response.The approach overcomes the problem that the calculation accuracy of the current homotopy stochastic finite element method is readily impacted by the selected sample points,and accomplishes the automated discovery of the optimal value of the whole domain of the convergence function.4.By appropriating stochastic function and solving stochastic static response of complex engineering structures(three-dimensional perforated thin plate and large cablestayed bridge),the calculation accuracy and solution efficiency of this method are compared in detail with those of Monte Carlo simulation method,perturbation stochastic finite element method,and spectral stochastic finite element method.The advantage of this method is verified when the probability distributions of structural parameters and loads are of arbitrary type and have large variability.5.The maximum lateral displacement of the 11-story frame-tube structure is subjected to global sensitivity analysis,and the calculation case takes into account the randomness of a total of 11 parameters,including the elastic modulus of the frame beam,floor slab,frame column,and tube,as well as the structural self-weight,floor live load,and wind load.The advantages of the computing efficiency of the approach in This thesis over the Monte Carlo simulation method are obvious.The contribution of the random characteristics of each member and load to the uncertainty of the maximum lateral displacement can be measured more precisely using the two-dimensional homotopy stochastic residual error method with second-order expansion.