Research On Stochastic And Reliability Analysis Of Elasticity Problems By Spline Fictitious Boundary Element Method

Stochastic analysis and reliability assessment of structures with uncertain parametershave drawn much attention in recent years. Numerical computation schemes in the frame offinite element method (FEM) have been developed in this area. The accuracy and efficiencyof such schemes are inevitably affected by the inherent defects of FEM. In this study, thespline fictitious boundary element method (SFBEM), a modified indirect boundary elementmethod (BEM), is applied to the area of stochastic analysis and reliability assessment of theelasticity problems with structural uncertainties. The work in this dissertation is described asfollows:(1) The basic concepts and main methods of stochastic analysis and reliabilityassessment are briefly introduced, and the development and application of BEM and SFBEMare summarized. The main BEMs for stochastic analysis and reliability assessment are thenintroduced systematically, and their advantages and disadvantages are also pointed out.(2) The formulation of deterministic SFBEM for elasticity problems is presented, and thenumerical stability, error estimates and domain-division techniques for concave andcomplex-connected domains are discussed. The effectiveness of the method in the area ofdeterministic analysis is also validated by numerical examples.(3) The stochastic SFBEM is proposed for stochastic analysis of elasticity problems withthe input parameters modeled as random fields under the assumption of small variation of theparameters. Two sets of governing differential equations described with the means anddeviations of structural responses are first derived by including the first-order terms ofdeviations. These equations are then solved by SFBEM using deterministic fundamentalsolutions, since they are in similar forms to those of deterministic problems. Numericalexamples are given to show the accuracy and efficiency of the proposed method, and theeffects on the analytic results of various factors, including the correlation types, correlationlengths, and the coefficients of variation, are investigated and certain conclusions are obtainedregarding the influence of the above factors.(4) The first-order-second-moment SFBEM, which is in the frame of the advancedfirst-order-second-moment (AFOSM) method in conjunction with SFBEM, is proposed forreliability analysis of elasticity problems. Two cases are considered. For the first one, theinput parameters are modeled as random fields, and the relationship between structuralresponses and the random vectors from random field discretization derived in stochasticSFBEM is utilized for reliability analysis with AFOSM method. For the second case, the input parameters are modeled as random variables, and the gradient of the performancefunction required in AFSOM method is obtained directly in the frame of SFBEM formulation.The accuracy, efficiency and applicability of the present method are investigated by numericalexamples.(5) The direct Monte-Carlo SFBEM is proposed for reliability analysis of elasticityproblems, in which SFBEM is used as a tool for each sample experiment in Monte-Carlosimulation (MCS). In order to improve the efficiency of the method, the techniques of Taylorexpansion and Neumann expansion are adopted to avoid generating influence matrices andcalculating their inverses during the repeated sample analyses. In addition, an importantsampling technique is also incorporated in the proposed method to reduce the samplingnumber. The accuracy and efficiency of the present approach are validated by numericalexamples.The work in this dissertation shows that a good precision and high efficiency can beobtained by SFBEM for stochastic analysis and reliability assessment. The proposed methodwill further extend the application area of SFBEM, and it will also provide a new approach tosolve the stochastic and reliability problems in elasticity analysis at high accuracy andefficiency.