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

The structural problems with random parameters appear frequently in engineering practices due to the stochastic nature of the loadings as well as the material properties and geometric parameters. It is obvious that a deterministic analysis can not capture the random nature of the structural response, since only expectation values rather than statistical information of the parameters are used in the computational model. More and more numerical mathod have been developed in this area. But the accuracy and efficiency of thes mathod are not both in good performance. In this study, the spline fictitious boundary element method (SFBEM), a modified indirect boundary element method (BEM), in conjunction with random field theory and reliability assessment mathod, are applied to the area of stochastic analysis and reliability assessment of the plate bending problems. The work in this dissertation is described as follows:(1) Some kinds of basic theories of the plate bending problems are briefly introduced. The main BEMs using in fields of the plate bending problems are also introduced in this paper. The main BEMs for stochastic analysis and reliability assessment are then introduced systematically, and their advantages and disadvantages are also pointed out.(2) Deterministic SFBEM for Reissner plate bending problems is introduced, which formulation is also presented detailedly in this paper. The numerical stability, error estimates and domain-division techniques are discussed. The high accuracy of the method in the area of deterministic analysis for Reissner plate bending problems is also validated by numerical examples.(3) The stochastic SFBEM is proposed for stochastic analysis of Kirchhoff plate bending problems. The input parameters are modeled as random fields, and the stochastic governing differential equation is divided into two sets of equations about the mean and deviation of structural responses. These equations are then solved by SFBEM using deterministic fundamental solutions, since they are in similar forms to those of deterministic problems. Numerical examples with single random field and multiple random fields are given to show the high accuracy and applicabity of the proposed method. The influence of the correlation function, the covariance length, the coefficient of variation, different random fields and the distance between the fictitious boundary and the real boundary is investigated on the results of stochastic analysis. The efficiency of the present method is also investigated by comparison with the traditional perturbation stochastic FEM.(4) The first-order-second-moment SFBEM of plate bending problems, which is in the frame of the advanced first-order-second-moment (AFOSM) method in conjunction with SFBEM, is proposed for reliability analysis of plate bending problems. Two cases are considered in this paper, which input parameters are modeled as random fields and random variables respectively. The accuracy and applicability of the present method are investigated by numerical examples with single domain and multiple domains. And the efficiency of the present method is also investigated by comparison with the stochastic FEM.(5) The Monte-Carlo simulation in conjunction with SFBEM, is proposed for reliability analysis of Reissner plate bending problems. In order to improve the efficiency of the method, the techniques of Taylor expansion and Neumann expansion are adopted to avoid generating influence matrices and calculating their inverses during the repeated sample analyses. In addition, an important sampling technique is also incorporated in the proposed method to reduce the sampling number. The accuracy and efficiency of the present approach are validated by numerical examples.SFBEM is a semi-analytical and semi-numerical method with high accuracy and efficiency. The study in this paper shows that the stochastic and reliability analysis methods in the frame of SFBEM and in conjunction with random field theory and reliability assessment mathod, are also performed well both in accuracy and efficiency. The proposed method will further extend the application area of SFBEM, and it will also provide a new approach for stochastic and reliability analysis of plate bending problems at high accuracy and efficiency.