The Spline Fictitious Boundary Element Method For Vibration And Buckling Analysis Of Thin Plate Problem

A large number of non-determinate factors are presented in the practical engineering. Due to the disturbance of the factors, the material parameters and the geometric parameters of a thin plate often present randomness. The conventional structure analytic methods are based on determinate thin plate models, in while the effect of the randomness can’t be taken into consideration. In fact, the effect of the randomness is not negligible. Therefore, it is more reasonable to employ stochastic structural systems to reflect the behavior of a thin plate, which is important in the structural analysis and condition assessment.As a semi-analytical and semi-numerical method, the stochastic spline fictitious boundary element method(SFBEM) has its unique advantages in the random field. In this study, SFBEM is applied to the area of dynamic analysis and buckling analysis of stochastic thin plate problems. This will further extend the application area of SFBEM, and more importantly, it will provide a new way to solve the random vibration and stability problems of stochastic structures at high accuracy and efficiency. The work in this dissertation is described as follows:(1) The basic concepts of stochastic structural systems are briefly introduced, and the development of the stochastic dynamic analysis, stochastic buckling analysis are summarized; The development of SFBEM is also summarized.(2) The commonly used statistic values and discretization methods for random fields are introduced. The basic theories of the static problem of a thin plate are summarized.(3) The SFBEM for dynamic model analysis of stochastic thin plate bending problems is proposed. Under the assumption of small variation of the material and geometric parameters, two sets of governing differential equations with respect to the mean and deviation of deflection are derived by including the first order terms of deviations. These equations are in similar forms to those of deterministic thin plate bending problems, and can be solved using deterministic fundamental solutions. The proposed method is validated by comparing the solutions obtained with other methods, and a good agreement of results is observed. The effects of variant factors on the stochastic dynamic characteristics are also investigated through numerical examples.(4) The SFBEM for dynamic response analysis of stochastic thin plate bending problems is proposed. Under the assumption of small variation of the material and geometric parameters, two sets of governing differential equations with respect to the mean and deviation of deflection are derived by including the first order terms of deviations. These equations are in similar forms to those of deterministic thin plate bending problems, and can be solved using deterministic fundamental solutions. The proposed method is validated by comparing the solutions obtained with other methods and a good agreement of results is observed. The effects of variant factors on the stochastic dynamic response are also investigated through numerical example.(5) The SFBEM for buckling analysis of stochastic thin plate problems is proposed. Under the assumption of small variation of the material and geometric parameters, two sets of governing differential equations with respect to the mean and deviation of deflection are derived by including the first order terms of deviations. These equations are in similar forms to those of deterministic thin plate bending problems, and can be solved using deterministic fundamental solutions. The proposed method is validated by comparing the solutions obtained with other methods and a good agreement of results is observed. The effects of variant factors on the stochastic critical buckling load are also investigated through numerical examples.The main innovative work in this dissertation is that SFBEM for random vibration and stability analysis of stochastic thin plate problems is systematically proposed. The corresponding calculation programs are also coded. Numerical examples show the proposed method is of high accuracy and efficiency. SFBEM presented in this study is so far a competitive method for random vibration problems of stochastic structures.