Based On Full-Probability Research Of Stochastic Structural Analysis And Reliability

The research of random vibration analysis and accurate reliability for stochastic structures based on the full-probability is one of the most important subjects and it is of much realistic engineering background and important theoretic signification. The analysis and research aimed at this subject are done in this paper, and some new theory, new models and methods for static analysis, sensitivity analysis; dynamic characteristic analysis; dynamic response analysis and accurate reliability of random consecutive structures and random truss. The main research works can be described as follows:1. In the first part of this paper, the sorts of uncertain variables, the research evolution of the random structures and the structural reliability are introduced simply, and the necessity of research on the random structural analysis and precise reliability based on the full probability is described in brief.2. For random consecutive structures, when the uncertain coefficients of the experimental function is determined and the determinate values are not taken, the coefficients obtained is the function expression of the structural parameters. The approximate function of the problem solution can then be obtained when the function of structural parameters is taken into the experimental function. From the distribution of random vector function and analyzing the characteristic of analytical function, a method is presented to compute the structural response by using the joint probabilistic density of the random consecutive structural parameters and the applied loads.3. For the random truss, by using random finite element method, the random information in the structural control equation can be separated by means of random factor method and the determinate part can be obtained with analysis software, so the relationship between random information of structural parameters and the structural random response is function. From the joint probabilistic density parameters of random truss and applied loads, a method of probability density of structural response, so the full probability of structural response under the random loads, which afford the data to compute the accurate structural reliability.4. From the probability density of structural displacement and stress obtained by the method in this paper, by using the theory of dimensions interference, the accurate reliability is computed, which is compared with the results of the moment method, and some useful conclusions are obtained.5. Based on the probability density of the displacement and stress of the random structures obtained by the method of this paper, the mean value and its probability density of the random sensitivity of structural response to the structural parameters are given, and the precise sensitivity of the structural reliability to structural parameters is then presented. 6. The dynamic characteristics of the random consecutive structures are analyzed, with the weighted residual method, after the uncertain coefficients of the experimental function are determined, the real values are not used, so the coefficients obtained above are the functions of the structural parameters. Taking the coefficients into experimental functions, the approximate functions of the solution can be obtained, that is, the function of structural natural frequency for every parameter. From the distribution of the random vector function, a method to obtain the probabilistic density of the structural frequency from the joint probabilistic density of parameters of random consecutive structures is presented, and the reliability of the structural dynamic characteristic is computed.7. Taking the random truss as the objects and using random finite element method and random factor method, the random information of the structural stiffness matrix and the mass matrix is separated, while the determinate part can be computed with software of the finite element Thus the function between the random information of the structural parameters and the random structural natural frequency can be given. A method of the probability density of structural frequencies from the joint probability density of the random truss is presented, and the full probability of structural response can be obtained. Finally, the reliability of structural dynamic characteristic is computed and the probability densities of modes and normal modes are given too. Through an example, the variances of every characteristic of random structures equal, and the randomness of the every vector of characteristics is full positive correlative.8. For random truss, the random information of structural control equation is separated by using random finite element method and random factor method, the steaty-state part of structural dynamic response is got by means of the mode superstition method is given, and the probability density of dynamic response from the joint probability density of the structural parameters of random truss and random applied loads is presented, and the full probability of structural dynamic response of random structures under random loads can be obtained, which offers the necessary data to compute structural dynamic reliability.9. For random truss, the joint probability density of the dynamic displacement and velocity response is obtained, and the dynamic reliability of random truss is presented.