Research On Special Topics Of Uncertain Structural (Mechanism) Analysis And Reliability Evaluation

A large number of errors and uncertainties exist in the actual structure, and these uncertain factors should be considered in structural analysis. There are three mainly models to deal with uncertainty, which are probability model, fuzzy model and convex model or interval analysis. Among these models, the interval analysis is simple and practical to deal with uncertain structures. For changeable structural forms and sorts of failure types, the reliability analysis of a mechanism is more difficult than a fixed structure. Recently, the theory of mechanism reliability analysis is still imperfect.Some researches on special topics are presented in this paper, which include the static response analysis, dynamic characteristic analysis, the non-probabilistic reliability calculating of an uncertain structure, the movement reliability of a mechanism.The main research works can be described as follows:1. Interval finite element methods (FEM) for uncertain structures are studied. Several efficient methods for solving the static governing equations of interval FEM are proposed, which include an interval-step-dividing method and an interval factor method. The interval-step-dividing method considers the correlation between matrix elements and the condition that each element obtains the interval's inner value. Therefore, it can get a result which is close to the exact one. The interval factor method is easy to solve the uncertain problem, which needs only once structural analysis to get the response intervals of the static displacement and stress.2. An approach by using universal grey numbers to solve static interval linear equations is discussed. This method changes interval linear equations to universal grey linear equations to solve, which is simple, but has some disadvantages in application. A new rule of transforming an interval number into universal grey one is presented. Computing results show that the new transforming rule is reasonable.3. Based on the interval FEM the dynamic characteristics of uncertain structures are analyzed. To solve the generalized interval eigenvalue equation, an interval-step-dividing method and an interval factor method are presented in this paper. The correctness and validity of the theory and method presented in this paper are inspected by several examples. The interval factor method is easy to analyze the effect of any parameter's uncertain on the dynamic characteristics.4. Based on the transfer matrix method, the dynamic characteristics of uncertain chain-structures are analyzed. A nonlinear interval equation of a chain system's natural frequency is developed, which is solved by using the interval dividing method. Based on the interval factor method, some expressions of interval variables about the structure's dynamic characteristics are derived.5. The deployment reliability analysis of a large satellite antenna is studied. The movement principium of a large satellite antenna is analyzed. Based on a random model, the movement reliability of the deployment mechanism and the seizure-preventing reliability of synchronous gears are calculated. The faulty tree of the deployment system is built by using the Faulty Tree Analysis method, and from the calculating result of the probability and importance degree of each base affair, some key factors to affect the deployment of the antenna are point out.6. Based on a non-probabilistic reliability model, two methods for structural reliability computation are produced, which are practicable for any performance functions. These two methods are equivalent for linear functions but a little different for nonlinear ones. The computing difference comes from two definitions about non-probabilistic reliability. The non-probabilistic model is also used to give the reliability analysis of a satellite antenna's deployment mechanism, and the result is compared with another one based on the probabilistic model. The result shows that the trends of their variation are alike.7. The grey theory and method is applied in the mechanism reliability research. The conception and model of grey reliability on a mechanism's movement is presented. From the limiting condition equations of movement requisition and accuracy, the computing formulae of the grey reliability are derived respectively. The research proves that the method is feasible and the result is reasonable.The theories founded in the paper are important and meaningful in the following aspects: enhancing the ability of the FEM in solving uncertain structures, completing the structural (mechanism) reliability theory, improving the application of the structural (mechanism) analysis in the aerospace engineering.