Uncertain Mechanical Structures Range Of Non-probabilistic Reliability Of Key Technologies

A great number of uncertainties exist widely in the actual engineering, and these uncertainties need to be described and treated rationally. At present, the probabilistic reliability method is the most commonly used approach to handling with uncertainties and its maturity has been demonstrated. However, for the probabilistic reliability method, the contradictions between the strong dependency upon the statistical information and the finiteness of the available data in the actual engineering have restricted to some extent the application of the approach in some engineering fields. Fortunately, as a complement to the probailitistic reliability method, a new reliability theory called the non-probabilistic reliability is proposed to overcome the above barriers.Based on the interval descriptions of the uncertain parameters, the critical technologies on the non-probabilistic reliability method in the analysis and design of the mechanical structures are discussed and researched in this dissertation, and the main contents include the following aspects:(1) Aimed at the case of scarcely statistic data on uncertain parameters in the mechanical structure design, a new non-probabilistic reliability model is presented, with the uncertain parameters in structural reliability being described by interval variables. Based on the principle of satisfaction degree of interval, the satisfaction degree of which the strength-interval is not less than the stress-interval or of which the performance function interval is not less than the real number 0 is taken as the measure of structural reliability. The interval analysis based on the first-order Taylor series is used to calculate the corresponding reliability index. The proposed model has been applied to non-probabilistic reliability analysis of the machine tool spindle and gear transmission system;(2) Based on the interval descriptions of the uncertain parameters, the static displacement response problem of linear structures is researched by the finite element method (FEM). Two approaches, interval analysis method and Neumann-series method, are proposed to solve the linear interval finite element controlling equation. The former is based on operation rules of intervals and operation properties of interval variables, and the latter is based on expansion of the Neumann-series. Both of them are applied to analyse the static displacement response of the 6-bar truss;(3) Based on the interval descriptions of the uncertain parameters, a new structural optimization method for non-probabilistic reliability is presented. In the proposed method, the non-probabilistic reliability indexes established in chapter 3 are considered in the constraint functions. By transforming and handling with the objection function and constraint functions, the uncertain optimization problem can be changed as a deterministic optimization problem. This method has been applied to optimize the weight of the spring structure and 3-bar truss, respectively.