Interval Non-Probabilistic Reliability Analysis Of Uncertainty Structure Based On Affine Algorithm

The performance of structures in practical engineering application will be affected by uncertainties from many aspects, such as structural material parameters, loads, geometrical parameters and etc. To ensure proper performance of a structure for supporting loads and bearing environment and normally working, it is essential to give a reliability analysis of this structure under service environment, assigned condition. In order to set up a reasonable reliability model and guarantee validity of reliability analysis, appropriate method should be adopted to deal with these uncertainties during the process of structure analysis. Recently, the method used of dealing with such uncertainties can be classified into non-probabilistic and probabilistic reliability analysis.However, the probabilistic reliability analysis is extremely sensitive to the statistical information, which is contradicted with the limited nature of available data in practical engineering applications. As an alternative analysis method, the non-probabilistic reliability analysis method can just make up this shortfall.Based on interval parameters and unascertained parameter structure, this thesis exploratory study the case that using interval arithmetic embedding with affine algorithm to analysis the non-probabilistic reliability and interval static displacement response of the structure. The main contents of this thesis are follows:1. Firstly, the basic theory of the interval arithmetic, the finite element and affine arithmetic are introduced. For the case of the limited uncertainty parameters in mechanical design, this thesis using interval variable to express the main factor that affect the structure of non-probabilistic reliability analysis, then establish a new reliability analysis model.2. For the interval expansion during solving the finite element equation, this thesis introduce several method for solving finite element model, such as interval truncation method, subintervals perturbation method, iterative method, for the purpose of limiting range expansion, this thesis selecting affine arithmetic to solve the problem of static displacement response, at the same time, by changing the uncertainty of the external load, material parameters on the structure to determine the effect of the external load and material parameter uncertainty on the reliability of the structure.3. Introducing affine arithmetic into the calculation of non-probabilistic reliability index, and in order to get more accurate results, combined gradual separation method with affine algorithm form an interval gradual separation method based on affine form, the method is applied to example and the results verified the method is correct by compared with other results that come up with other methods, at the same time, the results of the proposed interval gradual separation method based on affine form, interval algorithm, affine arithmetic applied to an engineering example show the superiority of this method proposed in this thesis.