Non-Stochastic Reliability And Optimization Of Uncertain Structural Systems

The traditional stochastic reliability method is an important tool to handling with uncertainties,and is widely used in engineering. Yet stochastic reliability method is strongly depends upon the available information,but in engineering,often only limited information is available,which greatly restricts the applications of stochastic reliability method in engineering. Against some drawbacks of stochastic reliability method in theory and applications,a new reliability theory called non-stochastic reliability,for uncertain structures was founded systematically in the paper. Some corresponding finite element methods (FEM) were presented. Moreover,the proposed theories were used in the reliability-based optimization of structures successfully. The detail contents were as follows(a) Firstly,based on the convex modeling of uncertainties,interval finite element methods for uncertain structures were studied. Some arithmetic rules for interval variables were developed and demonstrated. Several efficient methods for solving the static governing equations of interval FEM were put forward,which include:an iterative method for solving the interval types governing equations and advanced combinatorial methods for solving governing equations of linear static interval FEM. Compare with some presently used methods for solving interval equations and interval analysis of structures,the presented methods have high efficiency of calculation,low computational burden and high accuracy.(b) Secondly,the proposed methods for solving interval FEM were extended to the solving of fuzzy structures. Some arithmetic rules for fuzzy variables were developed. Several efficient methods for solving the static governing equations of fuzzy FEM were presented. By the presented methods,the possibility distribution of displacements and stresses of uncertain structures may be obtained according to thepossibility distribution of basic variables.(c) Thirdly,a new non-probabilistic reliability theory for structural systems was founded. A non-probabilistic reliability model based on interval analysis was presented. An approach for enumerating the significant failure mode for non-probabilistic structures,and a procedure for non-probabilistic reliability analysis of structural systems were put forward. We also compared the presented non-probabilistic reliability method with the traditional stochastic reliability method in the modeling of uncertainties,formulations for computation,and reliability design of structures,etc. Alike with the convex modeling of uncertainties,the presented method requires less for available information than probabilistic method,thereby,which provided a possible choice for the reliability analysis and design of structures when available information is lack or limited.(d) 4th,a possibilistic reliability theory for fuzzy structural systems was founded. A possibilistic reliability model in the context of possibility theory was presented. An approach for enumerating the significant failure mode for fuzzy structures,and a procedure for possibilistic reliability analysis of fuzzy structural systems were given. We also compared the proposed possibilistic reliability method with the traditional stochastic reliability method in concepts,modeling of uncertainties,formulations for calculation,and optimization of structures based on reliability,etc. Some advantages of the presented possibilistic reliability method were explained. The presentation of possibilistic reliability method have make it possible for reliability evaluation when only little information is available,or available information is limited or incomplete.(e) 5th,hybrid reliability theories of stochastic and non-probabilistic,stochastic and fuzzy,for structural systems were founded. A hybrid model of stochastic and non-probabilistic reliability,and a hybrid model of stochastic and fuzzy reliability were presented. Approaches for enumerating the significant failure mode for hybrid structures,and procedures for hybrid reliability analysis structural systems were...