On Reliability Analysis And Optimization Of Uncertain Structures

Uncertainties exist in engineering structures. Reliability method is an effective tool to deal with uncertainties of structures. The exploring research is made in order to solve the problem of structural reliability. The research includes non-probabilistic reliability model, non-probabilistic reliability measures and safety factors, hybrid structural reliability analysis and reliability-based optimization, reliability-based topology optimization of hybrid truss structures and so on. The main content is as follows:1. A structural non-probabilistic reliability model is proposed, in which uncertain parameters of structures is described as ellipsoidal convex model. The ratio of the volume of safe region to the total volume of the region constructed by the basic variables is utilized as the measurement of structural reliability. The compatibility of the non-probabilistic reliability model with the probabilistic reliability model is proved. In the case of interval vector determined from the ellipsoid of the uncertain parameter vector, a comparison between the two non-probabilistic reliability models based on ellipsoidal model and interval model is presented, in which their interrelation and difference illustrated.2. Safety factors and non-probabilistic reliability measures are investigated respectively. The functions of three kinds of safety factors named central, non-probabilistic and interval factors are established. A comparison between the two kinds of non-probabilistic reliability measures, which are reliability index and set-theoretic reliability measure, is presented. The connections between safety factors and non-probabilistic reliability measures are discussed. A bridge between safety factors and non-probabilistic reliability measures is made.3. A comparison between the non-probabilistic safety factor and non-probabilistic reliability methods for structural design is presented. The equivalence of non-probabilistic safety factor and non-probabilistic reliability index in the measurement of structural safety is proved. The differences and relations of design concept, measure method and representation formation, between the two non-probabilistic methods are investigated. The result from a numerical example shows that the differences of the two non-probabilistic methods in structure weight and bar sectional dimension.4. A reliability analysis and reliability-based optimization method of fuzzy and non- probabilistic hybrid structures is proposed. Based on possibility reliability theory, a reliability model of hybrid structures is established. The minimum fuzzy reliability index and the maximum failure possibility are utilized as the measurement of hybrid structural reliability. A reliability analysis method of hybrid structures is presented. By regarding the maximum failure possibility as constrains, a reliability-based optimization model of hybrid structures is developed. Three numerical examples show the method proposed is effective and feasible.5. A reliability-based topology optimization method of probabilistic and non- probabilistic hybrid truss structures is proposed. The hybrid reliability index is utilized as the measurement of structural reliability. A reliability-based optimization model of probabilistic and non-probabilistic hybrid truss structures is developed, in which the structure weight is taken as objective function, both the hybrid reliability index of structural displacement and bar stress are taken as constraint functions. The sensitivity of hybrid reliability index for design variables is derived. A numerical example illustrates the feasibility and validity of the method proposed.6. An uncertainty analysis method for multidisciplinary systems with uncertain-but-bounded parameters is presented. Based on Taylor series and global sensitivity equations, the numerical algorithms for the linking variables and the outputs of the systems are deduced using interval analysis method and convex models respectively. The comparison of the solved results between interval analysis method and convex models is performed through the mathematical proof and the numerical examples. The results show that the interval of solution obtained by interval analysis method is closer to Monte Carlo simulation than that obtained by convex models.