The Study Of Reliability Analysis Methods For Truss Structure

The subject of structural reliability has a great development from its naissance to the present. From the development of Stochastic Reliability based on probability to the development of None-probability reliability proposed recently and fuzzy reliability based on fuzzy theory, the theory of structural reliability has been enriched and perfected continually. It has been used widely in many subjects and fields. Analysis of structural reliability has been developed from only analysis of element to analysis of the structural system. Although the structural system is constituted by elements, analysis of structural reliability is hugely different from analysis of elements because its topologic structure has been changed in course of structural failure. It is more significant for analysis of structural system. Failure mechanisms of truss structure under different conditions have been studied in this paper, and the methods of truss reliability analysis under different conditions are proposed. Moreover, the method of fuzzy reliability in this paper is a beneficial attempt for exploring the research of structural reliability. The main works of this paper are as follows:1. The methods calculating structural reliability index are studied. Advanced First-Order Second Moment (AFOSM) calculating software is programmed. Sequential Response Surface Method is adapted by AFOSM calculating software proposed, and its calculating efficiency is improved.2. The theory of reliability analysis of truss structure is studied when static loads and electric loads are applied to the truss simultaneously. Taking into consideration the mechanical-electric coupling effect, the finite element mode of static force analysis is founded by using the theory of mechanics and piezoelectric constitutive equations in this paper. At the same time, failure mechanism of piezoelectric elements is discussed and failure criteria of piezoelectric members is proposed. The formula of safety margins of element is proposed by considering fracture strength, damage electric field strength, the section area of member and loads as random variables. On the base of above research, stochastic finite element method and structural reliability theory are adopted for analyzing reliability of the piezoelectric truss structure.3. The method of structural analysis under fatigue condition is proposed. The method of judging element's fatigue failure through the concept-risk value is given according to structural failure mechanism under fatigue loads. Using risk value as failure criteria, judging element's failure sequence, and the safe margin expression of the failure element is given. Furthermore, the main failure modes are found out by using the branch-and-bound method, and structural reliability index is computed through Probability Network Evaluation Technology (PNET) method.4. Structural stiffness reliability after element's decay is analyzed when the truss structure is under fatigue condition. Decay formula of modulus of elasticity is deduced based on the residual strength model. Stiffness reliability index of truss system under fatigue loads is got combining with stiffness matrix of tuss structure.5. Stable reliability of truss structure is discussed when the truss structure is considered under stable condition. Element's stiffness matrix of truss considering stableness is founded through Finite Element Method. The finite element equation of critical load of structure buckle is deduced through displacement condition of global stiffness matrix of truss system. Moreover, safety margin equation of structural stableness is proposed. In the end, stable reliability of truss system is analyzed by using AFSOM method.6. The fuzzy reliability analysis method of probability density function equivalent is proposed in this paper. Based on the membership function of Fuzzy Distribution Parameter (FDP),the prior distribution of FDP is built. Then the probability density function equivalent of random variables with FDP can be obtained by using BAYES THEORY. Moreover, the mathematical expectation and variance of random variables with FDP of traditional membership function are also deduced. In this way, reliability of truss structure with FDP can be analyzed next.