Research On Reliability Analysis And Optimization Design Of Stochastic Structures

The structural analysis and optimization design based on probability have wide engineering background and are of important theoretical significance and research worthiness. This paper mainly has the research of random factors presented in reliability analysis and optimization design based on probability of all kinds engineering structures (including truss and beam structures etc.). The main contents of the paper are as follows:1. The Random Factor Method is utilized to proceed structural reliability analysis which considered randomness of structures, including structural own material parameters such as physical parameters and geometric parameters, and some stochastic parameters involved in the loads applied. The 3 σ criterion of reliability theory is applied to analyze and compute the structural responses while the structural boundary conditions are stochastic. Several numerical examples show the correctness and validity of the theory and method.2. The Random Factor Method is utilized to study the probabilistic analysis and computational method of structural dynamic characteristic while the structural physical parameters and geometric parameters are stochastic variables respectively or simultaneously. The results of numerical examples indicate that the method derived in this paper is correct and valid.3. The structural sensitivity analysis based on reliability is preceded. The sensitivity computational expressions of reliability index with respect to design variables are derived. And the semi-analytical expressions for sensitivity computation are presented. Thus the sensitivity analysis based on reliability is transformed into regular sensitivity analysis. And then the sensitivity analysis based on reliability can be simplified greatly.4. Based on the reliability analysis and sensitivity analysis above, the dimensional optimization and shape optimization based on reliability are developed. The mathematical programming methods are applied in optimization. In optimization models, the structural total weights (or fabricating costs) are regarded as objective functions and reliability indexes of structural displacements and elemental stresses as constraint conditions.5. If the randomness of design variables were considered in optimization, then a regular optimization based on reliability would be transferred to a stochastic programming issue. A method, which is utilized to find the upper and lower bounds of design variables, is proposed in the paper. By the method, the structural stochastic programming model can be transformed to solve.6. The key problem of optimization based on structural system reliability constraints is the analysis and computation of system reliability. In the paper, based on the hypothesis that the failure of every poles is independent and by the method of reliability assign and reassign, the difficult problem of disposing the structure system reliability constraints is solved. Based on sensitivity information, the given system failure probability can be replaced by the sum of every element failure probability. And then the structural optimization design based on system reliability is preceded.7. With the assurance of structural precision accuracy and strength, the reliability analysis and computation method is presented for paraboloid antenna backup structures. And the reliability computational expressions for compression bar stability are derived. For stochastic parameters antenna structures with stochastic loads applied, the models of finite element analysis, reliability analysis and the optimization design based on reliability are constructed. And then the antenna backup structure dimensional and shape optimization designs based on probability are proceeded.