Research On Reliability Analysis And Optimization Design For Structures With Multi-source Uncertainties

Uncertainties are ubiquitous in practical mechanical systems or structures. Uncertaintiesof mechanical systems usually have multi-source, which can be classified into twodistinct types: aleatory uncertainty and epistemic uncertainty. Single mathematics modelis not enough to describe these uncertainties. Hence, performing the reaserch onreliability analysis and optimization design for structures with multi-sourceuncertainties has very important theory and engineering significance. In this dissertation,structural reliability theory and related topics have been intensively studied based on theprobabilistic model, fuzzy model and non-probabilistic model. Some structuralreliability analysis methods for complex engineering problems are established. On thebasis of theoretical research, reliability optimization design and robust optimizationdesign are also investigated. The main research work can be summarized as follows:1. Based on probabilistic reliability model, a missile suspension structure was taken asan example in order to studying reliability analysis method for complex structurediscribed by implicit limit state equation and involve Finite Element Analysis(FEA)process. Parametrization and automation analysis of static strength and fatigue life wasachieved by redevelopment language PCL (Patran Command Language). A missilesuspension fatigue life reliability analysis platform was developed to implement theautomation of reliability analysis.2. Based on the fuzzy theory, reliability analysis for two typical modes of structuralfailure, include fatigue failure and resonance failure, are studied. Three types ofmembership functions, including semi-trapezoidal, semi-normal, semi-Cauchy, are usedto describe the gradual failure process of structural fatigue. Generalized fatiguereliability analysis for structures with fuzzy state is carried out. In addition, ageneralized resonance reliability analysis method is established based on triangularmembership function under λ level sets.3. Based on convex set model and space-filling design, a non-probabilistic reliabilityanalysis method is established for structures with "unknown but bounded" parameters.Based on the definition of non-probabilistic reliability, an enhanced optimal Latinhypercube sampling method is proposed in order to obtain the upper and lower bound ofstructural performance function under the influence of uncertainty. This samplingmethod enables more sampling points scattered toward the borders of variableuncertainty space. Then the performance function bounds can be quickly determinedwith fewer sampling points. The method is simple, practical, and very suitable for non-probabilistic reliability analysis of complex engineering structures and systems.4. A non-probabilistic reliability analysis method is presented based on an idea ofadaptive importance sampling. Based on the physical meaning of the non-probabilisticreliability index, the solution of structural non-probabilistic reliability index can betransformed to searching for a point in the failure region, which has a minimum distanceto the origin that measured by infinity norm δ∞. Then, based on the idea ofspace-filling design, a point in the failure region which has a minimum distance to theorigin that measured by infinity norm δ∞in the standard vector expansion space. Thesearched point is named as design point, and it will be the sampling center of latteriterations. Then an iterative sampling process is performed until the analysis resultmeets the convergence criterion.5. A unified model of structural non-probabilistic reliability analysis is established forthree types of uncertainty convex model, including interval model, ellipsoid model andmulti-ellipsoid convex model. The uniform design is introduced into structuralnon-probabilistic reliability analysis to improve the poor space-filling ability oftraditional random sampling method. As the sampling point generated by uniformdesign can be uniformly scattered in the uncertainty region, it can greatly enhance theanalysis accuracy and sampling efficiency. To enhance the practicability of the proposedmethod for complex engineering structures, based on ANSYS software, a flowchart ofstructural non-probabilistic reliability and parameter sensitivity analysis is presented.6. Reliability optimization design and robust optimal optimization are intensivelystudied. Based on Matlab software, a technical framework of reliability optimizationdesign is proposed. In addition, based on Isight software,6σ robust optimizationdesign is studied. Taguchi robust optimization design is also studied in this dissertationbased on the probabilistic design module of ANSYS software. In terms of theoreticalinnovation, uniform design and add-point principle are introduced to build a moreaccurate Kriging meta-model and a double-loop Monte Carlo method is proposed toperform the robust optimal design analysis. In the proposed method, both theuncertainty of variables and that of meta-modeling are considered.