Structural Non-probabilistic Reliabilty Study Based On Interval Method

Currently, the main methods of researching the structural reliability model arethe probabilistic and non-probabilistic methods. When the sample space of theuncertain parameters were known, the traditional probabilistic method had a greatsuccess on the uncertain problems of a system and was widely used in various fieldsof engineering, such as life expectancy estimation, the probabilistic reliabilityanalysis, system optimization and so on. Many scholars have done a lot of researcheson the calculating method of the probabilistic model. However, the probabilisticmethod has its own limitations. When the stochastic information of the uncertainparameters was not obtained enough, the probabilistic model can not accuratelydescribed the uncertainties. Therefore, studies of non-probabilistic uncertainty modelsbecame the focus of scholars and the interval model became the hotspot ofresearching the non-probabilistic model. The interval model has the advantageswhich the probabilistic model cannot compare with. The interval model does notrequire any prior knowledge of the statistic information of the system uncertaintiesand only needs the upper and lower limits of the uncertain parameters. Thisovercomes the shortcomings of probabilistic models. But the interval arithmetic couldbring some interval extension problems, which is a defect of the interval method. Anumber of computing methods were proposed to control the interval extension, andobtained some satisfactory outcomes.This dissertation analyzed and studied the fatigue and reliability of structures, onthe basis of the interval method. The fatigue failure is the main failure mode of thecomponents or structures under the alternating loads. In the fields of modern industry,about eighty percent of the structural components were destroyed by the fatiguefailure. In this dissertation, the uncertain factors in the fatigue analysis were describedby the interval model, with the range of the uncertain parameters regarded as theinterval radius. After extending the interval of the fatigue performance function, theinterval perturbation method was used to compute the performance function with interval variables. The life interval of stress fatigue, the life interval of strain fatigueand the interval of endurance limit were analyzed and optimized.When using the interval model to analyze the reliability of the structural staticresponses and dynamic responses, the results of the perturbation method may be notvery precise if the interval radius of the structural parameters were big. Therefore, theEpsilon reanalysis method was applied in the reliability analysis of the structural staticresponses and dynamic responses. The static and dynamic non-probabilistic reliabilityindexes were calculated. Combining the Epsilon method and the interval method, thereliability of the static and dynamic responses were improved by controlling theinterval radius of the interval parameters. The multipurpose interval control of theinterval parameters was achieved.The specific contents are as followed:1. Interval estimation of traditional fatigue life.In the traditional fatigue tests, under the same environment which was definedsubjectively by people, the test results of the fatigue life were very different. This ismainly due to the uncertain factors which cannot be controlled by people, such as thematerial, size, surface roughness and temperature and so on. All these kinds ofuncertain factors will be regarded as the interval number in this dissertation. Whenestimating the fatigue life, these interval numbers will be the interval parameters inthe fatigue performance function. The interval perturbation method was applied tocontrol the interval extension problem and the second order interval perturbationmethod could enhance the computing precision of the fatigue life. Through theanalyses and computations of the stress fatigue life and strain fatigue life, it is shownthat the second order interval perturbation method is more precise than the first orderone, obtaining more reliable results.2. Optimization of design parameters of the endurance limit life based on intervalmodel based on the rigid-flexible coupling.In the fourth chapter of this dissertation, the design parameters of the endurancelimit life which were based on the interval model were optimized. In the process ofoptimization, the endurance limit performance functions were usually implicit. Theresponse surface method was used simulate the performance functions of thecomponents, and the design parameters were optimized. In the course of using theorthogonal method to choose the sample points, the finite element model of thestructure was analyzed. If the structure was complicated and needed a high precision, the finite element analysis could be very difficult. To improve the processing speed ofthe model effectively, the rigid-flex coupled model was used, regarding some parts ofthe system as rigid bodies and others as the flex bodies. Through this kind of method,the speed of analyzing the model was improved sharply. In the numerical example ofthe engine connecting rod, the connecting rod was regarded as the flex body, andother parts of the engine were regarded as the rigid bodies. The rigid bodies and theflex body were coupled, being analyzed and optimized to get the endurance limit offatigue life. Under the condition of satisfying the reliability of the rod fatigue life, theaim of minimizing the weight of the rod was achieved, enriching the fatigue reliabilitybased optimization design including interval parameters.3. The Epsilon algorithm was used to analyze the interval static response reliability,proposing the multipurpose interval control method to improve the displacementresponses.In the fifth chapter, the interval static response reliability based on the Epsilonalgorithm was proposed. The interval radius of the structural interval parameters wasregarded as the perturbation, doing the fast reanalysis of the structural staticdisplacement response, obtaining the upper and lower boundaries of the responseinterval and getting the non-probabilistic reliability index. Combined with the intervalcontrol method, the reliability index of the displacement was controlled and improved.The sensitivity matrix of the interval parameters and displacement vector were gottenby interval control method, achieving the multipurpose control of the multiple intervalparameters. The numerical examples show that the proposed method is more effectiveand easy to program.4. The Epsilon algorithm was used to analyze the interval dynamic responsereliability, proposing the multipurpose interval control method to improve thestructural eigenvalue reliability.The sixth chapter continued to analyze the structural dynamic response reliability,proposing the interval dynamic response reliability model based on the Epsilonalgorithm. Using this method to do a fast reanalysis of the perturbed structure to getthe eigenvectors response interval, the non-probabilistic reliability index of theeigenvalues corresponding to the eigenvectors was resolved. Combining the Epsilonalgorithm and the interval control method, the interval radius of the interval parameterin the structure was controlled to enhance the reliability index of the eigenvalue,achieving the interval parameter multipurpose control of the dynamic response. Numerical examples show the effectiveness of the proposed method.