Dissertation > Industrial Technology > General industrial technology > Engineering and basic science > Engineering Mathematics > The application of probability theory, mathematical statistics > Reliability theory

Research on Reliability Analysis Methods of Structural-Thermal Coupling and Structural Fatigue

Author YanBin
Tutor ChenJianJun
School Xi'an University of Electronic Science and Technology
Course Mechanical and Electronic Engineering
Keywords Transient temperature field Thermal response Random factormethod Thermoelastic coupling Thermo-structural coupling Thermal fatigue Space structures Fatigue cumulative damage Fatigue reliability Support vector regression
CLC TB114.3
Type PhD thesis
Year 2013
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In the process of analysis and design of practical structures, especially in the fieldsuch as aerospace and aviation, the thermal problem is becoming serious. Theprominent problems including thermal deformation and thermal stress generated bythermal loads, thermal fatigue under alternating thermal loads. With the increasingdemand of engineering precision and research issue, the thermal coupling has graduallybeen widespread concern, such as thermoelastic coupling and thermal-structuralcoupling, which correspond to different actual engineering, respectively. Taking intoaccount that there are a large number of errors and uncertainties in the practicalstructures, which will cause the physical parameters, geometrical parameters and loadstaking on uncertainties, the analysis of reliability of the structures under thermal load ismust be considered. So it is necessary to consider these factors, analyzing the reliabilityconsidering thermal coupling under thermal load. This is very important for the analysisand design of engineering structures, and it has important engineering significance andtheoretical significance. This article mainly study the random responses and thermalreliability considering thermal coupling, and do some research for fatigue reliabilityanalysis methods, the main research works can be described as follows.1. Thermal response analysis of stochastic pole structures under random transienttemperature fieldThe thermal response of stochastic elastic pole structure under random temperaturefield is researched in this paper. The transient temperature field is solved by using themethod of implicit difference and the numerical characteristics of node temperaturefield in every time step is obtained with Monte-Carlo simulation. The computationexpressions of mean and variance of displacement and stress in every time step arederived from finite element method based on random factor with consideration ofmechanical loads. An example of cantilever pole analysis shows the change to the meanvalue and mean-square deviation of displacement and stress of the random variables intransient duration, and the influence of the response dispersion due to the dispersion ofthe random parameters under both random static load and random thermal load.2. Dynamic response analysis of stochastic beam structures under thermoelasticcouplingTo research the beam with random parameters, its dynamic response has been analyzed under both thermal load and force load when considering the effect ofthermoelastic coupling. The dynamic model considering thermoelastic coupling is setup using the finite element method, then a coupling calculate method is proposed whichmake use of the finite difference method in the time domain and alternative iteration ineach time step. The computational expressions for the numerical characteristics of thetemperature field and dynamic response are derived by using the random factor method.Temperature field is worked out by applying the time integral method, while dynamicresponse can be found through Newmark-β integral method. Base on the numericalcharacteristics expressions of temperature field and dynamic response in each time step,the expressions in whole time domain are obtained by using coupling algorithm. Finally,a cantilever beam is taken as an example and the influence of dynamic response due tothermoelastic coupling and randomness of the parameters is showed.3. Probabilistic reliability of micro-resonators with thermoelastic coupling in shockenvironmentsAnalyzing the probabilistic reliability of micro-resonators is essential for thedesign of Microelectromechanical Systems (MEMS). In order to investigate morecomplex structures and take into account the random variation of the design parameters,the numerical method is used, an efficient thermoelastic finite element formulation isderived from Hamilton’s variational principle, by the formulation, and a generalizedeigenvalue equation can be obtained. The effect of thermoelastic coupling and therandomness of parameters on the natural frequency are studied by using anon-symmetric block Lanczos algorithm combine with the right and left eigenproblem.Considering the influence of thermoelastic coupling on temperature is little, thethermoelastic coupling term in heat conduction equation can be negligible, then the heatconduction equation is simplified as the linearization. Depend on the eigenproblem fortemperature field and thermal stress in micro-resonators, further analyzing therandomness of temperature and stress in micro-resonators. For reliability analysis, amethod which both considering strength and frequency is proposed, the strength failurecriteria is set based on fracture mechanics in shock environments, and frequencyreliability is taken into account the probabilistic of resonators when the naturalfrequency is close to the excitation frequency. Take a simply supported model ofmicro-resonators as an example, the numerical solutions of quality factor have shownlittle difference with the analytical solutions proposed by Zener and Lifshitz, verifingthe correctness of the model calculations, finally, the natural frequency shift and theprobabilistic reliability with temperature are calculated. 4. Randomness analysis of space structures considering thermo-structural couplingThe dynamic response for space structures consisting of thin walled pipe which aresubjected to solar heat flux has been analyzed, and then this problem has beendeveloped taking into account the thermo-structural coupling and the randomness ofparameters. For analyzing thermal vibration due to temperature difference in the crosssection conveniently, temperature field is divided into two parts including averagetemperature and disturbance temperature, then the dynamic model consideringthermo-structural coupling is set up using the finite element method. The model can besolved by the approximate calculation method through alternating iterative betweentemperature field and dynamic response in the time domain. Temperature field is solvedby using the method of time integral and Newton-iteration, while dynamic response canbe found through Newmark integral method. Starting from the solving iterative formatof each response, the computational expressions for the numerical characteristics oftemperature field and dynamic response are derived, respectively, by the method ofmoments and random factor. Through the alternate iterative algorithm in each time step,the mean value and variance of response in whole time domain are obtained. Finally,Hubble Space Telescope is taken as an example. Thermal flutter for thin-walledcantilever beam due to thermo-structural coupling is showed, and the influence ofdynamic response due to the randomness of parameters also be found, throughcomparing with the Monte Carlo method, validating the feasibility of the method in thispaper.5. Thermal fatigue reliability analysis for space structures composed of thin-walledtubeThe fatigue reliability of space structures composed of thin-walled tube elementhas been analyzed under alternating thermal load. In order to take into account thefatigue damage due to both average temperature and temperature difference in crosssection, an analytical method which uses the models of residual strength and fatiguecumulative damage is proposed. First of all, according to the principle of fatiguecumulative damage equal, the frequency of multi-level disturbance stress load caused bytemperature difference in cross section is equivalent to the times of constant amplitudestress load action under average temperature, thus all thermal stress loads will be unifiedfor a constant amplitude load, then the fatigue reliability can be analyzed by using theresidual strength model, finally, the dynamic reliability of structures in thecomprehensive consideration of two kinds of thermal fatigue state is obtained. Thismethod avoids the problem that critical damage value is difficult to determine when directly using the theory of cumulated fatigue damage, even it can reflect the realsituation for fatigue damage of metal. In the end, take Hubble Space Telescope as anexample, the dynamic reliability of the main beam with the role of cycle fatigue thermalload is analyzed, some meaningful conclusions are drawed.6. Support vector regression for structure fatigue reliability analysisReliability performance function based on fatigue life is established from fatiguefracture mechanics, considering the performance function has the characteristics ofimplicit and non-linear, so it is difficult to use classic reliability calculation method. Inview of SVR has excellent learning capacity and generalization capability with a smallamount of samples, it can be used to reconstruct the fatigue reliability performancefunction. In order to enhance generalization ability, the genetic algorithm is introducedto optimize the SVR parameters, then the best regression function is trained by using theoptimal parameters, according to the regression function, using FOSM method, fatiguereliability analysis could be completed. Finally, take an example to verify the feasibilityand effectiveness of the proposed method.

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