Research On Thermal-structural Uncertain Analysis Method And Its Reliability Analysis In Thermal Environment

A large number of errors and uncertainties exist in the actual structures, and single mathematics model is not enough to describe these uncertainties. With the accuracy requirements continue to increase in the analysis and design of complex engineering structure, so these uncertain factors should be considered in structural analysis. In this dissertation, based on the thermal-structural analysis of mechanical structure, the analysis of uncertain structure is mainly studied, and than the thermal-structural uncertain analysis methods are proposed. Among them, for the interval structure analysis: based on the interval finite element method, the transient temperature field of beam structure, the dynamic response and non-probabilistic resonance reliability of thermal-structural beam structure are studied, and then the analysis of non-probabilistic reliability with dependent interval variables are studied further. For the stochastic structure analysis: the meshless weighted least square method combining with the stochastic analysis is applied to solve the randomly steady and transient temperature field respectively. The contributions of this dissertation are summarized as follows:(1) Numerical analysis of transient temperature field of space structure with interval parameters. For the thin-walled tube space structures with interval parameters, which are subjected to solar heat flux sustainedly, the interval method is presented for the analysis of transient temperature field based on interval analysis theory. By virtue of the physical parameters of structure regarded as interval variables, the transient thermal analysis model of space structures is established by FEM. And the regions of space are discretized by finite elements and the regions of time are discretized by recursive computation of difference. Based on interval extension theory and Taylor series expansion, the interval finite element equation of structure is solved by matrix perturbation formulas, and then the range of temperature field response of the structure is obtained. The comparison between the result of the method and that of reference by numerical example, indicates that the efficiency of the computational model and the method.(2) Interval numerical analysis of dynamic response of a thermal-structural beam structure. Dynamic response of thermal-structural coupling of beam structure with interval parameters is studied under both thermal load and force load. Considering interaction of material deformation and heat conduction, the dynamic model of beam structure is set up using the finite element method. The calculation method is proposed for solving the transient temperature field and dynamical response by iterative solution. For structural response uncertainty, with uncertain parameters as a constraint variables,the interval bounds of structural response function is solved by the corresponding optimization problems, and the genetic algorithm is used to solve the global optimization model. Compared with the probabilistic analysis method,the numerical example indicates the feasibility and validity of the proposed method, and also found that the natural frequency of beam is increased and the amplitude of vibration is gradually decayed with thermal-structural coupling effect. The proposed method only needs to know the limits of the range where the uncertain parameters, without needing the probability information, and provides a way to solve such a complex problems of a thermal-structural coupling beam structure with uncertainty.(3) Non-probabilistic reliability analysis on resonance of thermal-structural coupling of beam. Since the implicit limit state function of thermal-structural coupling of beam is difficult to solve, a non-probabilistic resonance reliability method for thermal-structural coupling of beam is presented. The method is based on the theories of resonance reliability analysis, improved Kriging method and finite element analysis techniques. In the proposed method, the approximation model of non-probabilistic resonance reliability of beam structure is established by Kriging method, and further improved by active learning method. And then the interval variables are used to describe the parameters of beam structure, the approximation model of non-probabilistic resonance reliability of beam structure including ellipsoidal convex sets is created, and finally the non-probabilistic resonance reliability index of beam structure is calculated by the optimization method. The calculation results show that the proposed method can effectively achieve the non-probabilistic resonance reliability analysis of thermal-structural coupling of beam structure, and the calculation results are of high accuracy and effectiveness.(4) Analysis of non-probabilistic reliability index and sensitivity with dependent interval variables. On the basis of optimization methods for the non-probabilistic reliability index, considering the interval variables dependent each other, the calculation model for solving non-probabilistic reliability index with dependent interval variables is established. Furthermore, based on the finite difference theory, non-probabilistic reliability sensitivity model with dependent interval variables is also developed. The numerical example analyzes the influence of the dependent and independent interval variables on the non-probabilistic reliability index and non-probabilistic reliability sensitivity respectively, and show the effectiveness of the proposed method in the practical engineering.(5) Analysis of stochastic temperature field with the neumann expansions Monte Carlo meshless method. A meshless weighted least square(MWLS) method is investigated for the analysis of stochastic temperature field in this paper. Based on the Moving least-squares(MLS) approximation, and used penalty function method to satisfy the boundary conditions, the MWLS equation is derived in detail by variation principle for solving the temperature field problems. Compared with Galerkin based meshless method, the proposed method has no need of integration, and has a small amount of calculation, easy for process and some other advantages. And considering the randomness of physical parameters and boundary condition, the MWLS of stochastic temperature field with random variables was derived, and the statistics feature of response of stochastic temperature field was obtained by Neumann expansion Monte Carlo method. Numerical examples comparison between the results of the proposed method and the Finite Element Method simulation is presented to illustrate the effectiveness and validity of proposed method.