Research On Analysis Methods Of Uncertain Temperature Fields And Structures

In the process of analysis and design of practical structures, it is necessary to consider the thermal effect(such as thermal distortion, thermal stress, the temperature value smaller than the seted value,and so on) besides considering the structural mechanical behavior. But there are a large errors and uncertainties in the practical structures, which cause the physical parameters, geometrical parameters and loads taking on uncertainties. Consequently, studying the influence of these uncertainties on structural responses has important engineering meaning and academic meaning. The systemic studies on analysis methods of uncertain temperature fields and structures are maded in this dissertation. The main research work can be described as follows.1. The analysis for static random temperature fieldConsidering the randomness of heat conduction coefficient, heat exchange coefficient, heat flux density and environmental temperature, and so on, Firstly, the Neumann expansions Monte-Carlo stochastic finite element method is employed to analyse the temperature response. Giving the computing formulas of the mean,variance and possibility in some interval of node temperature. The effects of the amount of variances of random variables on node temperature responses are considered. Secondly, Asymptotic-Maximum Entropy Principle for solving the statistical characteristics of static random temperature response is presented. In this method, the asymptotic approximation of Laplace multidimensional integrals and functions'Taylor expansions are employed, then the approximate analytical expressions of the arbitrary order original moments of node temperature response are obtained. On the basis of maximum entropy principle, the Probability Density Function(PDF) of nodal temperature response are developed.2. The analysis for transient random temperature fieldConsidering the randomness of physical parameters and boundary conditions of transient heat transfer, the quasi-analytical expressions of numerical characteristics (the mean value and variance) of random temperature field response are derived by the random factor method and the algebra synthesis method which is employed to obtain the random variable's functional moments. The influence of the randomness of each parameter on the temperature field response is investigated. The proposed method has the merit that the numerical characteristics of stochastic temperature field response can be obtained by analyzing the random temperature field just in one time.3. Perturbed numerical algorithm of nonprobabilistic convex set theoretical models on the temperature fieldThe uncertain parameters of physical parameters and initial boundary conditions of heat conduction are described by the convex model. The perturbation formulas of the upper and lower bounds of temperature field response with unknown-but-bounded parameters are given via the combination of matrix perturbation theory and the convex set theory model.4. Numerical analysis for transient temperature field with interval parametersConsidering the uncertainties of the transient heat transfer, the physical parameters and initial boundary conditions are regarded as interval variables. In order to solve parabolic equation of heat conduction with interval parameters, the regions of space are discretized by finite elements and the regions of time are discretized by finite difference. The interval finite element method based on the element is established via the combination of interval analysis and the traditional finite element method. Then the interval finite equation of structure is solved by matrix perturbation formulas, and the range of temperature field response of the structure is obtained. In addition, a simple method for solving the structural static interval finite element equations is presented. In this method, the global stiffness matrix is first order expanded at the middle value of interval variables by Taylor. And the expansion expression of stiffness matrix is dealt approximatively, the inverse matrix of uncertain stiffness matrix is expressed as a series of Neumann expansion series. The full use of sub-distribution law and other arithmetic rules of interval analysis are made to reduce the extension caused by interval analysis. Finally, the computational formulas of the upper and lower boundaries of the uncertain structures responses are developed.5. The analysis for temperature field with fuzzy-random parameters based on general density functionThe mixture modeling of fuzzy and random variables in heat transfer is discussed. The fuzzy variables are transformed into random variables based on general density function method. The mean values and variance values of transformed random variables are obtained using the formulas for solving random variables'numerical characteristics. So the fuzzy-random temperature field is converted to the pure random temperature field, correspondingly. The mean values and variance values of the random temperature field responses are obtained by employing the conventional stochastic perturbation method. The influence of the uncertainty of each parameter on the structural temperature field responses is analyzed through the example.6. The maximum entropy stochastic finite element method based on the dimension-reduction methodThe maximum entropy analysis method for solving the static response of random structures is presented on basis of dimension-reduction method. In this method, the multi-dimensional random response functions are decomposed into the combination of one-dimensional response functions by the univariate dimension-reduction method, so the multi-dimensional integration which is employed to calculate statistical moments of response of stochastic structures is transformed into one-dimensional integration, and the one-dimensional integration is numerically calculated by the Gauss-Hermite integration. After getting the statistical moments of response of structures, the explicit expression of probability density function of structure's response is obtained using the Maximum Entropy Principle.7. The eigenfrequencies characteristic analysis for random structure systemsConsidering the statistical characteristic of eigenfrequencies of random structure systems, the multi-dimensional random eigenvalues functions are decomposed into the combination of one-dimensional random eigenvalues functions by the univariate dimension-reduction method, so the multi-dimensional integrations which are employed to calculate statistical moments of eigenvalues of random structure systems are transformed into one-dimensional integrations, and the one-dimensional integration is calculated by the Gauss-Hermite 8-point numerical integration. Once getting the first four origin moments of eigenfrequencies of stochastic structure systems, the explicit expressions of probability density function of eigenvalues of structures can be obtained employing the Maximum Entropy Principle.