The Stochastic Calculation Method Based On Nodal Integration And Its Research In Heat Transfer Problem

The heat transfer problem is widespread in engineering field.There are two major numerical methods for analyzing such problem,namely the finite elemen t method and the meshless method.In practical engineering,there are a lot of uncertain parameters in the heat transfer structure s due to the errors of manufacture and service environment.With the complexity of the heat transfer problem and the improve ment of reliability requirements,the deterministic numerical algorithm can no longer meet the design requirements.Therefore,the uncertainty algorithm is more and more popular and important in the high accuracy reliability problem.Although the stochastic heat transfer problem analysis has received attentions and developments for a long time,it still needs to be developed and perfected as a whole,especially for complex stochastic heat transfer problems,such as the uncertain engineering thermal analysis with multi-source,the stochastic heat transfer analysis under random heterogeneous materials and the uncertainty analysis of complex three-dimensional heat transfer problem.A series of technical problems remain to be solved.This dissertation conducts a syste matical research for the uncertain heat transfer problem of structures in combination with the relevant uncertainty algorithms,and aims at developing some uncertainty models and analysis methods.The related research work mainly includes:1.The generalized perturbation stochastic nodal-based smoothed finite element is presented for stochastic analysis of heat transfer problem.The flexible triangular elements(tetrahedrons)can be used to divide the entire problem domain,and are insensitive to element distortion.Therefore,the accuracy and efficiency are improved more than traditional stochastic finite element.So it can be applied to more comple x engineering problems.The generalized n-order perturbation algorithm based on node integral is extended to heat transfer problems,and the precision of the random algorithm can be controlled by the size of the expansion order.2.A random field model based on nodal integration domain is presented to solve the stochastic heat transfer problem.The random field subd omain is constructed by the node-based smoothed finite element method(NS-FEM),the Karhunen-Loève(KL)expansion is employed to describe the random field and quantifies the uncertain characteristics of non-homogeneous materials.The random field is then i nserted into the constitutive equations in order to establish the stochastic equilibrium equation,and thereby the structural response with the random spatial distributed materials ca n be calculated.The statistical moments of the structural responses usin g the perturbation method are also performed and compared with the solutions of Monte Carlo simulation.3.A probabilistic moment analysis method of structures is proposed to calculate the probability density function(PDFs)and failure probability of structu ral response in stochastic heat transfer problems.Based on the Taylor expansion,the first four moments of the structural response propagated from uncertain parameters are calculated.By using the maximum entropy theory and taking the first four moments as constraints,the PDFs of the structural response in the normal space are estimated on the base of the Lagrange multiplier method,and then it will be transformed back to the origin space,there is no need for loop iterations to increase the efficiency of structural probabilistic analysis.