This thesis herein proposes a stochastic stable node-based smoothed finite element method for uncertainty and reliability analysis of thermo-mechanical problems. First, the deterministic ingredient of the thermo-mechanical solution is accurately solved by our proposed stable node-based smoothed finite element method (SNS-FEM); and the stochastic ingredient including the fourth-order moment and probability density functions (PDFs) is obtained via stochastic response analysis. Furthermore, we extend the work to the reliability field by innovatively exploring several mathematical models for reliability analysis, such as structural failure probability (Pf) of thermal stress. At last, several thermo-mechanical related examples, including 2D and 3D, are hereby demonstrated to verify the accuracy and efficiency of the proposed stochastic stable node-based smoothed finite element method, by comparing with the direct classic Monte Carlo simulation (MCS). In addition, the effects of different uncertain parameters on the solution to the stochastic response and reliability analysis are illustrated and discussed.

本文提出一种基于随机稳定节点的平滑有限元方法，用于热机械问题的不确定性和可靠性分析。首先，通过我们提出的基于节点的稳定平滑有限元方法（SNS-FEM）精确求解热机械解决方案的确定性成分；通过随机响应分析获得包括四阶矩和概率密度函数（PDFs）的随机成分。此外，我们通过创新性地探索几种用于可靠性分析的数学模型，例如热应力的结构破坏概率（Pf），将工作扩展到可靠性领域。最后，列举了一些热力学相关的示例，包括2D和3D，本文通过与直接经典蒙特卡罗模拟（MCS）进行比较，证明了它们可以验证所提出的基于随机稳定节点的平滑有限元方法的准确性和效率。此外，还说明并讨论了不同不确定参数对随机响应和可靠性分析的影响。