Stochastic stable node-based smoothed finite element method for uncertainty and reliability analysis of thermo-mechanical problems

摘要

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.