A fast reanalysis solver for 3D transient thermo-mechanical problems with temperature-dependent materials

Abstract

A fast reanalysis solver using linear tetrahedral elements is developed for 3D transient thermo-mechanical problems with temperature-dependent materials. The core idea is to formulate the reanalysis framework of a stable node-based smoothed finite element reanalysis method. In the developed solver, the stable node-based smoothed finite element method (SNS-FEM) is used as the main solver due its accuracy and stability. The combined approximations (CA) method is the auxiliary tool for improving the efficiency of the SNS-FEM. In the developed reanalysis framework, binomial series expressions are used as high-quality basis vectors for the reduced basis method. The transient temperature and displacement fields can then be calculated without solving the complete set of nonlinear or linear system equations. The performance of the developed solver is evaluated through several numerical examples with different kinds of mixed boundary conditions. The results show that the reanalysis framework with two or three basis vectors is 20–50 times faster than the complete analysis and that the solver is much more efficient and stable than other solvers that use the traditional finite element method (FEM) or the smoothed finite element method (NS-FEM). Therefore, the performance of the developed solver is demonstrated.