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.

中文翻译：

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用于温度相关材料的 3D 瞬态热机械问题的快速再分析求解器

摘要 开发了一种使用线性四面体单元的快速再分析求解器，用于解决具有温度相关材料的 3D 瞬态热机械问题。其核心思想是建立一种基于稳定节点的平滑有限元再分析方法的再分析框架。在开发的求解器中，基于稳定节点的平滑有限元法（SNS-FEM）因其准确性和稳定性而被用作主要求解器。组合逼近 (CA) 方法是提高 SNS-FEM 效率的辅助工具。在开发的再分析框架中，二项式级数表达式被用作简化基方法的高质量基向量。然后可以计算瞬态温度和位移场，而无需求解完整的非线性或线性系统方程组。开发的求解器的性能通过具有不同类型混合边界条件的几个数值示例进行评估。结果表明，具有两个或三个基向量的再分析框架比完整分析快 20-50 倍，并且求解器比使用传统有限元法 (FEM) 或平滑有限元法的其他求解器更高效和稳定。单元法 (NS-FEM)。因此，证明了开发的求解器的性能。结果表明，具有两个或三个基向量的再分析框架比完整分析快 20-50 倍，并且求解器比使用传统有限元法 (FEM) 或平滑有限元法的其他求解器更高效和稳定。单元法 (NS-FEM)。因此，证明了开发的求解器的性能。结果表明，具有两个或三个基向量的再分析框架比完整分析快 20-50 倍，并且求解器比使用传统有限元法 (FEM) 或平滑有限元法的其他求解器更高效和稳定。单元法 (NS-FEM)。因此，证明了开发的求解器的性能。