四川大学学报（自然科学版）2026，Vol.63Issue(3)：548-558,11.DOI:10.19907/j.0490-6756.250178
热-力耦合问题的高阶多尺度分析
Higher order multiscale analysis for thermo-mechanical coupling problems
摘要
Abstract
In this paper higher-order multiscale analysis method for thermo-mechanical coupling problems in quasi-periodic composite structures is considered.A second-order two-scale(SOTS)asymptotic expansion method is developed based on the steady-state nonlinear thermo-mechanical coupling governing equations for effectively predicting the thermomechanical behavior of quasi-periodic materials.In the method,multiscale as-ymptotic expansions of the temperature and displacement fields is firstly utilized,then the first-order and second-order cell functions and homogenized coefficients are computed to establish corresponding homog-enized equations,finally the second-order two-scale approximate solutions are obtained.A specialized finite el-ement algorithm is designed to address the nonlinear nature of the problem through representative macro-scopic temperature sampling,computation of temperature-dependent cell functions and homogenized coeffi-cients,interpolation-based determination of homogenized material parameters and cell functions,and direct it-eration method for solving homogenized equations.Numerical examples demonstrate that the proposed method can achieve remarkable computational efficiency while maintaining excellent accuracy in comparison with the conventional finite element approaches.This significant improvement in computational performance makes the method particularly valuable for large-scale engineering applications,especially in nuclear reactor safety assessment where both accuracy and efficiency are crucial for thermal-mechanical analysis.Further-more,the method has great potential for optimal design applications in advanced composite materials,where repeated multiscale simulations are often required for parameter optimization and performance evaluation.关键词
拟周期性/复合材料/热-力耦合问题/二阶双尺度渐进展开Key words
quasi-periodic/composite materials/thermo-mechanical coupling/second-order two-scale as-ymptotic expansion分类
数理科学引用本文复制引用
叶舒愉,唐庆粦,马强..热-力耦合问题的高阶多尺度分析[J].四川大学学报（自然科学版）,2026,63(3):548-558,11.基金项目
国家重点研发计划(2024YFA1012803) （2024YFA1012803）
四川省自然科学基金(2024NSFSC0438) （2024NSFSC0438）
