Abstract A novel second-order reduced homogenization (SORH) approach is introduced for analyzing dynamic thermo-mechanical coupling problems in axisymmetric inelastic structures with periodic micro-configuration. The axisymmetric heterogeneous structures are periodically distributed in radial and axial directions and homogeneous distribution in circumferential directions. Firstly, the nonlinear coupled thermo-mechanical model is proposed, and the high-order nonlinear local problems, effective material parameters and the nonlinear homogenization equations are derived successively by the multiscale asymptotic expansion. Further, in order to reduce the large computational amount evaluated by the classical multiscale homogenization approach, the reduced-order nonlinear multiscale models and the corresponding finite-element algorithms are established in detail. The key features of the proposed approach are that an efficient reduced-model form based on transformation field analysis (TFA) to analyze nonlinear local cell problems is proposed and a nonlinear thermo-mechanical problem which considers the mutual coupling for the temperature and displacement fields is computed. In particular, a new SORH algorithm is proposed for investigating the axisymmetric inelastic structures. Finally, three typical numerical experiments are carried out, and the effectiveness and correctness of our presented algorithms in simulating and predicting the macroscopic behavior of the heterogeneous structures are confirmed.

中文翻译：

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具有周期性微构型的轴对称结构非线性热机械问题的新型二阶均化方法

摘要 引入了一种新的二阶均化（SORH）方法来分析具有周期性微构型的轴对称非弹性结构中的动态热-机械耦合问题。轴对称异质结构在径向和轴向上呈周期性分布，在圆周方向上呈均匀分布。首先提出非线性热机耦合模型，通过多尺度渐近展开依次推导出高阶非线性局部问题、有效材料参数和非线性均匀化方程。此外，为了减少经典多尺度均质化方法评估的大量计算量，详细建立了降阶非线性多尺度模型和相应的有限元算法。该方法的主要特点是提出了一种基于变换场分析 (TFA) 的有效简化模型形式来分析非线性局部单元问题，并提出了一个考虑温度场和位移场相互耦合的非线性热机械问题。计算。特别是，提出了一种新的 SORH 算法来研究轴对称非弹性结构。最后，进行了三个典型的数值实验，证实了我们提出的算法在模拟和预测异质结构宏观行为方面的有效性和正确性。该方法的主要特点是提出了一种基于变换场分析 (TFA) 的有效简化模型形式来分析非线性局部单元问题，并提出了一个考虑温度场和位移场相互耦合的非线性热机械问题。计算。特别是，提出了一种新的 SORH 算法来研究轴对称非弹性结构。最后，进行了三个典型的数值实验，证实了我们提出的算法在模拟和预测异质结构宏观行为方面的有效性和正确性。该方法的主要特点是提出了一种基于变换场分析 (TFA) 的有效简化模型形式来分析非线性局部单元问题，并提出了一个考虑温度场和位移场相互耦合的非线性热机械问题。计算。特别是，提出了一种新的 SORH 算法来研究轴对称非弹性结构。最后，进行了三个典型的数值实验，证实了我们提出的算法在模拟和预测异质结构宏观行为方面的有效性和正确性。