| Citation: | ZHU Xiaopeng, HUANG Jun, CHEN Lei, et al. Physical interpretation of mathematical homogenization method for thermomechanical problem[J]. Journal of Beijing University of Aeronautics and Astronautics, 2019, 45(11): 2139-2151. doi: 10.13700/j.bh.1001-5965.2019.0088(in Chinese)
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The mathematical expression of high-order mathematical homogenization method (MHM) is formulated by constructing decoupling form of each order perturbation for the thermomechanical problem of periodical composite structure, and it is converted into a matrix form by weighted residual method, which is convenient for use as standard finite element method. The elastic influence function and the heat influence function are respectively compared to the elastic virtual displacement and the thermal virtual displacement, and the physical interpretation of each order influence function and perturbation displacement are revealed by the self-balancing characteristics and dimensional analysis and geometric visualization. The second-order perturbation displacement is emphasized for the analysis of micro structure. The numerical results verify the correctness of high-order MHM matrix form and the analysis of physical interpretation.
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