周期复合材料结构高阶多尺度方法的数值精度提高策略

doi:10.12288/szjs.s2021-0808

数值计算与计算机应用 ›› 2023, Vol. 44 ›› Issue (1): 12-24.DOI: 10.12288/szjs.s2021-0808

• 论文 • 上一篇

周期复合材料结构高阶多尺度方法的数值精度提高策略

董灏¹, 崔俊芝², 聂玉峰³

1. 西安电子科技大学数学与统计学院, 信息与计算科学系, 西安 710071;
2. 中国科学院数学与系统科学研究院, 计算数学与科学工程计算研究所, 北京 100190;
3. 西北工业大学数学与统计学院, 计算科学系, 西安 710129

收稿日期:2021-11-18 发布日期:2023-03-16
基金资助:
国家自然科学基金（12001414）；陕西省科学技术协会青年人才托举计划项目（20220506）；西安市科学技术协会青年人才托举计划项目（095920221338）；中央高校基本科研业务费（JB210702）和新材料力学理论与应用湖北省重点实验室（武汉理工大学）开放课题（WUT-TAM202104）资助.

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董灏, 崔俊芝, 聂玉峰. 周期复合材料结构高阶多尺度方法的数值精度提高策略[J]. 数值计算与计算机应用, 2023, 44(1): 12-24.

Dong Hao, Cui Junzhi, Nie Yufeng. THE IMPROVEMENT STRATEGY OF NUMERICAL ACCURACY OF HIGH-ORDER MULTI-SCALE METHOD FOR PERIODIC COMPOSITE STRUCTURES[J]. Journal on Numerica Methods and Computer Applications, 2023, 44(1): 12-24.

THE IMPROVEMENT STRATEGY OF NUMERICAL ACCURACY OF HIGH-ORDER MULTI-SCALE METHOD FOR PERIODIC COMPOSITE STRUCTURES

Dong Hao¹, Cui Junzhi², Nie Yufeng³

1. Department of Information and Computing Science, School of Mathematics and Statistics, Xidian University, Xi'an 710071, China;
2. Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100190, China;
3. Department of Computing Science, School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710129, China

Received:2021-11-18 Published:2023-03-16

高阶多尺度方法在计算数学、计算力学和计算材料学等领域得到了广泛的应用，为了进一步挖掘高阶多尺度方法的计算潜力，本文结合单胞边界条件优化选择和边界层构造，提出了一种高阶多尺度方法的数值精度提高策略，并给出了施加数值精度提高策略的高阶多尺度方法的误差分析.然后，建立了周期复合材料结构弹性力学问题具有数值精度提高策略的新的多尺度数值算法.最后，通过对周期复合材料结构弹性力学问题的模拟，验证了所提出数值精度提高策略的有效性和最优的数值精度.

关键词： 高阶多尺度方法, 数值精度, 边界层构造, 周期复合材料结构

The high-order multi-scale method has been widely used in the fields of computational mathematics, computational mechanics and computational materials, etc. In order to further tap the computational potential of the high-order multi-scale method, this study presents an advanced strategy for the numerical accuracy improvement of the high-order multi-scale method, which combined with the optimal selection of unit cell boundary conditions and the construction of boundary layer. Furthermore, the error analysis of high-order multiscale method with improvement strategy of numerical accuracy is derived. Afterwards, the corresponding multi-scale numerical algorithm with improvement strategy is brought forward for the elastic problems of periodic composite structures at length. Finally, the effectiveness and optimal numerical accuracy of the proposed strategy are verified by simulating the elastic problems of periodic composite structures.

Key words: high-order multi-scale method, numerical accuracy, boundary layer establishment, periodic composite structures

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周期复合材料结构高阶多尺度方法的数值精度提高策略

THE IMPROVEMENT STRATEGY OF NUMERICAL ACCURACY OF HIGH-ORDER MULTI-SCALE METHOD FOR PERIODIC COMPOSITE STRUCTURES

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