Two-scale convergence analysis and numerical simulation for periodic Kirchhoff plates
Homogenization analysis methods provide a high-efficiency tool to address periodic structures. However, the popular Asymptotic Homogenization Method (AHM) cannot be directly applied to the homogenization of periodic plate structures due to less periodicity in the bending deformation direction. In th...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-02-01
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| Series: | Heliyon |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2405844025003809 |
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| author | Zhiwei Huang Xiaomiao Zeng Chen Wang Chongren Liu |
| author_facet | Zhiwei Huang Xiaomiao Zeng Chen Wang Chongren Liu |
| author_sort | Zhiwei Huang |
| collection | DOAJ |
| description | Homogenization analysis methods provide a high-efficiency tool to address periodic structures. However, the popular Asymptotic Homogenization Method (AHM) cannot be directly applied to the homogenization of periodic plate structures due to less periodicity in the bending deformation direction. In this paper, we propose a two-scale asymptotic analysis technique to cope with the bending problem of periodic thin plates. By ignoring the normal strains along the thickness direction and using the Kirchhoff plate theory, the three-dimensional structure problem is transformed as a two-dimensional periodic plate problem by a fourth-order partial differential equation with periodic coefficients. Besides, the well-posedness analysis of the PDE is verified by the Lax-Milgram theorem, and the reasonability of the two-scale asymptotic expansion solution by the AHM is mathematically verified through the proof of two-scale convergence. Finally, numerical experiments verify the availability and accuracy of the proposed homogenization method for periodic Kirchhoff plates. |
| format | Article |
| id | doaj-art-896a368ca1bd437d821efb4f3accff88 |
| institution | Kabale University |
| issn | 2405-8440 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Heliyon |
| spelling | doaj-art-896a368ca1bd437d821efb4f3accff882025-01-29T05:01:30ZengElsevierHeliyon2405-84402025-02-01113e42000Two-scale convergence analysis and numerical simulation for periodic Kirchhoff platesZhiwei Huang0Xiaomiao Zeng1Chen Wang2Chongren Liu3AVIC General Huanan Aircraft Industry Co. Ltd., Zhuhai 519040, China; School of Aeronautic Science and Engineering, Beihang University (BUAA), Beijing 100083, China; Corresponding author. AVIC General Huanan Aircraft Industry Co. Ltd., Zhuhai 519040, China.AVIC General Huanan Aircraft Industry Co. Ltd., Zhuhai 519040, ChinaAVIC General Huanan Aircraft Industry Co. Ltd., Zhuhai 519040, ChinaAVIC General Huanan Aircraft Industry Co. Ltd., Zhuhai 519040, ChinaHomogenization analysis methods provide a high-efficiency tool to address periodic structures. However, the popular Asymptotic Homogenization Method (AHM) cannot be directly applied to the homogenization of periodic plate structures due to less periodicity in the bending deformation direction. In this paper, we propose a two-scale asymptotic analysis technique to cope with the bending problem of periodic thin plates. By ignoring the normal strains along the thickness direction and using the Kirchhoff plate theory, the three-dimensional structure problem is transformed as a two-dimensional periodic plate problem by a fourth-order partial differential equation with periodic coefficients. Besides, the well-posedness analysis of the PDE is verified by the Lax-Milgram theorem, and the reasonability of the two-scale asymptotic expansion solution by the AHM is mathematically verified through the proof of two-scale convergence. Finally, numerical experiments verify the availability and accuracy of the proposed homogenization method for periodic Kirchhoff plates.http://www.sciencedirect.com/science/article/pii/S2405844025003809Kirchhoff plateAsymptotic analysisPartial differential equationPeriodicTwo-scale convergence method |
| spellingShingle | Zhiwei Huang Xiaomiao Zeng Chen Wang Chongren Liu Two-scale convergence analysis and numerical simulation for periodic Kirchhoff plates Heliyon Kirchhoff plate Asymptotic analysis Partial differential equation Periodic Two-scale convergence method |
| title | Two-scale convergence analysis and numerical simulation for periodic Kirchhoff plates |
| title_full | Two-scale convergence analysis and numerical simulation for periodic Kirchhoff plates |
| title_fullStr | Two-scale convergence analysis and numerical simulation for periodic Kirchhoff plates |
| title_full_unstemmed | Two-scale convergence analysis and numerical simulation for periodic Kirchhoff plates |
| title_short | Two-scale convergence analysis and numerical simulation for periodic Kirchhoff plates |
| title_sort | two scale convergence analysis and numerical simulation for periodic kirchhoff plates |
| topic | Kirchhoff plate Asymptotic analysis Partial differential equation Periodic Two-scale convergence method |
| url | http://www.sciencedirect.com/science/article/pii/S2405844025003809 |
| work_keys_str_mv | AT zhiweihuang twoscaleconvergenceanalysisandnumericalsimulationforperiodickirchhoffplates AT xiaomiaozeng twoscaleconvergenceanalysisandnumericalsimulationforperiodickirchhoffplates AT chenwang twoscaleconvergenceanalysisandnumericalsimulationforperiodickirchhoffplates AT chongrenliu twoscaleconvergenceanalysisandnumericalsimulationforperiodickirchhoffplates |