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| A novel unit cell boundary condition of mathematical homogenization method for periodical composite structure |
| Received:December 27, 2018 Revised:May 30, 2019 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx20181227001 |
| KeyWord:periodical composite structure mathematical homogenization method boundary condition potential energy functional |
| Author | Institution |
| 朱晓鹏 |
安徽华电工程咨询设计有限公司, 合肥 |
| 陈磊 |
北京航空航天大学 航空科学与工程学院, 北京 ;北京航空航天大学合肥创新研究院, 合肥 |
| 黄俊 |
北京航空航天大学 航空科学与工程学院, 北京 ;北京航空航天大学合肥创新研究院, 合肥 |
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| Abstract: |
| Mathematical homogenization method (MHM) is one of the most effective methods for dealing with periodical structures,and its calculation accuracy and efficiency largely depend on the rationality of the unit cell boundary conditions which directly determines the accuracy of influence functions and perturbation displacements.In this paper,the influence function is treated as a virtual displacement firstly,and the real boundary conditions of a unit cell in the structure are obtained.The results show that clamped boundary condition is not fit as a boundary condition of a unit cell for a two-dimensional periodical structure.Secondly,for a two-dimension periodical structure,a super unit cell periodical boundary condition is proposed which effectively improves calculation accuracy of the influence functions and the virtual potential energy functional corresponding to the virtual displacement is proposed to verify the validity of the super unit cell's periodical boundary condition.Finally,numerical analysis is utilized to verify the accuracy of the mathematical homogenization method in the case of a super unit cell boundary condition and the necessity of second-order perturbation is emphasized. |
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