期刊
COMPOSITE STRUCTURES
卷 285, 期 -, 页码 -出版社
ELSEVIER SCI LTD
DOI: 10.1016/j.compstruct.2021.115091
关键词
Composites structures; Periodic media; Asymptotic homogenization; Boundary layer corrector; Edge effect
资金
- French National Association for Research and Technology (ANRT) [CIFRE 2019/1715]
The asymptotic homogenization method is commonly used in the multiscale analysis of periodic structures to achieve computational feasibility and efficiency. This paper proposes a post-processing scheme within a finite element framework for periodic linear elastic composite materials, which assesses the boundary layer effect and introduces a new general method for various boundary conditions. The efficiency, accuracy, and limitations of the proposed approach are studied on various numerical examples.
Asymptotic homogenization method is often used in multiscale analysis of periodic structures instead of conducting a full field heterogeneous analysis, in order to achieve computational feasibility and efficiency. When completed with a relocalization process, this method may provide relevant estimates to microscale fields within the material. Nevertheless, the construction of a solution near the boundaries remains beyond the capabilities of classical relocalization schemes due to the loss of periodicity in the vicinity of the boundaries. This paper proposes a post-processing scheme in order to conduct the relocalization step within a finite element framework for periodic linear elastic composite materials. It also assesses the boundary layer effect and a new general method, effective for various boundary conditions (Dirichlet, Neumann or mixed), is proposed based on the idea of computing corrective terms as solution of auxiliary problems on the unit-cell. These terms are finally added to the usual fields obtained from the relocalization process to obtain the corrected solution near the boundaries. The efficiency, accuracy and limitation of the proposed approach are studied on various numerical examples.
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