{"title":"Asymptotic Model of a Piezoelectric Composite Beam","authors":"I. V. Andrianov, A. A. Kolpakov, L. Faella","doi":"10.1134/s0021894424020160","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>This paper presents a method of transforming from the three-dimensional piezoelastic problem for a composite material to the one-dimensional problem for a piezoelastic beam. This is done using the asymptotic homogenization technique based on the separation of fast and slow variables in the solution. A special feature of the problem is the presence of two small parameters, one of which characterizes the microstructure of the composite material, and the other defines the cross-sectional size. Homogenized relations describing the piezoelastic beam and fast correctors were obtained. Their joint use makes it possible to correctly describe the total stress-strain state of the original three-dimensional body. The proposed method is suitable for solving the three-dimensional problem of deformation of an extended body with an arbitrary periodic structure as well as for solving new problems (e.g., the torsion problem) that have no analogues in the theory of piezoelastic plates.</p>","PeriodicalId":608,"journal":{"name":"Journal of Applied Mechanics and Technical Physics","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Mechanics and Technical Physics","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1134/s0021894424020160","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper presents a method of transforming from the three-dimensional piezoelastic problem for a composite material to the one-dimensional problem for a piezoelastic beam. This is done using the asymptotic homogenization technique based on the separation of fast and slow variables in the solution. A special feature of the problem is the presence of two small parameters, one of which characterizes the microstructure of the composite material, and the other defines the cross-sectional size. Homogenized relations describing the piezoelastic beam and fast correctors were obtained. Their joint use makes it possible to correctly describe the total stress-strain state of the original three-dimensional body. The proposed method is suitable for solving the three-dimensional problem of deformation of an extended body with an arbitrary periodic structure as well as for solving new problems (e.g., the torsion problem) that have no analogues in the theory of piezoelastic plates.
期刊介绍：
Journal of Applied Mechanics and Technical Physics is a journal published in collaboration with the Siberian Branch of the Russian Academy of Sciences. The Journal presents papers on fluid mechanics and applied physics. Each issue contains valuable contributions on hypersonic flows; boundary layer theory; turbulence and hydrodynamic stability; free boundary flows; plasma physics; shock waves; explosives and detonation processes; combustion theory; multiphase flows; heat and mass transfer; composite materials and thermal properties of new materials, plasticity, creep, and failure.
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