{"title":"A dimensionless study of Functionally Graded Material membranes wrinkling using the Asymptotic Numerical Method","authors":"Siham Khalil , Oussama Elmhaia , Abdellah Hamdaoui , Bouazza Braikat , Heng Hu , Adnane Boukamel , Noureddine Damil","doi":"10.1016/j.ijsolstr.2025.113259","DOIUrl":null,"url":null,"abstract":"<div><div>In this work, by making dimensionless the equations of the variational problem governing the wrinkling of Functionally Graded Material (FGM) membranes under tension, we highlight five dimensionless parameters that control the appearance and disappearance of wrinkles. These parameters are related to the aspect ratios, the properties of the FGM membrane, and the applied loading. The other two parameters are related to the properties of the FGM membrane which represent the ratio between the Young’s moduli of the upper and lower surfaces of the FGM membrane, and <span><math><mi>p</mi></math></span> describes the variation of Young’s modulus across the thickness of the FGM membrane. The fifth parameter is related to the imposed loading and the geometric and material characteristics of the membrane. For this purpose, we will use the full expression for thin-membrane deformation without approximating membrane effects, employing an extended Föppl von Kármán (eFvK) model. The nonlinear equations will be solved numerically using the Asymptotic Numerical Method (ANM). Several numerical simulations are presented to study the effects of these dimensionless parameters on the appearance and disappearance of wrinkles.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"311 ","pages":"Article 113259"},"PeriodicalIF":3.4000,"publicationDate":"2025-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Solids and Structures","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0020768325000459","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this work, by making dimensionless the equations of the variational problem governing the wrinkling of Functionally Graded Material (FGM) membranes under tension, we highlight five dimensionless parameters that control the appearance and disappearance of wrinkles. These parameters are related to the aspect ratios, the properties of the FGM membrane, and the applied loading. The other two parameters are related to the properties of the FGM membrane which represent the ratio between the Young’s moduli of the upper and lower surfaces of the FGM membrane, and describes the variation of Young’s modulus across the thickness of the FGM membrane. The fifth parameter is related to the imposed loading and the geometric and material characteristics of the membrane. For this purpose, we will use the full expression for thin-membrane deformation without approximating membrane effects, employing an extended Föppl von Kármán (eFvK) model. The nonlinear equations will be solved numerically using the Asymptotic Numerical Method (ANM). Several numerical simulations are presented to study the effects of these dimensionless parameters on the appearance and disappearance of wrinkles.
期刊介绍：
The International Journal of Solids and Structures has as its objective the publication and dissemination of original research in Mechanics of Solids and Structures as a field of Applied Science and Engineering. It fosters thus the exchange of ideas among workers in different parts of the world and also among workers who emphasize different aspects of the foundations and applications of the field.
Standing as it does at the cross-roads of Materials Science, Life Sciences, Mathematics, Physics and Engineering Design, the Mechanics of Solids and Structures is experiencing considerable growth as a result of recent technological advances. The Journal, by providing an international medium of communication, is encouraging this growth and is encompassing all aspects of the field from the more classical problems of structural analysis to mechanics of solids continually interacting with other media and including fracture, flow, wave propagation, heat transfer, thermal effects in solids, optimum design methods, model analysis, structural topology and numerical techniques. Interest extends to both inorganic and organic solids and structures.
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