A dimensionless study of Functionally Graded Material membranes wrinkling using the Asymptotic Numerical Method

IF 3.8 3区工程技术 Q1 MECHANICS International Journal of Solids and Structures Pub Date : 2025-04-01 Epub Date: 2025-02-08 DOI:10.1016/j.ijsolstr.2025.113259

Siham Khalil , Oussama Elmhaia , Abdellah Hamdaoui , Bouazza Braikat , Heng Hu , Adnane Boukamel , Noureddine Damil

{"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":3.8000,"publicationDate":"2025-04-01","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":"2025/2/8 0:00:00","PubModel":"Epub","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

p

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.

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

基于渐近数值方法的功能梯度材料膜起皱无量纲研究

在这项工作中，通过使控制功能梯度材料（FGM）膜在张力下起皱的变分问题的方程无因次化，我们突出了控制起皱出现和消失的五个无因次参数。这些参数与长径比、FGM膜的性能和施加的载荷有关。另外两个参数与FGM膜的特性有关，表示FGM膜上下表面的杨氏模量之比，p描述了杨氏模量在FGM膜厚度上的变化。第五个参数与施加的载荷以及膜的几何和材料特性有关。为此，我们将使用不近似膜效应的薄膜变形的完整表达式，采用扩展的Föppl von Kármán （eFvK）模型。采用渐近数值方法（ANM）对非线性方程进行数值求解。通过数值模拟研究了这些无量纲参数对褶皱产生和消失的影响。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文去求助

来源期刊

International Journal of Solids and Structures 物理-力学

CiteScore

6.70

自引率

8.30%

发文量

405

审稿时长

70 days

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.