{"title":"利用 LDTM 和非局部弹性理论研究 CNT 的大弯曲行为","authors":"B.R.K.L.L. Mawphlang, P.K. Patra","doi":"10.1016/j.ijnonlinmec.2024.104828","DOIUrl":null,"url":null,"abstract":"<div><p>The general expressions for vertical deflection, horizontal displacement, and strain energy in a bent cantilevered carbon nanotube (CNT) are derived herein under a uniformly distributed load. This derivation employs nonlocal elasticity theory, crucial for understanding nanoscale mechanics due to size effects, and accounts for the nonlinear relationship between bending curvature and deflection under large bending conditions, a novel contribution. In the limiting cases, our expressions for large bending give the corresponding expressions reported in the literature for small bending. Additionally, we introduce the Laplace-Differential Transformation Method (LDTM) for the first time, providing efficient solutions to explore the influence of parameters like aspect ratio and small-scale factors on CNT bending behavior. Comparison with the analytical method validates the accuracy and efficacy of LDTM, offering a rapid solution for nonlinear equations. Our findings reveal that strain energy deviates more prominently from quadratic behavior in CNTs with high aspect ratios, while small-scale parameters have a pronounced effect on CNTs with smaller aspect ratios. These results will be relevant to designing and applying the nanoscale-sized cantilevered CNTs used in MEMs/NEMs.</p></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":null,"pages":null},"PeriodicalIF":2.8000,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Study of the large bending behavior of CNTs using LDTM and nonlocal elasticity theory\",\"authors\":\"B.R.K.L.L. Mawphlang, P.K. Patra\",\"doi\":\"10.1016/j.ijnonlinmec.2024.104828\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The general expressions for vertical deflection, horizontal displacement, and strain energy in a bent cantilevered carbon nanotube (CNT) are derived herein under a uniformly distributed load. This derivation employs nonlocal elasticity theory, crucial for understanding nanoscale mechanics due to size effects, and accounts for the nonlinear relationship between bending curvature and deflection under large bending conditions, a novel contribution. In the limiting cases, our expressions for large bending give the corresponding expressions reported in the literature for small bending. Additionally, we introduce the Laplace-Differential Transformation Method (LDTM) for the first time, providing efficient solutions to explore the influence of parameters like aspect ratio and small-scale factors on CNT bending behavior. Comparison with the analytical method validates the accuracy and efficacy of LDTM, offering a rapid solution for nonlinear equations. Our findings reveal that strain energy deviates more prominently from quadratic behavior in CNTs with high aspect ratios, while small-scale parameters have a pronounced effect on CNTs with smaller aspect ratios. These results will be relevant to designing and applying the nanoscale-sized cantilevered CNTs used in MEMs/NEMs.</p></div>\",\"PeriodicalId\":50303,\"journal\":{\"name\":\"International Journal of Non-Linear Mechanics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.8000,\"publicationDate\":\"2024-07-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Non-Linear Mechanics\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0020746224001938\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Non-Linear Mechanics","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0020746224001938","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
Study of the large bending behavior of CNTs using LDTM and nonlocal elasticity theory
The general expressions for vertical deflection, horizontal displacement, and strain energy in a bent cantilevered carbon nanotube (CNT) are derived herein under a uniformly distributed load. This derivation employs nonlocal elasticity theory, crucial for understanding nanoscale mechanics due to size effects, and accounts for the nonlinear relationship between bending curvature and deflection under large bending conditions, a novel contribution. In the limiting cases, our expressions for large bending give the corresponding expressions reported in the literature for small bending. Additionally, we introduce the Laplace-Differential Transformation Method (LDTM) for the first time, providing efficient solutions to explore the influence of parameters like aspect ratio and small-scale factors on CNT bending behavior. Comparison with the analytical method validates the accuracy and efficacy of LDTM, offering a rapid solution for nonlinear equations. Our findings reveal that strain energy deviates more prominently from quadratic behavior in CNTs with high aspect ratios, while small-scale parameters have a pronounced effect on CNTs with smaller aspect ratios. These results will be relevant to designing and applying the nanoscale-sized cantilevered CNTs used in MEMs/NEMs.
期刊介绍:
The International Journal of Non-Linear Mechanics provides a specific medium for dissemination of high-quality research results in the various areas of theoretical, applied, and experimental mechanics of solids, fluids, structures, and systems where the phenomena are inherently non-linear.
The journal brings together original results in non-linear problems in elasticity, plasticity, dynamics, vibrations, wave-propagation, rheology, fluid-structure interaction systems, stability, biomechanics, micro- and nano-structures, materials, metamaterials, and in other diverse areas.
Papers may be analytical, computational or experimental in nature. Treatments of non-linear differential equations wherein solutions and properties of solutions are emphasized but physical aspects are not adequately relevant, will not be considered for possible publication. Both deterministic and stochastic approaches are fostered. Contributions pertaining to both established and emerging fields are encouraged.