{"title":"Growth of an Elastic Rod Perfectly Bonded to a von Kármán Elastic Surface","authors":"Akarsh Raj, Animesh Pandey, Anurag Gupta","doi":"10.1007/s10659-024-10082-9","DOIUrl":null,"url":null,"abstract":"<div><p>An elastic rod is perfectly bonded to a von Kármán elastic plate such that, except for a relative twist, no relative displacements are allowed between the rod and the plate. The deformation of the confined rod is strongly coupled to that of the flexible environment to which it has to necessarily confirm. A framework is developed where, for a given distribution of growth strains in the rod, the shape as well as the internal forces and the internal moments of the rod-plate system can be determined. The nature of mechanical interaction between the rod and the plate is discussed in detail. The boundary-value-problems, to be solved for a scalar stress function and a scalar transverse displacement field, both piecewise-smooth in the plate domain, include in-plane strain compatibility conditions and transverse force equilibrium equations on, and away from, the curve of rod-plate intersection.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"156 3","pages":"1015 - 1044"},"PeriodicalIF":1.8000,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Elasticity","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s10659-024-10082-9","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
An elastic rod is perfectly bonded to a von Kármán elastic plate such that, except for a relative twist, no relative displacements are allowed between the rod and the plate. The deformation of the confined rod is strongly coupled to that of the flexible environment to which it has to necessarily confirm. A framework is developed where, for a given distribution of growth strains in the rod, the shape as well as the internal forces and the internal moments of the rod-plate system can be determined. The nature of mechanical interaction between the rod and the plate is discussed in detail. The boundary-value-problems, to be solved for a scalar stress function and a scalar transverse displacement field, both piecewise-smooth in the plate domain, include in-plane strain compatibility conditions and transverse force equilibrium equations on, and away from, the curve of rod-plate intersection.
一根弹性杆与一块 von Kármán 弹性板完美地结合在一起，除了相对扭转之外，杆与板之间不允许有任何相对位移。受限杆的变形与它必须确认的柔性环境的变形密切相关。我们建立了一个框架，在此框架下，对于杆中给定的生长应变分布，可以确定杆-板系统的形状、内力和内力矩。详细讨论了杆和板之间机械相互作用的性质。要解决的边界值问题是标量应力函数和标量横向位移场，两者在板域内都是片状光滑的，包括板内应变相容条件和杆-板交汇曲线上以及远离杆-板交汇曲线的横向力平衡方程。
期刊介绍：
The Journal of Elasticity was founded in 1971 by Marvin Stippes (1922-1979), with its main purpose being to report original and significant discoveries in elasticity. The Journal has broadened in scope over the years to include original contributions in the physical and mathematical science of solids. The areas of rational mechanics, mechanics of materials, including theories of soft materials, biomechanics, and engineering sciences that contribute to fundamental advancements in understanding and predicting the complex behavior of solids are particularly welcomed. The role of elasticity in all such behavior is well recognized and reporting significant discoveries in elasticity remains important to the Journal, as is its relation to thermal and mass transport, electromagnetism, and chemical reactions. Fundamental research that applies the concepts of physics and elements of applied mathematical science is of particular interest. Original research contributions will appear as either full research papers or research notes. Well-documented historical essays and reviews also are welcomed. Materials that will prove effective in teaching will appear as classroom notes. Computational and/or experimental investigations that emphasize relationships to the modeling of the novel physical behavior of solids at all scales are of interest. Guidance principles for content are to be found in the current interests of the Editorial Board.
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