A unified analysis of a micro-beam,droplet and CNT ring adhered on a substrate:Calculation of variation with movable boundaries  

作　　者：Jian-Lin Liu Re Xia 

机构地区：[1]School of Pipeline and Civil Engineering, China University of Petroleum [2]School of Power and Mechanical Engineering, Wuhan University

出　　处：《Acta Mechanica Sinica》2013年第1期62-72,共11页力学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China (11272357 and 11102140);Doctoral Fund of Ministry of Education of China (200804251520 and 20110141120024);Natural Science Foundation of Shandong Province (ZR2009AQ006)

摘　　要：In this study, we developed a general method to analytically tackle a kind of movable boundary problem from the viewpoint of energy variation. Having grouped the adhesion of a micro-beam, droplet and carbon nanotube （CNT） ring on a substrate into one framework, we used the developed line of reasoning to investigate the adhesion behaviors of these systems. Based upon the derived governing equations and transversality conditions, explicit solutions involving the critical parameters and morphologies for the three systems are successfully obtained, and then the parameter analogies and common characteristics of them are thor- oughly investigated. The presented method has been verified via the concept of energy release rate in fracture mechanics. Our analyses provide a new approach for exploring the mechanism of different systems with similarities as well as for understanding the unity of nature. The analysis results may be beneficial for the design of nano-structured materi- als, and hold potential for enhancing their mechanical, chemical, optical and electronic properties.In this study, we developed a general method to analytically tackle a kind of movable boundary problem from the viewpoint of energy variation. Having grouped the adhesion of a micro-beam, droplet and carbon nanotube （CNT） ring on a substrate into one framework, we used the developed line of reasoning to investigate the adhesion behaviors of these systems. Based upon the derived governing equations and transversality conditions, explicit solutions involving the critical parameters and morphologies for the three systems are successfully obtained, and then the parameter analogies and common characteristics of them are thor- oughly investigated. The presented method has been verified via the concept of energy release rate in fracture mechanics. Our analyses provide a new approach for exploring the mechanism of different systems with similarities as well as for understanding the unity of nature. The analysis results may be beneficial for the design of nano-structured materi- als, and hold potential for enhancing their mechanical, chemical, optical and electronic properties.

关 键 词：Variational theory - Transversality condition Beam adhesion Droplet adhesion Carbon nanotube ring adhesion 

分 类 号：O35[理学—流体力学]