On the stability of elastic annular rods |
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| Affiliation: | 1. School of Mechanical Engineering, Xiangtan University, Hunan 411105, China;2. Foshan Green Intelligent Manufacturing Research Institute of Xiangtan University, Guangdong 528311, China;3. Department of Engineering Mechanics, Hohai University, Nanjing 210098, China;4. School of Civil Engineering, Chongqing University, Chongqing 400044, China;5. Jiangsu Key Laboratory of Engineering Mechanics, School of Civil Engineering, Southeast University, Nanjing, Jiangsu 210096, China;1. Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA, USA;2. Department of Chemistry, Emory University, Atlanta, GA, USA |
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| Abstract: | The stability of equilibrium of non-linearly elastic rods, whose deformations obey the classical Kirchhoff’s equations, is considered. A variational formulation of the equilibrium problem is given, and the equilibrium equations for infinitesimal deformations superimposed to a finite transformation of a rod are deduced. The stability of annular rings, in which the twisting strain is non-null, is investigated by study of the second variation of the energy functional. |
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