Buckling of a twisted and compressed rod |
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| Affiliation: | 1. School of Mathematical Sciences, Xiamen University, Xiamen Fujian, 361005, China;2. Department of Civil Engineering, Xiamen University, Xiamen Fujian, 361005, China;3. Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computation, Xiamen University, Xiamen Fujian, 361005, China;1. State Key Laboratory of Advanced Electromagnetic Engineering and Technology, Huazhong University of Science and Technology, Wuhan 430074, China;2. Electric Power Security and High Efficiency Laboratory, Huazhong University of Science and Technology, Wuhan 430074, China;3. State Grid Sichuan ELectric Power Company Technical Training Center, Chengdu 610072, China;1. DICEAA, Dipartimento di Ingegneria Civile, Edile-Architettura e Ambientale, University of L’Aquila, 67100 L’Aquila, Italy;2. International Center M&MOCS “Mathematics and Mechanics of Complex System”, University of L’Aquila, Palazzo Caetani, Via San Pasquale snc, Cisterna di Latina, Italy |
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| Abstract: | We consider the problem of determining the stability boundary for an elastic rod under thrust and torsion. The constitutive equations of the rod are such that both shear of the cross-section and compressibility of the rod axis are considered. The stability boundary is determined from the bifurcation points of a single nonlinear second order differential equation that is obtained by using the first integrals of the equilibrium equations. The type of bifurcation is determined for parameter values. It is shown that the bifurcating branch is the branch with minimal energy. Finally, by using the first integral, the solution for one specific dependent variable is expressed in terms of elliptic integrals. The solution pertaining to the complete set of equilibrium equations is obtained by numerical integration. |
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