Bending and buckling of thin strain gradient elastic beams |
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| Authors: | KA Lazopoulos AK Lazopoulos |
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| Institution: | 1. School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, China;2. State Key Laboratory of Digital Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China;1. Department of Civil and Mechanical Engineering, University of Cassino and Southern Lazio, via G. Di Biasio 43, Cassino, FR 03043, Italy;2. Department of Structures for Engineering and Architecture, University of Naples Federico II, via Claudio 21, Naples 80125, Italy;3. Department of Mechanical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran |
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| Abstract: | Bending of strain gradient elastic thin beams is studied adopting Bernoulli-Euler principle. Simple linear strain gradient elastic theory with surface energy is employed. The governing beam equations with its boundary conditions are derived through a variational method. It turns out that new terms are introduced, indicating the importance of the cross-section area in bending of thin beams. Those terms are missing from the existing strain gradient beam theories. Those terms increase highly the stiffness of the thin beam. The buckling problem of the thin beams is also discussed. |
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