Bending and stability analysis of gradient elastic beams |
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| Affiliation: | 1. General Department, School of Technology, Aristotle University of Thessaloniki, GR-54006 Thessaloniki, Greece;2. Department of Mechanical Engineering and Aeronautics, University of Patras, GR-26500 Patras, Greece;3. Structural Engineering Division, Department of Civil Engineering, University of Patras, GR-26500 Patras, Greece;1. Department of Architecture and Civil Engineering, City University of Hong Kong, Kowloon, Hong Kong, PR China;2. City University of Hong Kong Shenzhen Research Institute, Shenzhen 518057, PR China;3. Mechanical Engineering Department, Texas A&M University, College Station, TX 77843-3123, USA;1. College of Civil Engineering, Xi’an University of Architecture & Technology, Xi’an 710055, China;2. School of Civil Engineering and Architecture, Changsha University of Science and Technology, Changsha 410004, China;3. Department of Architectural Engineering, Logistic Engineering University of PLA, Chongqing 400041, China |
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| Abstract: | The problems of bending and stability of Bernoulli–Euler beams are solved analytically on the basis of a simple linear theory of gradient elasticity with surface energy. The governing equations of equilibrium are obtained by both a combination of the basic equations and a variational statement. The additional boundary conditions are obtained by both variational and weighted residual approaches. Two boundary value problems (one for bending and one for stability) are solved and the gradient elasticity effect on the beam bending response and its critical (buckling) load is assessed for both cases. It is found that beam deflections decrease and buckling load increases for increasing values of the gradient coefficient, while the surface energy effect is small and insignificant for bending and buckling, respectively. |
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