Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.ijengsci.2007.04.004
Title: Nonlocal theories for bending, buckling and vibration of beams
Authors: Reddy, J.N. 
Keywords: Analytical solutions
Beam theories
Bending
Buckling
Free vibration
Nonlocal elasticity
Issue Date: Feb-2007
Source: Reddy, J.N. (2007-02). Nonlocal theories for bending, buckling and vibration of beams. International Journal of Engineering Science 45 (2-8) : 288-307. ScholarBank@NUS Repository. https://doi.org/10.1016/j.ijengsci.2007.04.004
Abstract: Various available beam theories, including the Euler-Bernoulli, Timoshenko, Reddy, and Levinson beam theories, are reformulated using the nonlocal differential constitutive relations of Eringen. The equations of motion of the nonlocal theories are derived, and variational statements in terms of the generalized displacements are presented. Analytical solutions of bending, vibration and buckling are presented using the nonlocal theories to bring out the effect of the nonlocal behavior on deflections, buckling loads, and natural frequencies. The theoretical development as well as numerical solutions presented herein should serve as references for nonlocal theories of beams, plates, and shells. © 2007 Elsevier Ltd. All rights reserved.
Source Title: International Journal of Engineering Science
URI: http://scholarbank.nus.edu.sg/handle/10635/60898
ISSN: 00207225
DOI: 10.1016/j.ijengsci.2007.04.004
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