Nonlocal theories for bending, buckling and vibration of beams

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.

authors

• Reddy, Junuthula

published proceedings

• INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE

altmetric score

• 1

author list (cited authors)

• Reddy, J. N.

citation count

• 1296

complete list of authors

• Reddy, JN

publication date

• February 2007

publisher

• Elsevier  Publisher

published in

• International Journal of Engineering Science  Journal

keywords

• Analytical Solutions
• Beam Theories
• Bending
• Buckling
• Free Vibration
• Nonlocal Elasticity

Digital Object Identifier (DOI)

• 10.1016/j.ijengsci.2007.04.004

start page

• 288

end page

• 307

volume

• 45

issue

• 2-8

URL

• http://dx.doi.org/10.1016/j.ijengsci.2007.04.004