Microstructure-dependent couple stress theories of functionally graded beams

abstract

• A microstructure-dependent nonlinear EulerBernoulli and Timoshenko beam theories which account for through-thickness power-law variation of a two-constituent material are developed using the principle of virtual displacements. The formulation is based on a modified couple stress theory, power-law variation of the material, and the von Krmn geometric nonlinearity. The model contains a material length scale parameter that can capture the size effect in a functionally graded material, unlike the classical EulerBernoulli and Timoshenko beam theories. The influence of the parameter on static bending, vibration and buckling is investigated. The theoretical developments presented herein also serve to develop finite element models and determine the effect of the geometric nonlinearity and microstructure-dependent constitutive relations on post-buckling response. 2011 Elsevier Ltd. All rights reserved.

authors

• Reddy, Junuthula

published proceedings

• JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS

author list (cited authors)

• Reddy, J. N.

citation count

• 494

complete list of authors

• Reddy, JN

publication date

• November 2011

publisher

• Elsevier  Publisher

published in

• Journal of the Mechanics and Physics of Solids  Journal

keywords

• Bending
• Buckling
• Modified Couple Stress Theory
• Natural Vibration
• Von Karman Nonlinearity

Digital Object Identifier (DOI)

• 10.1016/j.jmps.2011.06.008

start page

• 2382

end page

• 2399

volume

• 59

issue

• 11

URL

• http://dx.doi.org/10.1016/j.jmps.2011.06.008