期刊
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
卷 59, 期 11, 页码 2382-2399出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jmps.2011.06.008
关键词
Bending; Buckling; Modified couple stress theory; Natural vibration; Von Karman nonlinearity
资金
- National Science Foundation [CMMI-1030836, CMMI-1000790]
- Div Of Civil, Mechanical, & Manufact Inn
- Directorate For Engineering [1030836] Funding Source: National Science Foundation
A microstructure-dependent nonlinear Euler-Bernoulli 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 Karman geometric nonlinearity. The model contains a material length scale parameter that can capture the size effect in a functionally graded material, unlike the classical Euler-Bernoulli 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. (C) 2011 Elsevier Ltd. All rights reserved.
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