Journal
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
Volume 82, Issue -, Pages 159-177Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijengsci.2014.05.006
Keywords
Beams; Eringen's differential model; Material length scales; Finite element models; Numerical results
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Funding
- Texas A&M University at Qatar
- Tunisian Ministry of Higher Education and Scientific Research
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The primary objective of this paper is two-fold: (a) to formulate the governing equations of the Euler-Bernoulli and Timoshenko beams that account for moderate rotations (more than what is included in the conventional von Karman strains) and material length scales based on Eringen's nonlocal differential model, and (b) develop the nonlinear finite element models of the equations. The governing equations of the Euler-Bernoulli and Timoshenko beams are derived using the principle of virtual displacements, wherein the Eringen's nonlocal differential model and modified von Karman nonlinear strains are taken into account. Finite element models of the resulting equations are developed, and numerical results are presented for various boundary conditions, showing the effect of the nonlocal parameter on the deflections. (C) 2014 Elsevier Ltd. All rights reserved.
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