A finite element formulation of a nonclassical beam theory based on the Gurtin–Murdoch model for continua with deformable elastic surfaces is presented. The governing equations for thin and thick beams are used together with a weighted residual formulation to explicitly obtain the beam stiffness and mass matrices. Numerical solutions for selected test cases are compared with the analytical results available in literature for beam static deflections, natural frequencies, and buckling loads. The modified bending stiffness corresponding to the present model agrees closely with a recently reported rigorous solution. The maximum influence of surface energy effects is observed for cantilever beams. The finite element scheme provides an efficient tool to analyze, design, and predict the mechanical response of beam elements encountered in nanoelectromechanical systems and other nanoscale devices.
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e-mail: rajapaks@sfu.ca
e-mail: srikanth@mech.ubc.ca
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Finite Element Modeling of Beams With Surface Energy Effects
C. Liu,
C. Liu
Department of Mechanical Engineering,
University of British Columbia
, Vancouver, V6T 1Z4, Canada
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R. K. N. D. Rajapakse,
R. K. N. D. Rajapakse
Faculty of Applied Science,
e-mail: rajapaks@sfu.ca
Simon Fraser University
, Burnaby, V5A 1S6, Canada
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A. S. Phani
A. S. Phani
Department of Mechanical Engineering,
e-mail: srikanth@mech.ubc.ca
University of British Columbia
, Vancouver, V6T 1Z4, Canada
Search for other works by this author on:
C. Liu
Department of Mechanical Engineering,
University of British Columbia
, Vancouver, V6T 1Z4, Canada
R. K. N. D. Rajapakse
Faculty of Applied Science,
Simon Fraser University
, Burnaby, V5A 1S6, Canadae-mail: rajapaks@sfu.ca
A. S. Phani
Department of Mechanical Engineering,
University of British Columbia
, Vancouver, V6T 1Z4, Canadae-mail: srikanth@mech.ubc.ca
J. Appl. Mech. May 2011, 78(3): 031014 (10 pages)
Published Online: February 16, 2011
Article history
Received:
February 27, 2010
Revised:
December 28, 2010
Posted:
January 5, 2011
Published:
February 16, 2011
Online:
February 16, 2011
Connected Content
A correction has been published:
Erratum: “Finite Element Modeling of Beams With Surface Energy Effects” [Journal of Applied Mechanics, 2011, 78(3), p. 031014]
Citation
Liu, C., Rajapakse, R. K. N. D., and Phani, A. S. (February 16, 2011). "Finite Element Modeling of Beams With Surface Energy Effects." ASME. J. Appl. Mech. May 2011; 78(3): 031014. https://doi.org/10.1115/1.4003363
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