A new inextensible theory of beam and plate deformation has been developed. For validation of this inextensible beam and plate theory, computational codes for the static and dynamic nonlinear beam and plate modal equations have been developed. The computations and experiments for static loading and deformation of a beam show that the inextensible theory produces results in excellent agreement with experiment. Also, a comparison of the inextensible theory for a plate with a static experiment is encouraging. Finally, a numerical study of dynamic deflection for an inextensible beam and plate has also been made. The results show a hysteresis dynamic response that depends on whether the excitation frequency is increasing or decreasing for the stiffness nonlinearity only or for the inertia nonlinearity only. The inertia nonlinear force has a significant effect on the dynamic response in the resonant frequency range.
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June 2014
Research-Article
Inextensible Beam and Plate Theory: Computational Analysis and Comparison With Experiment
Deman Tang,
Deman Tang
Research Scientist
Materials Science,
Duke University,
Durham, NC 27708-0300
e-mail: demant@duke.edu
Department of Mechanical Engineering and
Materials Science,
Duke University,
Box 90300, Hudson Hall
,Durham, NC 27708-0300
e-mail: demant@duke.edu
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Minghui Zhao,
Minghui Zhao
Bejing University of Technology
,Beijing 100124
, China
;
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Earl H. Dowell
Earl H. Dowell
1
William Holland Hall Professor
Materials Science,
Durham, NC 27708-0300
e-mail: dowell@ee.duke.edu
Department of Mechanical Engineering and
Materials Science,
Box 90300, Hudson Hall
,Durham, NC 27708-0300
e-mail: dowell@ee.duke.edu
1Corresponding author.
Search for other works by this author on:
Deman Tang
Research Scientist
Materials Science,
Duke University,
Durham, NC 27708-0300
e-mail: demant@duke.edu
Department of Mechanical Engineering and
Materials Science,
Duke University,
Box 90300, Hudson Hall
,Durham, NC 27708-0300
e-mail: demant@duke.edu
Minghui Zhao
Bejing University of Technology
,Beijing 100124
, China
;
Earl H. Dowell
William Holland Hall Professor
Materials Science,
Durham, NC 27708-0300
e-mail: dowell@ee.duke.edu
Department of Mechanical Engineering and
Materials Science,
Box 90300, Hudson Hall
,Durham, NC 27708-0300
e-mail: dowell@ee.duke.edu
1Corresponding author.
Manuscript received June 11, 2013; final manuscript received February 3, 2014; accepted manuscript posted February 11, 2014; published online February 28, 2014. Assoc. Editor: Glaucio H. Paulino.
J. Appl. Mech. Jun 2014, 81(6): 061009 (10 pages)
Published Online: February 28, 2014
Article history
Received:
June 11, 2013
Revision Received:
February 3, 2014
Accepted:
February 7, 2014
Citation
Tang, D., Zhao, M., and Dowell, E. H. (February 28, 2014). "Inextensible Beam and Plate Theory: Computational Analysis and Comparison With Experiment." ASME. J. Appl. Mech. June 2014; 81(6): 061009. https://doi.org/10.1115/1.4026800
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