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A Constraint on the Consistence of Transverse Shear Strain Energy in the Higher-Order Shear Deformation Theories of Elastic Plates

[+] Author and Article Information
Guangyu Shi

e-mail: shi_guangyu@163.com

Xiaodan Wang

e-mail: guozhenshile@126.com
Department of Mechanics,
Tianjin University,
Tianjin 300072, China

1 Corresponding author.

Manuscript received Febraury 19, 2010; final manuscript received January 15, 2012; accepted manuscript posted October 8, 2012; published online May 16, 2013. Assoc. Editor: Prof. Krishna Garikipati.

J. Appl. Mech 80(4), 044501 (May 16, 2013) (9 pages) Paper No: JAM-10-1048; doi: 10.1115/1.4007790 History: Received February 19, 2010; Revised January 15, 2012; Accepted October 08, 2012

This paper studies how to improve the third-order shear deformation theories of isotropic plates, which is a question raised by late Reissner in 1985 (ASME Appl. Mech. Rev., 38, pp.1453–1464). It is demonstrated in this paper that a proper displacement field with the higher-order shear deformations given by the method of displacement assumption should satisfy the constraint on the consistence of the transverse shear strain energy a priori in addition to the traction conditions on plate surfaces. This additional constraint on the assumed displacement fields with the higher-order shear deformations is in line with Love's criterion of the consistent first approximation to the strain energy wherein the transverse shear strain energy is included. The constraint on the consistence of the transverse shear strain energy is physically similar to the requirement for the use of the shear coefficients in the first-order shear deformation plate theories proposed by Reissner and Mindlin, respectively. A procedure to improve the assumed displacement field with the third-order shear deformations is presented. The present study shows that the various displacement fields with the simple third-order shear deformations would be identical when the constraint on the consistence of the transverse shear strain energy is enforced.

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References

Figures

Grahic Jump Location
Fig. 1

The equilibrium of an incremental beam segment in terms of generalized transverse force

Grahic Jump Location
Fig. 2

The shear force distribution along a cantilevered beam given by Bickford's beam theory

Grahic Jump Location
Fig. 3

The shear force distribution along a cantilevered beam given by Shi and Voyiadjis

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