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Research Papers

The 2011 Koiter Lecture: The Simple Logic of Classical Nonlinear Thermodynamic Shell Theory

[+] Author and Article Information
J. G. Simmonds

 University of Virginia, Charlottesville, VA 22904-4742jgs@virginia.edu

J. Appl. Mech 79(4), 041005 (May 16, 2012) (5 pages) doi:10.1115/1.4005536 History: Received July 06, 2011; Revised July 24, 2011; Posted January 25, 2012; Published May 16, 2012

A classical nonlinear thermodynamic theory of elastic shells is derived by specializing the three-dimensional equations of motion and the second law of thermodynamics to a very general, shell-like body. No assumptions are made on how unknowns vary through the thickness. Extensional and bending strains are derived from the equations of motion via the principle of virtual power. The Coleman-Noll procedure plus the second law applied to an assumed form of the first law leads to constitutive relations plus reduced forms of the first and second laws. To avoid potential ill conditioning, a Legendre-Fenchel transformation is used to define a mixed-energy density, the logical place to impose the constitutive Kirchhoff hypothesis, if desired, because such an energy density rests, ultimately, on experiments. The Ladevèze-Pécastaings treatment of three-dimensional edge effects to obtain accurate two-dimensional solutions is discussed.

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Copyright © 2012 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 2

Koiter, the author, and Koiter’s wife

Grahic Jump Location
Figure 1

Geometry (courtesy of Will Crosby)

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