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Research Papers

Thermoelastodynamics in Transversely Isotropic Media With Scalar Potential Functions1

[+] Author and Article Information
Morteza Eskandari-Ghadi

Department of Engineering Science,
College of Engineering,
University of Tehran,
P.O. Box 11155-4563,
Tehran, Iran
e-mail: ghadi@ut.ac.ir

Mohammad Rahimian

Department of Civil Engineering,
College of Engineering,
University of Tehran,
P.O. Box 11155-4563,
Tehran, Iran
e-mail: rahimian@ut.ac.ir

Stein Sture

Department of Civil, Environmental,
and Architectural Engineering,
University of Colorado,
Boulder, CO 80309-0428
e-mail: stein.sture@colorado.edu

Maysam Forati

Department of Civil Engineering,
College of Engineering,
University of Tehran,
P.O. Box 11155-4563,
Tehran, Iran
e-mail: mforati@ut.ac.ir

1Dedicated to Morton E. Gurtin.

2Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received March 5, 2013; final manuscript received March 8, 2013; accepted manuscript posted May 7, 2013; published online September 16, 2013. Editor: Yonggang Huang.

J. Appl. Mech 81(2), 021013 (Sep 16, 2013) (7 pages) Paper No: JAM-13-1103; doi: 10.1115/1.4024417 History: Received March 05, 2013; Revised March 08, 2013; Accepted May 07, 2013

A complete set of potential functions consisting of three scalar functions is presented for coupled displacement-temperature equations of motion and heat equation for an arbitrary x3-convex domain containing a linear thermoelastic transversely isotropic material, where the x3-axis is parallel to the axis of symmetry of the material. The proof of the completeness theorem is based on a retarded logarithmic potential function, retarded Newtonian potential function, repeated wave equation, the extended Boggio's theorem for the transversely isotropic axially convex domain, and the existence of a solution for the heat equation. It is shown that the solution degenerates to a set of complete potential functions for elastodynamics and elastostatics under certain conditions. In a special case, the number of potential functions is reduced to one, and the required conditions are discussed. Another special case involves the rotationally symmetric configuration with respect to the axis of symmetry of the material.

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