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Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 929176, 16 pages
http://dx.doi.org/10.1155/2011/929176
Research Article

On Spatial Evolution of the Solution of a Nonstandard Problem in Linear Thermo-Microstretch Elasticity

Faculty of Mathematics, Alexandra Ioan Cuza University, 700506 Iasi, Romania

Received 3 May 2011; Accepted 17 June 2011

Academic Editor: Angelo Luongo

Copyright © 2011 Emilian Bulgariu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

An anisotropic and nonhomogeneous compressible linear thermo-microstretch elastic cylinder is subject to zero body loads and heat supply and zero lateral specific boundary conditions. The motion is induced by a time-dependent displacement, microrotation, microstretch, and temperature variation specified pointwise over the base. Further, the motion is constrained such that the displacement, microrotation, microstretch and temperature variation and their derivatives with respect to time at points in the cylinder and at a prescribed time are given in proportion to, but not identical with, their respective initial values. Two different cases for these proportional constants are treated. It is shown that certain integrals of the solution spatially evolve with respect to the axial variable. Conditions are derived that show that the integrals exhibit alternative behavior and in particular for the semi-infinite cylinder that there is either at least exponential growth or at most exponential decay.