Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Optimal temperature paths for thermorheologically simple viscoelastic materials with constant Poisson's ratio are canonical

Authors: Morton E. Gurtin and Lea F. Murphy
Journal: Quart. Appl. Math. 41 (1984), 457-460
MSC: Primary 73U05
DOI: https://doi.org/10.1090/qam/724056
MathSciNet review: 724056
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Abstract: In this note we discuss the thermal stress problem for a thermorheologically-simple linearly-viscoelastic body, subjected to a spatially-uniform temperature field and homogeneous boundary conditions, assuming that Poisson's ratio is constant and inertia negligible. In particular, we consider the following optimization problem: of all temperature paths $ \theta (t), 0 \le t \le {t_f}$, which belong to a given function class, is there one which renders a given stress measure a minimum at time $ {t_f}$. We show that a resulting optimal path $ \theta \left( t \right)$ (if it exists) is canonical: $ \theta \left( t \right)$ is independent of the shape of the body and of the particular homogeneous boundary conditions.

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DOI: https://doi.org/10.1090/qam/724056
Article copyright: © Copyright 1984 American Mathematical Society

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