OPTIMAL TEMPERATURE PATHS FOR THERMORHEOLOGICALLY SIMPLE VISCOELASTIC MATERIALS WITH CONSTANT POISSON'S RATIO ARE CANONICAL

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 th...

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Veröffentlicht in:	Quarterly of applied mathematics 1984-01, Vol.41 (4), p.457-460
Hauptverfasser:	GURTIN, MORTON E., MURPHY, LEA F.
Format:	Artikel
Sprache:	eng
Schlagworte:	Boundary conditions Exact sciences and technology Fundamental areas of phenomenology (including applications) Mathematical constants Mathematical functions Physics Poisson ratio Shear stress Solid mechanics Static elasticity (thermoelasticity...) Structural and continuum mechanics Temperature distribution Thermal stress
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container_title	Quarterly of applied mathematics
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creator	GURTIN, MORTON E. MURPHY, LEA F.
description	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 θ(t), 0 ≤ t ≤ tf, which belong to a given function class, is there one which renders a given stress measure a minimum at time tf. We show that a resulting optimal path θ(t) (if it exists) is canonical: θ(t) is independent of the shape of the body and of the particular homogeneous boundary conditions.
doi_str_mv	10.1090/qam/724056
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In particular, we consider the following optimization problem: of all temperature paths θ(t), 0 ≤ t ≤ tf, which belong to a given function class, is there one which renders a given stress measure a minimum at time tf. 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In particular, we consider the following optimization problem: of all temperature paths θ(t), 0 ≤ t ≤ tf, which belong to a given function class, is there one which renders a given stress measure a minimum at time tf. 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In particular, we consider the following optimization problem: of all temperature paths θ(t), 0 ≤ t ≤ tf, which belong to a given function class, is there one which renders a given stress measure a minimum at time tf. We show that a resulting optimal path θ(t) (if it exists) is canonical: θ(t) is independent of the shape of the body and of the particular homogeneous boundary conditions.</abstract><cop>Providence, RI</cop><pub>Brown University</pub><doi>10.1090/qam/724056</doi><tpages>4</tpages><oa>free_for_read</oa></addata></record>
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source	American Mathematical Society Publications (Freely Accessible); Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; JSTOR Mathematics & Statistics; Jstor Complete Legacy; American Mathematical Society Journals
subjects	Boundary conditions Exact sciences and technology Fundamental areas of phenomenology (including applications) Mathematical constants Mathematical functions Physics Poisson ratio Shear stress Solid mechanics Static elasticity (thermoelasticity...) Structural and continuum mechanics Temperature distribution Thermal stress
title	OPTIMAL TEMPERATURE PATHS FOR THERMORHEOLOGICALLY SIMPLE VISCOELASTIC MATERIALS WITH CONSTANT POISSON'S RATIO ARE CANONICAL
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