Zanaboni’s formulation of Saint-Venant’s principle extended to linear thermo-elasticity

Knops, R. J.

doi:10.1007/s10665-014-9712-7

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2017

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(2 citation statements)

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“…A subsequence, again denoted by a n+1 r , now may be extracted from (6.7) which for > 0 and sufficiently large n 0 , satisfies the condition 12) for all k ≥ 0. Here, s, r lie in the interval [0, r 0 ], and r 0 is given by (6.11).…”

Section: Monotone Sequencementioning

confidence: 99%

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Spatial decay in transient heat conduction for general elongated regions

Knops

Quintanilla

2017

Quart. Appl. Math.

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Zanaboni's procedure for establishing Saint-Venant's principle is extended to anisotropic homogeneous transient heat conduction on regions that are successively embedded in each other to become indefinitely elongated. No further geometrical restrictions are imposed. The boundary of each region is maintained at zero temperature apart from the common surface of intersection which is heated to the same temperature assumed to be of bounded time variation. Heat sources are absent. Subject to these conditions, the thermal energy, supposed bounded in each region, becomes vanishingly small in those parts of the regions sufficiently remote from the heated common surface. As with the original treatment, the proof involves certain monotone bounded sequences, and does not depend upon differential inequalities or the maximum principle. A definition is presented of an elongated region.

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Section: Monotone Sequencementioning

confidence: 99%

“…The general procedure is that originally devised by Zanaboni [19] but modified to incorporate certain simplications introduced in [14]. Linear thermoelasticity is similarly treated in [12].…”

Section: Introductionmentioning

confidence: 99%

Spatial decay in transient heat conduction for general elongated regions

Knops

Quintanilla

2017

Quart. Appl. Math.

View full text Add to dashboard Cite

show abstract

Zanaboni’s formulation of Saint-Venant’s principle extended to linear thermo-elasticity

Cited by 1 publication

References 10 publications

Spatial decay in transient heat conduction for general elongated regions

Spatial decay in transient heat conduction for general elongated regions

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