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Computable estimates of the modeling error related to Kirchhoff-Love plate model


Repin, S I; Sauter, S (2010). Computable estimates of the modeling error related to Kirchhoff-Love plate model. Analysis and Applications, 8(4):409-442.

Abstract

The Kirchhoff-Love plate model is a widely used in the
analysis of thin elastic plates. It is well known that Kirchhoff-Love solutions
can be viewed as certain limits of displacements and stresses for
elastic plates where the thickness tends to zero. In this paper, we consider
the problem from a different point of view and derive computable
upper bounds of the difference between the exact three-dimensional solution
and a solution computed by using the Kirchhoff-Love hypotheses.
This estimate is valid for any value of the thickness parameter.
In combination with a posteriori error estimates for approximation errors,
this estimate allows the direct measurement of both, approximation
and modeling errors, encompassed in a numerical solution of the
Kirchhoff-Love model. We prove that the upper bound possess necessary
asymptotic properties and, therefore, does not deteriorate as the
thickness tends to zero.

Abstract

The Kirchhoff-Love plate model is a widely used in the
analysis of thin elastic plates. It is well known that Kirchhoff-Love solutions
can be viewed as certain limits of displacements and stresses for
elastic plates where the thickness tends to zero. In this paper, we consider
the problem from a different point of view and derive computable
upper bounds of the difference between the exact three-dimensional solution
and a solution computed by using the Kirchhoff-Love hypotheses.
This estimate is valid for any value of the thickness parameter.
In combination with a posteriori error estimates for approximation errors,
this estimate allows the direct measurement of both, approximation
and modeling errors, encompassed in a numerical solution of the
Kirchhoff-Love model. We prove that the upper bound possess necessary
asymptotic properties and, therefore, does not deteriorate as the
thickness tends to zero.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2010
Deposited On:22 Sep 2011 08:27
Last Modified:26 Jan 2017 08:49
Publisher:World Scientific Publishing
ISSN:0219-5305
Publisher DOI:https://doi.org/10.1142/S0219530510001709

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