Date
2020-11-16Subject
510 Mathematics 620 Engineering Kirchhoff-Love plate theoryEinschlussGrenzflächeRissEnergieRissausbreitungBruchmechanikMetadata
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Aufsatz
First-Order Shape Derivative of the Energy for Elastic Plates with Rigid Inclusions and Interfacial Cracks
Abstract
Within the framework of Kirchhoff–Love plate theory, we analyze a variational model for elastic plates with rigid inclusions and interfacial cracks. The main feature of the model is a fully coupled nonpenetration condition that involves both the normal component of the longitudinal displacements and the normal derivative of the transverse deflection of the crack faces. Without making any artificial assumptions on the crack geometry and shape variation, we prove that the first-order shape derivative of the potential deformation energy is well defined and provide an explicit representation for it. The result is applied to derive the Griffith formula for the energy release rate associated with crack extension.
Citation
In: Applied Mathematics & Optimization Volume 84 / Issue 3 (2020-11-16) , S. 2775-2802 ; eissn:1432-0606Sponsorship
Gefördert im Rahmen des Projekts DEALCitation
@article{doi:10.17170/kobra-202109064714,
author={Rudoy, Evgeny and Shcherbakov, Viktor},
title={First-Order Shape Derivative of the Energy for Elastic Plates with Rigid Inclusions and Interfacial Cracks},
journal={Applied Mathematics & Optimization},
year={2020}
}
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2021-09-15T12:42:15Z 2021-09-15T12:42:15Z 2020-11-16 doi:10.17170/kobra-202109064714 http://hdl.handle.net/123456789/13246 Gefördert im Rahmen des Projekts DEAL eng Namensnennung 4.0 International http://creativecommons.org/licenses/by/4.0/ Kirchhoff-Love elastic plate rigid inclusion interfacial crack variational model shape derivative of energy Griffith formula 510 620 First-Order Shape Derivative of the Energy for Elastic Plates with Rigid Inclusions and Interfacial Cracks Aufsatz Within the framework of Kirchhoff–Love plate theory, we analyze a variational model for elastic plates with rigid inclusions and interfacial cracks. The main feature of the model is a fully coupled nonpenetration condition that involves both the normal component of the longitudinal displacements and the normal derivative of the transverse deflection of the crack faces. Without making any artificial assumptions on the crack geometry and shape variation, we prove that the first-order shape derivative of the potential deformation energy is well defined and provide an explicit representation for it. The result is applied to derive the Griffith formula for the energy release rate associated with crack extension. open access Rudoy, Evgeny Shcherbakov, Viktor doi:10.1007/s00245-020-09729-5 Kirchhoff-Love plate theory Einschluss Grenzfläche Riss Energie Rissausbreitung Bruchmechanik publishedVersion eissn:1432-0606 Issue 3 Applied Mathematics & Optimization 2775-2802 Volume 84 false
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