First-Order Shape Derivative of the Energy for Elastic Plates with Rigid Inclusions and Interfacial Cracks Full article
| Journal |
Applied Mathematics and Optimization
ISSN: 0095-4616 |
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| Output data | Year: 2021, Volume: 84, Number: 3, Pages: 2775-2802 Pages count : 28 DOI: 10.1007/s00245-020-09729-5 | ||||
| Tags | Griffith formula; Interfacial crack; Kirchhoff–Love elastic plate; Rigid inclusion; Shape derivative of energy; Variational model | ||||
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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.
Cite:
Rudoy E.
, Shcherbakov V.
First-Order Shape Derivative of the Energy for Elastic Plates with Rigid Inclusions and Interfacial Cracks
Applied Mathematics and Optimization. 2021. V.84. N3. P.2775-2802. DOI: 10.1007/s00245-020-09729-5 WOS Scopus РИНЦ OpenAlex
First-Order Shape Derivative of the Energy for Elastic Plates with Rigid Inclusions and Interfacial Cracks
Applied Mathematics and Optimization. 2021. V.84. N3. P.2775-2802. DOI: 10.1007/s00245-020-09729-5 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Apr 28, 2020 |
| Accepted: | Oct 7, 2020 |
| Published online: | Nov 16, 2020 |
| Published print: | Dec 1, 2021 |
Identifiers:
| Web of science: | WOS:000589990400001 |
| Scopus: | 2-s2.0-85096068902 |
| Elibrary: | 45174505 |
| OpenAlex: | W3101205253 |