On modeling elastic bodies with defects Full article
| Journal |
Сибирские электронные математические известия / Siberian Electronic Mathematical Reports
ISSN: 1813-3304 |
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| Output data | Year: 2018, Volume: 15, Pages: 153-166 Pages count : 14 DOI: 10.17377/semi.2018.15.015 | ||||
| Tags | Damage parameter; Defect; Derivative of energy functional; Non-penetration boundary conditions; Optimal control; Variational inequality | ||||
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Abstract:
The paper concerns a mathematical analysis of equilibrium problems for 2D elastic bodies with thin defects. The defects are characterized with a damage parameter. A presence of defects implies that the problems are formulated in a nonsmooth domain with a cut. Nonlinear boundary conditions at the cut faces are considered to prevent a mutual penetration between the faces. Weak and strong formulations of the problems are analyzed. The paper provides an asymptotic analysis with respect to the damage parameter. We obtain invariant integrals over curves surrounding the defect tip. An optimal control problem is investigated with a cost functional equal to the derivative of the energy functional with respect to the defect length, and the damage parameter being a control function.
Cite:
Khludnev A.M.
On modeling elastic bodies with defects
Сибирские электронные математические известия / Siberian Electronic Mathematical Reports. 2018. V.15. P.153-166. DOI: 10.17377/semi.2018.15.015 WOS Scopus РИНЦ
On modeling elastic bodies with defects
Сибирские электронные математические известия / Siberian Electronic Mathematical Reports. 2018. V.15. P.153-166. DOI: 10.17377/semi.2018.15.015 WOS Scopus РИНЦ
Dates:
| Submitted: | Dec 29, 2017 |
| Published print: | Feb 15, 2018 |
Identifiers:
| Web of science: | WOS:000438412200015 |
| Scopus: | 2-s2.0-85045711912 |
| Elibrary: | 36998659 |