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On modeling elastic bodies with defects. / Khludnev, Alexandr Mikhailovich.
в: Сибирские электронные математические известия, Том 15, 01.01.2018, стр. 153-166.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - On modeling elastic bodies with defects
AU - Khludnev, Alexandr Mikhailovich
PY - 2018/1/1
Y1 - 2018/1/1
N2 - 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.
AB - 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.
KW - Damage parameter
KW - Defect
KW - Derivative of energy functional
KW - Non-penetration boundary conditions
KW - Optimal control
KW - Variational inequality
UR - http://www.scopus.com/inward/record.url?scp=85045711912&partnerID=8YFLogxK
U2 - 10.17377/semi.2018.15.015
DO - 10.17377/semi.2018.15.015
M3 - Article
AN - SCOPUS:85045711912
VL - 15
SP - 153
EP - 166
JO - Сибирские электронные математические известия
JF - Сибирские электронные математические известия
SN - 1813-3304
ER -
ID: 12690618