E.M. Rudoy, “Differentiation of energy functionals in two-dimensional elasticity theory for solids with curvilinear cracks”, Prikl. Mekh. Tekh. Fiz., 45:6 (2004), 83–94; J. Appl. Mech. Tech. Phys., 45:6 (2004), 843

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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2004, Volume 45, Issue 6, Pages 83–94 (Mi pmtf2444)

This article is cited in 22 scientific papers (total in 22 papers)

Differentiation of energy functionals in two-dimensional elasticity theory for solids with curvilinear cracks

E.M. Rudoy

Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk, 630090, Russia

Full-text PDF (265 kB) Citations (22)

Abstract: This paper considers the equations of two-dimensional elasticity theory in nonsmooth domains. The domains contain curvilinear cracks of variable length. On the crack faces, conditions are specified in the form of inequalities describing mutual nonpenetration of the crack faces. It is proved that the solutions of equilibrium problems with a perturbed crack converge to the solution of the equilibrium problem with an unperturbed crack in the corresponding space. The derivative of the energy functional with respect to the length of a curvilinear crack is obtained.

Keywords: elasticity, crack, Griffiths criterion, variational inequality, derivative of energy functional, nonsmooth domain.

Received: 12.01.2004
Accepted: 09.03.2004

English version:
Journal of Applied Mechanics and Technical Physics, 2004, Volume 45, Issue 6, Pages 843–852
DOI: https://doi.org/10.1023/B:JAMT.0000046033.10086.86

Bibliographic databases:

Document Type: Article

UDC: 539.375

Language: Russian

Citation: E.M. Rudoy, “Differentiation of energy functionals in two-dimensional elasticity theory for solids with curvilinear cracks”, Prikl. Mekh. Tekh. Fiz., 45:6 (2004), 83–94; J. Appl. Mech. Tech. Phys., 45:6 (2004), 843–852

Citation in format AMSBIB

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\crossref{https://doi.org/10.1023/B:JAMT.0000046033.10086.86}

Linking options:

https://www.mathnet.ru/eng/pmtf2444

https://www.mathnet.ru/eng/pmtf/v45/i6/p83

This publication is cited in the following 22 articles:

E. V. Pyatkina, “Equilibrium of a Three-Layer Plate with a Crack”, J. Appl. Ind. Math., 16:1 (2022), 122
Victor A. Kovtunenko, Karl Kunisch, “Shape Derivative for Penalty-Constrained Nonsmooth–Nonconvex Optimization: Cohesive Crack Problem”, J Optim Theory Appl, 194:2 (2022), 597
Evgeny Rudoy, Viktor Shcherbakov, “First-Order Shape Derivative of the Energy for Elastic Plates with Rigid Inclusions and Interfacial Cracks”, Appl Math Optim, 84:3 (2021), 2775
I. V. Fankina, “Optimal Control by the Rigid Layer Size of a Construction”, J Math Sci, 237:4 (2019), 521
V. A. Kovtunenko, K. Ohtsuka, “Shape Differentiability of Lagrangians and Application to Stokes Problem”, SIAM J. Control Optim., 56:5 (2018), 3668
A.M. Khludnev, V.V. Shcherbakov, “A note on crack propagation paths inside elastic bodies”, Applied Mathematics Letters, 79 (2018), 80
Hiromichi Itou, Victor A Kovtunenko, Kumbakonam R Rajagopal, “Nonlinear elasticity with limiting small strain for cracks subject to non-penetration”, Mathematics and Mechanics of Solids, 22:6 (2017), 1334
N.P. Lazarev, E.M. Rudoy, “Shape sensitivity analysis of Timoshenko's plate with a crack under the nonpenetration condition”, Z Angew Math Mech, 94:9 (2014), 730
A. Khludnev, G. Leugering, M. Specovius-Neugebauer, “Optimal Control of Inclusion and Crack Shapes in Elastic Bodies”, J Optim Theory Appl, 155:1 (2012), 54
H. Itou, A.M. Khludnev, E.M. Rudoy, A. Tani, “Asymptotic behaviour at a tip of a rigid line inclusion in linearized elasticity”, Z Angew Math Mech, 92:9 (2012), 716
A.M. Khludnev, G. Leugering, “Optimal control of cracks in elastic bodies with thin rigid inclusions”, Z Angew Math Mech, 91:2 (2011), 125
M. Hintermüller, V. A. Kovtunenko, “From shape variation to topological changes in constrained minimization: a velocity method-based concept”, Optimization Methods and Software, 26:4-5 (2011), 513
A. Gaudiello, A. M. Khludnev, “Crack on the boundary of two overlapping domains”, Z. Angew. Math. Phys., 61:2 (2010), 341
Alexander Khludnev, “Optimal control of crack growth in elastic body with inclusions”, European Journal of Mechanics - A/Solids, 29:3 (2010), 392
Alexander Khludnev, Günter Leugering, “On elastic bodies with thin rigid inclusions and cracks”, Math. Meth. Appl. Sci., 2010, n/a
Alexander Khludnev, Jan Sokołowski, Katarzyna Szulc, “Shape and topological sensitivity analysis in domains with cracks”, Appl Math, 55:6 (2010), 433
E. M. Rudoy, “Asymptotics of the energy functional for a fourth-order mixed boundary value problem in a domain with a cut”, Siberian Math. J., 50:2 (2009), 341–354
E.M. Rudoy, “Differentiation of energy functionals in the problem of a curvilinear crack in a plate with a possible contact of the crack faces”, J. Appl. Mech. Tech. Phys., 49:5 (2008), 832–845
Alexander M. KHLUDNEV, Victor A. KOVTUNENKO, Atusi TANI, “Evolution of a crack with kink and non-penetration”, J. Math. Soc. Japan, 60:4 (2008)
A.M. Khludnev, “On crack problem with overlapping domain”, Z Angew Math Mech, 88:8 (2008), 650

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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