Optimal location of a finite set of rigid inclusions in contact problems for inhomogeneous two-dimensional bodies

Lazarev, N. P.; Rudoy, E. M.

doi:10.1016/j.cam.2021.113710

Cited by 7 publications

(5 citation statements)

References 30 publications

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“…Moreover, this also concerns elastic bodies with inclusions of different nature in the cases with delaminations, i.e. when we have cracks between the inclusions and the surrounding elastic body [9][10][11][12][13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Thin inclusion at the junction of two elastic bodies: non-coercive case

Khludnev

2024

Phil. Trans. R. Soc. A.

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This article addresses an analysis of the non-coercive boundary value problem describing an equilibrium state of two contacting elastic bodies connected by a thin elastic inclusion. Nonlinear conditions of inequality type are imposed at the joint boundary of the bodies providing a mutual non-penetration. As for conditions at the external boundary, they are Neumann type and imply the non-coercivity of the problem. Assuming that external forces satisfy suitable conditions, a solution existence of the problem analysed is proved. Passages to limits are justified as the rigidity parameters of the inclusion and the elastic body tend to infinity. This article is part of the theme issue ‘Non-smooth variational problems with applications in mechanics’.

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Section: Introductionmentioning

confidence: 99%

Thin inclusion at the junction of two elastic bodies: non-coercive case

Khludnev

2024

Phil. Trans. R. Soc. A.

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“…The classical theory of inverse problems and its applications in mathematical physics can be found in [35]. For relevant tasks, see optimal control of partial differential equations (PDEs) [7], shape control of VIs [2], and optimal object location [36]. The shape optimization approach was applied for the inverse problem of identification of interfaces [14], geometric objects [31], inhomogeneities [6], and breaking lines [16].…”

Section: Introductionmentioning

confidence: 99%

Lagrangian approach and shape gradient for inverse problem of breaking line identification in solid: contact with adhesion

Kovtunenko

2023

Inverse Problems

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A class of inverse identification problems constrained by variational inequalities is studied with respect to its shape differentiability. The specific problem appearing in failure analysis describes elastic bodies with a breaking line subject to simplified adhesive contact conditions between its faces. Based on the Lagrange multiplier approach and smooth Lavrentiev penalization, a semi-analytic formula for the shape gradient of the Lagrangian linearized on the solution is proved, which contains both primal and adjoint states. It is used for the descent direction in a gradient algorithm for identification of an optimal shape of the breaking line from boundary measurements. The theoretical result is supported by numerical simulation tests of destructive testing in 2D configuration with and without contact.

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“…In the optimal control problem under consideration, the role of the cost functional is played by an arbitrary continuous functional on the space of solutions, whereas the location parameter of one rigid inclusion is taken for a control. The solvability of the optimal location problem was established in [3] for a family of contact problems with finitely many volume rigid inclusions. The result of [3] was obtained under the assumption that the inclusions are at a nonzero distance from each other.…”

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confidence: 99%

“…The solvability of the optimal location problem was established in [3] for a family of contact problems with finitely many volume rigid inclusions. The result of [3] was obtained under the assumption that the inclusions are at a nonzero distance from each other. Unlike [3], in this paper, the case of arbitrarily close inclusions is admitted.…”

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confidence: 99%

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The Problem of the Location of an Inclusion in a Two-Dimensional Elastic Body with Two Thin Rigid Inclusions

Lazarev

Semenova

2023

J Math Sci

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We study the optimal control problem for nonlinear mathematical models describing the equilibrium state of an inhomogeneous body, where the nonlinearity is caused by the Signorini contact condition. We establish the solvability of the optimal control problem and prove that the equilibrium problem for an elastic body with two joined rigid inclusions is the limit for a family of equilibrium problems for bodies with two separate inclusions. Bibliography: 7 titles.

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Optimal location of a finite set of rigid inclusions in contact problems for inhomogeneous two-dimensional bodies

Cited by 7 publications

References 30 publications

Thin inclusion at the junction of two elastic bodies: non-coercive case

Thin inclusion at the junction of two elastic bodies: non-coercive case

Lagrangian approach and shape gradient for inverse problem of breaking line identification in solid: contact with adhesion

The Problem of the Location of an Inclusion in a Two-Dimensional Elastic Body with Two Thin Rigid Inclusions

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