Domain decomposition technique for a model of an elastic body reinforced by a Timoshenko’s beam

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

doi:10.1016/j.cam.2017.11.019

Cited by 17 publications

(5 citation statements)

References 32 publications

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“…where the constants c > 0 is independent of χ (see [39]). The above properties of the energy functional Π(χ), the bilinear form B(Ω γ , •, •), and the set K t allow one to establish the existence of a unique solution ξ t = (U t , u t , φ t ) ∈ K t for problem (6); see [34]. Symmetry and continuity of the bilinear form B(Ω γ , •, •) and the properties of the set K t provide the equivalence of problem (6) to the variational inequality…”

Section: A Family Of Equilibrium Problemsmentioning

confidence: 99%

“…For an arbitrary continuous functional G(χ) : H(Ω γ ) → R we can define the cost functional J : [0, T] → R with the help of the equality J(t) = G(ξ t ), where ξ t is the solution of the problem (6). The mentioned continuity property is fulfilled for many physically motivated functionals, for example, the functional…”

Section: A Family Of Equilibrium Problemsmentioning

confidence: 99%

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Optimal location of a thin rigid inclusion for a problem describing equilibrium of a composite Timoshenko plate with a crack

2020

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We consider equilibrium problems for a cracked composite plate with a thin cylindrical rigid inclusion. Deformation of an elastic matrix is described by the Timoshenko model. The plate is assumed to have a through crack that does not touch the rigid inclusion. In order to describe mutual nonpenetration of the crack faces we impose a boundary condition in the form of inequality on the crack curve. For a family of appropriate variational problems, we analyze the dependence of their solutions on the location of the rigid inclusion. We formulate an optimal control problem with a cost functional defined by an arbitrary continuous functional on the solution space, while the location parameter of inclusion is chosen as the control parameter. The existence of a solution to the optimal control problem and a continuous dependence of the solutions in a suitable Sobolev space with respect to the location parameter are proved.

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Section: A Family Of Equilibrium Problemsmentioning

confidence: 99%

Section: A Family Of Equilibrium Problemsmentioning

confidence: 99%

Optimal location of a thin rigid inclusion for a problem describing equilibrium of a composite Timoshenko plate with a crack

2020

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“…Nonlinear boundary conditions in the form of a system of equalities and inequalities, specified on the crack faces, ensure their mutual nonpenetration. A large number of results on the existence of a solution, the existence and formulas of derivatives with respect to the shape of a domain, optimal control problems, contact problems, inverse problems can be found, for example, in [1][2][3][4][5][6][7][8][9][10][11][12][13]. The study of equilibrium problems for elastic bodies with Euler-Bernoulli inclusions and cracks was carried out in [14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Noncoercive problems for elastic bodies with thin elastic inclusions

Khludnev

Fankina

2023

Math Methods in App Sciences

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The paper concerns boundary value problems for an elastic body with a thin elastic inclusion for a noncoercive case. The inclusion is assumed to be delaminated thus forming a crack between the inclusion and the surrounding elastic body. To provide a mutual nonpenetration between crack faces, we consider inequality type boundary conditions with unknown set of a contact. In the paper, a solution existence of the equilibrium problems is proved for the cases when one or two given points of the inclusion are fixed as well as and for the case without these restrictions.

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“…At the moment, a lot of papers are published related to analysis of elastic bodies with thin inclusions of different nature. We can mention results for equilibrium problems, optimal control problems, and asymptotic analysis of solutions for deformable bodies with elastic, rigid, and semi-rigid inclusions [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. All these and many other papers concern the analysis of homogeneous inclusions; nonhomogeneity may appear in junction problems with two or more homogeneous inclusions being in a contact.…”

Section: Introductionmentioning

confidence: 99%

Elastic body with thin nonhomogeneous inclusion in non-coercive case

Khludnev

Rodionov

2023

Mathematics and Mechanics of Solids

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The paper addresses analysis of equilibrium state of an elastic body with a thin nonhomogeneous inclusion in a non-coercive case. We assume that a part of the inclusion is located outside the elastic body, and the traction free boundary condition at the external boundary of the elastic body does not provide a coercivity of the problem. The inclusion is delaminated from the surrounding elastic material that implies a presence of the interfacial crack. Constraint boundary conditions at the crack faces describe a mutual nonpenetration and have an inequality type form. We prove a solution existence of the equilibrium problem, analyze a passage to the limit as the rigidity parameter of the inclusion tends to zero, and prove a solution existence of an inverse problem. The inverse problem assumes that along with the displacement field we have to find an elasticity coefficient for the inclusion provided that an additional information is given which can be found from a measurement.

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Domain decomposition technique for a model of an elastic body reinforced by a Timoshenko’s beam

Cited by 17 publications

References 32 publications

Optimal location of a thin rigid inclusion for a problem describing equilibrium of a composite Timoshenko plate with a crack

Optimal location of a thin rigid inclusion for a problem describing equilibrium of a composite Timoshenko plate with a crack

Noncoercive problems for elastic bodies with thin elastic inclusions

Elastic body with thin nonhomogeneous inclusion in non-coercive case

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