Optimal control of rigidity parameters of thin inclusions in composite materials

Khludnev, A. M.; Faella, Luisa; Perugia, Carmen

doi:10.1007/s00033-017-0792-x

Cited by 15 publications

(7 citation statements)

References 32 publications

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“…Considering (19) with test functionsW = W +W ,W ∈ H 1 (Ω γ ), [W ]ν ≥ 0 on γ, we obtain by the Green's formulas (11), (12) the following boundary conditions (20) [σ ν (W ) − θ] = 0, σ τ (W ) = 0 on γ.…”

Section: Equivalent Differential Statementmentioning

confidence: 99%

Equilibrium problem for an thermoelastic Kirchhoff–Love plate with a nonpenetration condition for known configurations of crack edges

Lazarev¹

2020

Sib. Elektron. Mat. Izv.

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We formulate a new variational problem on the equilibrium of a thermoelastic KirchhoLove plate in a domain with a cut. It is assumed that the plate is under the special loads for which the conguration of crack's edges is known in advance. This circumstance makes it possible to write down the general boundary condition of nonpenetration in a rened form, which, in turn, leads to new relations describing the possible mechanical interaction of opposite crack edges. The initial formulation of a problem presupposes the fulllment of boundary conditions on the crack curve in the form of system of two inequalities and an equality. Solvability of the problem is proved, an equivalent dierential setting is found.

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Section: Equivalent Differential Statementmentioning

confidence: 99%

Equilibrium problem for an thermoelastic Kirchhoff–Love plate with a nonpenetration condition for known configurations of crack edges

Lazarev¹

2020

Sib. Elektron. Mat. Izv.

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“…Moreover we refer to [42] and [9,10,11] for the exact controllability of hyperbolic problems with oscillating coefficients in fixed and in perforated domains respectively, to [36,37] and [34,35,54] for the optimal control and the exact controllability, respectively, of hyperbolic problems in composites with imperfect interface. Moreover in [38] it is faced the optimal control of rigidity parameters of thin inclusions in composite materials. In [21] and [22,23] the authors study, respectively, the correctors and the approximate control for a class of parabolic equations with interfacial contact resistance, while in [27] the authors study the approximate controllability of linear parabolic equations in perforated domains.…”

Section: γ Interface Boundary ∂ωmentioning

confidence: 99%

“…In [14]÷ [18], [31]÷ [33] and [53], the authors study the optimal control and exact controllability problems in domains with highly oscillating boundary. We refer the reader to [38,39] for the optimal control of hyperbolic problems in composites with imperfect interface and to [42] for the optimal control of rigidity parameters of thin inclusions in composite materials. We quote [23]÷ [25] and [34] for the correctors and the approximate control for a class of parabolic equations with interfacial contact resistance.…”

Section: Introductionmentioning

confidence: 99%

Homogenization and exact controllability for problems with imperfect interface

Monsurrò¹,

Perugia²

2019

Networks &Amp; Heterogeneous Media

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In this paper we study the internal exact controllability for a second order linear evolution equation defined in a two-component domain. On the interface we prescribe a jump of the solution proportional to the conormal derivatives, meanwhile a homogeneous Dirichlet condition is imposed on the exterior boundary. Due to the geometry of the domain, we apply controls through two regions which are neighborhoods of a part of the external boundary and of the whole interface, respectively. Our approach to internal exact controllability consists in proving an observability inequality by using the Lagrange multipliers method. Eventually we apply the Hilbert Uniqueness Method, introduced by J. -L. Lions, which leads to the construction of the exact control through the solution of an adjoint problem. Finally we find a lower bound for the control time depending not only on the geometry of our domain and on the matrix of coefficients of our problem but also on the coefficient of proportionality of the jump with respect to the conormal derivatives.

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“…In the framework of solid mechanics, nonlinear Signorini-type constraints impose certain behaviour of displacements by suitable boundary conditions on contacting surfaces of two independent bodies or on opposite crack faces. This approach of mathematical modelling implies methods of variational inequalities and has been actively developing, see [4][5][6][7][8][9][10][11][12]. Among this type of nonlinear mathematical models, a wide range of various problems for Kirchhoff-Love plates in the framework of elastic constitutive relations has been studied [4,6,[13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Equilibrium problem for a thermoelastic Kirchhoff–Love plate with a delaminated flat rigid inclusion

Lazarev

2022

Phil. Trans. R. Soc. A.

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A new mathematical model describing an equilibrium of a thermoelastic heterogeneous Kirchhoff–Love plate is considered. A corresponding nonlinear variational problem is formulated with respect to a two-dimensional domain with a cut. This cut corresponds to an interfacial crack located on a given part of the boundary of a flat rigid inclusion. The flat inclusion is described by a cylindrical surface. Due to the presence of the flat rigid inclusion in the plate, restrictions of the functions describing displacements to the corresponding curves satisfy special constraints having a linear form. Displacement boundary conditions of an inequality type are set on the crack faces that ensure a mutual non-penetration of opposite crack faces. Solvability of the problem is proved. Under the assumption that the solution of the variational problem is smooth enough, an equivalent differential formulation is found. This article is part of the theme issue ‘Non-smooth variational problems and applications’.

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Optimal control of rigidity parameters of thin inclusions in composite materials

Cited by 15 publications

References 32 publications

Equilibrium problem for an thermoelastic Kirchhoff–Love plate with a nonpenetration condition for known configurations of crack edges

Equilibrium problem for an thermoelastic Kirchhoff–Love plate with a nonpenetration condition for known configurations of crack edges

Homogenization and exact controllability for problems with imperfect interface

Equilibrium problem for a thermoelastic Kirchhoff–Love plate with a delaminated flat rigid inclusion

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