Existence of an optimal shape of the thin rigid inclusions in the Kirchhoff-Love plate

Shcherbakov, V. V.

doi:10.1134/s1990478914010116

Cited by 24 publications

(14 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Due to estimate (13) and the equalities w ε m,1 (±d, z 2 ) = εw ε ± (0, z 2 ) for z 2 ∈ (a, b) (see definition of the set K ε ), we obtain…”

Section: Limit Problemmentioning

confidence: 99%

“…Estimates (13) and (14) entail the existence of functions 0, 1, 2, 3, such that for some subsequence {ε n } ∞ n=1 still denoted by ε, the following convergences:…”

Section: Limit Problemmentioning

confidence: 99%

“…We mention [7,8,9], in which thin elastic inclusions in pates were studied. Papers [10,11,12,13] are devoted investigations of thin rigid inclusions. At last, we refer to [14,15,16,17,18] for asymptotic analyses for different models of bonded structures in Elasticity.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Asymptotic Justification of Models of Plates Containing Inside Hard Thin Inclusions

Rudoy¹

2020

Preprint

View full text Add to dashboard Cite

An equilibrium problem of the Kirchhoff-Love plate containing a nonhomogeneous inclusion is considered. It is assumed that elastic properties of the inclusion depend on a small parameter characterizing width of the inclusion $\varepsilon$ as $\varepsilon^N$ with $N<1$. The passage to the limit as the parameter $\varepsilon$ tends to zero is justified, and an asymptotic model of a plate containing a thin inhomogeneous hard inclusion is constructed. It is shown that there exists two types of thin inclusions: rigid inclusion ($N<-1$) and elastic inclusion ($N=-1$). The inhomogeneity disappears in the case of $N\in (-1,1)$.

show abstract

“…Due to estimate (13) and the equalities w ε m,1 (±d, z 2 ) = εw ε ± (0, z 2 ) for z 2 ∈ (a, b) (see definition of the set K ε ), we obtain…”

Section: Limit Problemmentioning

confidence: 99%

“…Estimates (13) and (14) entail the existence of functions 0, 1, 2, 3, such that for some subsequence {ε n } ∞ n=1 still denoted by ε, the following convergences:…”

Section: Limit Problemmentioning

confidence: 99%

See 1 more Smart Citation

Asymptotic Justification of Models of Plates Containing Inside Hard Thin Inclusions

Rudoy¹

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…We can mention many other papers related to equilibrium problems with thin elastic and rigid inclusions and cracks; see [6,7,[10][11][12][13][14]30]. Optimal control problems for such models can be found in [15,[33][34][35]. Volume rigid inclusions in elastic bodies are analyzed in [9,26,28]; see also [37].…”

Section: Introductionmentioning

confidence: 98%

Junction problem for rigid and semirigid inclusions in elastic bodies

Khludnev

Попова

2016

Arch Appl Mech

View full text Add to dashboard Cite

The paper is concerned with equilibrium problems for 2D elastic bodies having thin inclusions with different properties. In particular, rigid and semirigid inclusions are considered. It is assumed that inclusions have a joint point, and we analyze a junction problem for these inclusions. Existence of solutions is proved for each equilibrium problem, and different equivalent formulations of these problems are discussed. In particular, junction conditions at the joint point are found. A delamination of the inclusions is also assumed. This means that we have a crack, and inequality-type boundary conditions are imposed at the crack faces to prevent a mutual penetration between crack faces. We discuss a convergence to zero and infinity of a rigidity parameter of the semirigid inclusion and analyze limit problems.

show abstract

“…Problems for different models of elastic bodies containing rigid inclusions and cracks with both linear and nonlinear boundary conditions has been under active study; see [4,7,8,11,14,31,35]. It is known that various problems for bodies with rigid inclusions may be successfully formulated and investigated using variational methods, see for example [11,23,27,32,34]. In particular, a framework for two-dimensional elasticity problems with nonlinear Signorini-type conditions on a part of boundary of a thin delaminated rigid inclusion is proposed in [11].…”

Section: Introductionmentioning

confidence: 99%

Optimal control of the thickness of a rigid inclusion in equilibrium problems for inhomogeneous two-dimensional bodies with a crack

Lazarev

2015

Z. Angew. Math. Mech.

View full text Add to dashboard Cite

The equilibrium problems for two-dimensional elastic body with a rigid delaminated inclusion are considered. In this case, there is a crack between the rigid inclusion and the elastic body. Non-penetration conditions on the crack faces are given in the form of inequalities. We analyze the dependence of solutions and derivatives of the energy functionals on the thickness of rigid inclusion. The existence of the solution to the optimal control problem is proved. For that problem the cost functional is defined by derivatives of the energy functional with respect to a crack perturbation parameter while the thickness parameter of rigid inclusion is chosen as the control function.

show abstract

Existence of an optimal shape of the thin rigid inclusions in the Kirchhoff-Love plate

Cited by 24 publications

References 4 publications

Asymptotic Justification of Models of Plates Containing Inside Hard Thin Inclusions

Asymptotic Justification of Models of Plates Containing Inside Hard Thin Inclusions

Junction problem for rigid and semirigid inclusions in elastic bodies

Optimal control of the thickness of a rigid inclusion in equilibrium problems for inhomogeneous two-dimensional bodies with a crack

Contact Info

Product

Resources

About