Geodesic
Asymptotics of solutions for two elastic plates with thin junction
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 2, pp. 484-501.

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The paper concerns an equilibrium problem for two elastic plates connected by a thin junction (bridge) in a case of Neumann boundary conditions, which provide a non-coercivity for the problem. An existence of solutions is proved. Passages to limits are justified with respect to the rigidity parameter of the junction. In particular, the rigidity parameter tends to infinity and to zero. Limit models are investigated.
Keywords: Thin junction, elastic plate, rigidity parameter, non-coercive boundary value problem, thin inclusion. 
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A. M. Khludnev. Asymptotics of solutions for two elastic plates with thin junction. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 2, pp. 484-501. http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a36/

[1] H. Attouch, G. Buttazzo, G. Michaille, Variational analysis in Sobolev and BV spaces. Applications to PDEs and optimization, SIAM, Philadelphia, 2014 | MR | Zbl

[2] R. Ballarini, P. Villaggio, “Elastic stress diffusion around a thin corrugated inclusion”, IMA J. Appl. Math., 76:4 (2011), 633–641 | DOI | MR | Zbl

[3] M. Goudarzi, F. Dal Corso, D. Bigoni, A. Simone, “Dispersion of rigid line inclusions as stiffeners and shear band instability triggers”, Int. J. Solids Structures, 210-211 (2021), 255–272 | DOI

[4] L. Freddi, R. Paroni, T. Roubíček, C. Zanini, “Quasistatic delamination models for Kirchhoff-Love plates”, Z. Angew. Math. Mech., 91:11 (2011), 845–865 | DOI | MR | Zbl

[5] L. Freddi, T. Roubíček, C. Zanini, “Quasistatic delamination of sandwich-like Kirchhoff-Love plates”, J. Elasticity, 113:2 (2013), 219–250 | DOI | MR | Zbl

[6] A.I. Furtsev, “On contact between a thin obstacle and a plate containing a thin inclusion”, J. Math. Sci., New York, 237:4 (2019), 530–545 | DOI | MR | Zbl

[7] A. Furtsev, E. Rudoy, H. Itou, “Modeling of bonded elastic structures by a variational method: theretical and numerical simulation”, Int. J. Solids Structures, 182-183 (2020), 100–111 | DOI

[8] A. Gaudiello, G. Panasenko, A. Piatnitski, “Asymptotic analysis and domain decomposition for a biharmonic problem in a thin multistructure”, Commun. Contemp. Math., 18:5 (2016), 1550057 | DOI | MR | Zbl

[9] A.M. Khludnev, V.A. Kovtunenko, Analysis of cracks in solids, WIT Press, Southampton–Boston, 2000

[10] A.M. Khludnev, Elasticity problems in non-smooth domains, Fizmatlit, M., 2010

[11] A.M. Khludnev, “On bending an elastic plate with a delaminated thin rigid inclusion”, J. Appl. Ind. Math., 5:4 (2011), 582–594 | DOI | MR | Zbl

[12] A.M. Khludnev, “Thin rigid inclusions with delaminations in elastic plates”, Eur. J. Mech. A, Solids, 32 (2012), 69–75 | DOI | MR | Zbl

[13] A.M. Khludnev, G. Leugering, “Delaminated thin elastic inclusion inside elastic bodies”, Math. Mech. Complex Syst., 2:1 (2014), 1–21 | DOI | MR | Zbl

[14] A.M. Khludnev, G. Leugering, “On Timoshenko thin elastic inclusions inside elastic bodies”, Math. Mech. Solids, 20:5 (2015), 495–511 | DOI | MR | Zbl

[15] A.M. Khludnev, T.S. Popova, “On crack propagations in elastic bodies with thin inclusions”, Sib. Èlektron. Mat. Izv., 14 (2017), 586–599 | MR | Zbl

[16] A.M. Khludnev, “On modeling elastic bodies with defects”, Sib. Èlektron. Mat. Izv., 15 (2018), 153–166 | MR | Zbl

[17] V.A. Kovtunenko, G. Leugering, “A shape-topological control problem for nonlinear crack-defect interaction: the antiplane variational model”, SIAM J. Control Optim., 54:3 (2016), 1329–1351 | DOI | MR | Zbl

[18] N.P. Lazarev, V.A. Kovtunenko, “Signorini-type problems over non-convex sets for composite bodies contacting by sharp edges of rigid inclusions”, MDPI Mathematics, 10:2 (2022), 250 | DOI

[19] V.A. Kozlov, V.G. Maz'ya, A.B. Movchan, Asymptotic analysis of fields in a multi-structure, Oxford University Press, Oxford, 1999 | MR | Zbl

[20] P. Mallick, Fiber-reinforced Composites. Materials, Manufacturing, and Design, Marcel Dekker, New York, 1993

[21] A. Morassi, E. Rosset, S. Vessella, “Stable determination of a rigid inclusion in an anisotropic elastic plate”, SIAM J. Math. Anal., 44:3 (2012), 2204–2235 | DOI | MR | Zbl

[22] A. Morassi, E. Rosset, S. Vessella, “Optimal stability in the identifcation of a rigid inclusion in an isotropic Kirchhoff-Love plate”, SIAM J. Math. Anal., 51:2 (2019), 731–747 | DOI | MR | Zbl

[23] G. Saccomandi, M.F. Beatty, “Universal relations for fiber-reinforced elastic materials”, Math. Mech. Solids, 7:1 (2002), 95–110 | DOI | MR | Zbl