Reinforcement of a Mindlin–Timoshenko plate by a thin layer

Rahmani, Leïla

doi:10.1007/s00033-015-0562-6

Cited by 7 publications

(1 citation statement)

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“…Finalizing the introduction, we give a short review of the works related to thin inclusion (thin inhomogeneity) problems in the theory of elasticity. Asymptotic analysis was performed for different models of elasticity with a wide range of constitutive relations, such as elastic models [18][19][20][21][22], multiphysics models [23,24], and models of plates [25][26][27][28][29]. In this line, let us mention also the recent articles [25,[29][30][31][32][33][34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

A quasi-static model of a thermoelastic body reinforced by a thin thermoelastic inclusion

Fankina,

Furtsev,

Rudoy

et al. 2024

Mathematics and Mechanics of Solids

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The problem of description of quasi-static behavior is studied for a planar thermoelastic body incorporating an inhomogeneity, which geometrically is a strip with a small cross-section. This problem contains a small positive parameter [Formula: see text] describing the thickness of the inhomogeneity, i.e., the size of the cross-section. Relying on the variational formulation of the problem, we investigate the behavior of solutions as [Formula: see text] tends to zero. As the result, by the version of the method of formal asymptotic expansions, we derive a closed limit model in which the inhomogeneity is thin (of zero width). After this, using the Galerkin method and the classical techniques of derivation of energy estimates, we prove existence, uniqueness, and stability of a weak solution to this model.

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