Asymptotic modeling of steady vibrations of thin inclusions in a thermoelastic composite

Furtsev, Alexey I.; Fankina, Irina V.; Rodionov, Alexander A.; Ponomarev, Dmitri A.

doi:10.1007/s00033-023-02088-5

Cited by 2 publications

(1 citation statement)

References 26 publications

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“…See, e.g. papers [2][3][4][5][6][7][8], in which static and dynamical problems are analysed for different models of elastic bodies, and also papers [9][10][11][12][13][14][15][16][17][18] that deal with thermoelasticity. Owing to the similarity of such an asymptotic analysis, we do not perform it in the present paper.…”

Section: Introductionmentioning

confidence: 99%

The homogenized dynamical model of a thermoelastic composite stitched with reinforcing filaments

Rudoy,

Sazhenkov

2024

Phil. Trans. R. Soc. A.

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The dynamical problem of linear thermoelasticity for a body with incorporated thin rectilinear inclusions is studied. It is assumed that the inclusions (i.e. filaments and threads) are parallel to each other and the problem contains a small parameter ϵ > 0 , which characterizes the distance between two neighbouring inclusions. Using the two-scale convergence approach, we find the limiting problem as ϵ → 0 . As a result, we get a well-posed homogenized model of an anisotropic inhomogeneous body with effective characteristics inheriting thermomechanical properties of inclusions. This article is part of the theme issue ‘Non-smooth variational problems with applications in mechanics’.

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Section: Introductionmentioning

confidence: 99%

The homogenized dynamical model of a thermoelastic composite stitched with reinforcing filaments

Rudoy,

Sazhenkov

2024

Phil. Trans. R. Soc. A.

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Impedance operator of a curved thin layer in linear elasticity with voids

Abdallaoui,

Berkani,

Kelleche

2024

Math Methods in App Sciences

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We consider a two‐dimensional transmission problem of linear elasticity with voids in a fixed domain coated by a curved thin layer . Our aim is to model the effect of the thin layer on the fixed domain by an impedance boundary condition. For that, we use the techniques of asymptotic expansion to approximate the transmission problem by an impedance problem set in the fixed domain , and we prove an error estimate for the approximate impedance problem.

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Asymptotic modeling of steady vibrations of thin inclusions in a thermoelastic composite

Cited by 2 publications

References 26 publications

The homogenized dynamical model of a thermoelastic composite stitched with reinforcing filaments

The homogenized dynamical model of a thermoelastic composite stitched with reinforcing filaments

Impedance operator of a curved thin layer in linear elasticity with voids

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