An analytical solution to the axisymmetric thermoelasticity problem for a cylinder with arbitrarily varying thermomechanical properties

Tokovyy, Yu. V.; Chyzh, A. I.; Ma, Chien‐Ching

doi:10.1007/s00707-017-2012-3

Cited by 9 publications

(3 citation statements)

References 33 publications

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“…Traditionally, problems concerning the theory of elasticity for a heterogeneous medium are described by a system of partial differential equations with variable coefficients. Analytical solutions of such equations are known only for certain cases of canonical domains and laws of change of elastic moduli in space [57][58][59] and do not have a standard approach.…”

Section: Introductionmentioning

confidence: 99%

Analytical Model of Deformation of a Functionally Graded Ceramic Coating under Local Load

Shatskyi,

Makoviichuk,

Ropyak

et al. 2023

Ceramics

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In this article, an analytical approach to the study of the behavior of functionally graded FG coatings under local load is developed. The method is suitable for coatings with a specific structure. We consider that the coating can be conditionally divided into two zones: a relatively rigid outer and a relatively compliant inner. The outer layer is modeled by a non-homogeneous plate that bends. We submit the inner substrate to the hypothesis of a non-homogeneous thin Winkler layer. The solution of the formulated boundary value problem is constructed in analytical form. Simulation examples for FG aluminum oxide coatings grown from aluminum sprayed on steel and from compact alloy D16T are considered. The distributions of equivalent stresses, safety factors and normalized equivalent stresses in the coatings are studied. It is noted that in a heterogeneous material, the location of the minimum of the safety factor does not always coincide with the location of the maximum of the equivalent stress.

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Section: Introductionmentioning

confidence: 99%

Analytical Model of Deformation of a Functionally Graded Ceramic Coating under Local Load

Shatskyi,

Makoviichuk,

Ropyak

et al. 2023

Ceramics

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“…There are developed refined models taking into account the characteristic features of composite materials, in particular, high anisotropy in the transverse direction [3][4][5]. The exact solutions of thermoelasticity problems for layered shells are constructed on the base of three-dimensional equations in [6,7]. Using the equations of classical and various refined theories, the analytical solutions are obtained in [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Determination and analysis of the thermoelastic state of layered orthotropic cylindrical shells

Musii,

Zhydyk,

Svidrak

et al. 2023

Math. Model. Comput.

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The fundamental relations of the quasi-static problem of thermoelasticity are written for a finite layered orthotropic cylindrical shell of an antisymmetric structure. Under convective heat transfer on the surfaces of this shell and under a linear dependence of temperature on the transverse coordinate, the basic system of equations for the integral characteristics of temperature is given. The method is proposed for solving the formulated problems of thermoelasticity and thermal conductivity, using the double finite integral Fourier transform with respect to the corresponding coordinates of the transformation and Laplace transform with respect to the time. The results of a numerical analysis of temperature, deflections, and stresses for the considered two-layer shell hinged at the edges under local heating by the initially specified temperature field are presented.

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“…Therefore, an important engineering task is to build mathematical models and conduct research on layered structures to analyze their performance [3][4][5][6]. Temperature fields and stresses in layered structures were studied both on the basis of three-dimensional equations [7,8] and two-dimensional ones [9][10][11]. Analytical [12]]and numerical [13] methods were used to construct the solutions.…”

Section: Introductionmentioning

confidence: 99%

Stressed and strained state of layered cylindrical shell under local convective heating

Musii¹,

Zhydyk²,

Turchyn³

et al. 2022

Math. Model. Comput.

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The stress-strain state of a layered composite cylindrical shell under local heating by the environment due to convective heat exchange has been studied. The equation of the six-modal theory of thermoelasticity and the two-dimensional equation of thermal conductivity of inhomogeneous anisotropic shells are used for this purpose. The solution of the nonstationary heat transfer problem and the quasi-static thermoelasticity problem for a finite hinged orthogonally reinforced shell of symmetric structure is found by the methods of integral Fourier and Laplace transforms. Numerical results are given for the three-layer shell.

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An analytical solution to the axisymmetric thermoelasticity problem for a cylinder with arbitrarily varying thermomechanical properties

Cited by 9 publications

References 33 publications

Analytical Model of Deformation of a Functionally Graded Ceramic Coating under Local Load

Analytical Model of Deformation of a Functionally Graded Ceramic Coating under Local Load

Determination and analysis of the thermoelastic state of layered orthotropic cylindrical shells

Stressed and strained state of layered cylindrical shell under local convective heating

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