Solution of the Problem of Gradient Thermoelasticity for a Coated Strip

Vatul’yan, A. O.; Нестеров, С. А.

doi:10.26907/2541-7746.2021.2.181-196

Cited by 3 publications

(5 citation statements)

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“…In the Cartesian coordinate system, the expressions for the nonzero components of the Cauchy stress tensors, couple and total stresses have the form [11]:…”

Section: Statement Of the Gradient Thermoelasticity Problem For A Coa...mentioning

confidence: 99%

“…To simplify the calculations, we assume that the gradient parameter is the same for the coating and the substrate. We take additional conditions: 1) at the lower boundary The dimensionless problem of gradient thermoelasticity for a coated strip has the form [11]:…”

Section: Statement Of the Gradient Thermoelasticity Problem For A Coa...mentioning

confidence: 99%

“…The solution was carried out using the integral Fourier transform and its numerical inversion. In [11], asymptotic solutions of the problem of gradient thermoelasticity for a strip with a coating were obtained for small values of the scale parameter. In [12], a study of the SSS of an infinitely long thermoelastic cylinder was carried out taking into account the scale effects.…”

Section: Introductionmentioning

confidence: 99%

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Modeling of thermoelastic deformation of a thin-layer “coating-substrate” system

Vatul’yan

Нестеров

2022

J. Phys.: Conf. Ser.

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The problem of thermoelastic deformation of a thin-layer coated strip is considered. To consider scale effects, a one-parameter gradient thermoelasticity model is used. The solution to the problem is based on the application of the Fourier transform in the longitudinal coordinate. The inversion of transformants is carried out on the basis of Filon’s quadrature formula. The stress-strain state of the coated strip was calculated both in gradient setting and in classical setting. The analysis of the influence of the scale parameter on the distribution of displacements and stresses is made.

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“…In the Cartesian coordinate system, the expressions for the nonzero components of the Cauchy stress tensors, couple and total stresses have the form [11]:…”

Section: Statement Of the Gradient Thermoelasticity Problem For A Coa...mentioning

confidence: 99%

Section: Statement Of the Gradient Thermoelasticity Problem For A Coa...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Modeling of thermoelastic deformation of a thin-layer “coating-substrate” system

Vatul’yan

Нестеров

2022

J. Phys.: Conf. Ser.

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“…В работах [26,27] в рамках классической теории упругости и термоупругости получены аналитические решения задачи деформирования системы «покрытие -подложка», как в случае однородного, так и функциональноградиентного покрытия. Для уточнения НДС системы «покрытие -подложка» на основе градиентной модели получены аналитические решения в случае механического нагружения [28][29][30][31]. Так, в работах [28] в рамках модели Лурье исследуется задача равновесия двухслойного покрытия, находящегося под действием локализованной нормальной нагрузки.…”

Section: Introductionunclassified

“…Так, в работах [28] в рамках модели Лурье исследуется задача равновесия двухслойного покрытия, находящегося под действием локализованной нормальной нагрузки. В исследовании [30] решается задача изгиба микробалки с частичным покрытием. Исследовано влияние изменения масштабного параметра на изменения распределения смещений, напряжений и нейтральной линии.…”

Section: Introductionunclassified

Investigation of the stress-strain state of a hollow cylinder with a coating based on the gradient model of thermoelasticity

Vatulyan¹,

Nesterov²,

Yurov³

2021

PNRPU Mechanics Bulletin

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The study of the stress-strain state of a thermoelastic hollow cylinder with a homogeneous coating is carried out taking into account the scale effects. Aifantis' one-parameter gradient model is used to account for scale effects. Equilibrium equations and boundary conditions for a composite hollow thermoelastic cylinder are obtained on the basis of the Lagrange variational principle. In comparison with the classical formulation of the problem, additional boundary conditions and conjugation conditions are set for moment stresses and displacement gradients. The dimensionlessness of the task of thermoelasticity has been carried out. Solving the problem of uncoupled thermoelasticity begins with finding the radial temperature distribution of a layered cylinder on the basis of solving the problem of heat conduction in the classical formulation. The solution of the problem in displacements is presented as a sum of solutions in the classical formulation of the problem and additional boundary layer terms found on the basis of the asymptotic properties of the modified Bessel functions. Simplified analytical expressions are obtained for finding radial displacements, radial and circumferential Cauchy stresses, nonzero components of the tensor of moment and total stresses. On specific examples, calculations of the radial distribution of displacements and stresses of a composite cylinder in the case of both mechanical and thermal loading are carried out. The limits of applicability of the asymptotic solution of the problem are investigated. The difference between the radial distribution of displacements and stresses found on the basis of solutions to the problem in the classical formulation and in the gradient formulation is shown. It was found that the Cauchy radial stresses experience a jump at the boundary of the cylinder and the coating, which is explained by the continuity of radial displacements and their first derivatives. The components of the moment stress tensor either take on peak values or experience a jump at the interface. The moment stresses are proportional to the square of the gradient parameter, at small values of which they have values that are much less than the values of the total stresses. With an increase in the dimensionless scale parameter, the values of radial displacements and total circumferential stresses decrease, but moment stresses increase.

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The Scale-Dependent Deformation Model of a Layered Rectangle

Vatulyan,

Nesterov

2024

Sib Math J

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Solution of the Problem of Gradient Thermoelasticity for a Coated Strip

Cited by 3 publications

References 0 publications

Modeling of thermoelastic deformation of a thin-layer “coating-substrate” system

Modeling of thermoelastic deformation of a thin-layer “coating-substrate” system

Investigation of the stress-strain state of a hollow cylinder with a coating based on the gradient model of thermoelasticity

The Scale-Dependent Deformation Model of a Layered Rectangle

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