Direct and Inverse Problems of Thermomechanics Concerning the Optimization and Identification of the Thermal Stressed State of Deformed Solids

Kalynyak, B. M.; Tokovyy, Yu. V.; Yasinskyy, Anatoliy

doi:10.1007/s10958-018-4095-3

Cited by 17 publications

(5 citation statements)

References 19 publications

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“…Let us determine the temperature field and thermal stresses in the considered tribocouple by making use of condition (10) in order to identify the unknown temperature distribution t * 1 (τ) on the inner circumference of the cylinder.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…This can be explained by the fact that the components of the stress–strain state have the form of integral dependences on the temperature at all points of a solid, including its boundary [ 1 , 8 , 9 ]. For non-stationary processes, these conditions usually express the fitting between the input data at the initial moment of time or interrelation of the mechanical components on the surfaces of the solid [ 1 , 10 ]. Some methods for solving one- and two-dimensional inverse thermoelasticity problems have been addressed in [ 11 , 12 , 13 , 14 , 15 , 16 ].…”

Section: Introductionmentioning

confidence: 99%

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Inverse Thermoelastic Analysis of a Cylindrical Tribo-Couple

et al. 2021

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Within the framework of the one-dimensional model for a tribo-couple consisting of two elastic cylinders accounting for the frictional heat generation on the interface due to the roughness of the contacting dissimilar materials, a problem on the identification of the unknown temperature on one of the limiting surfaces of either inner or outer cylindrical layers is formulated and reduced to an inverse thermoelasticity problem via the use of the circumferential strain given on the other surface. To solve the latter problem, a semi-analytical algorithm is suggested, and its stability with respect to the small errors in the input data is analyzed. The efficiency of the proposed solution algorithm is validated numerically by comparing its results with the solution of a corresponding direct problem. The temperature and thermal stresses in the tribo-couple are analyzed.

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Section: Formulation Of the Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Inverse Thermoelastic Analysis of a Cylindrical Tribo-Couple

et al. 2021

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“…Ключевые уравнения. В работах [25,27] с использованием метода непосредственного интегрирования [26,29] уравнения (1)-( 4) сведены к системе ключевых уравнений в напряжениях вида…”

Section: построение решенияunclassified

“…Несмотря на преимущество полученных в явном виде форм решений, использование какого-либо из них для кон кретного трансверсально-изотропного матери-ала требует предварительных исследова ний собственных чисел ключевых уравнений. С целью устранения такого недостатка в работе [27] предложена методика сведения ключевых уравнений указанной задачи к ин тегральным уравнениям второго рода [28,29]. Преимуществом данного подхода является получение универсальной для различных свойств трансверсально-изотропных материалов формы асимптотически убывающего при удалении от нагруженного участка границы решения, построенного в явном виде с использованием метода резольвент [30].…”

Section: Introductionunclassified

Определение Трехмерных Напряжений В Полубесконечном Упругом Трансверсально-Изотропном Композите

Бойко¹,

Токовый²

2021

mkm

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Предложена методика решения пространственной задачи теории упругости для трансверсально-изотропного полупространства, плоскость изотропии которого параллельна границе, где заданы произвольные локальные силовые воздействия. С помощью метода непосредственного интегрирования исходные уравнения задачи сведены к ключевым интегральным уравнениям второго рода для отдельных компонент тензора напряжений, явные решения которых получены в пространстве двойного интегрального преобразования Фурье с использованием метода резольвент. Построенное таким образом решение позволяет точно удовлетворить исходным уравнениям и краевым условиям задачи, а также обеспечить убывание решения в соответствии с принципом Сен-Венана при отдалении от нагруженного участка границы для всевозможных соотношений между упругими модулями трансверсально-изотропных сред.

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“…The technique is based on applying the direct integration method [ 6 ], which implies the reduction of a corresponding boundary value problem to the governing equations for individual stress tensor components by using the relationships derived via the integration of the equilibrium equations. This method has been efficiently used to analyze numerous direct and inverse boundary value problems in different coordinate systems [ 26 , 27 ]. In [ 28 ], this method was used to develop a technique for solving a three-dimensional elasticity problem for a transversely isotropic half-space.…”

Section: Introductionmentioning

confidence: 99%

Elastic and Thermoelastic Responses of Orthotropic Half-Planes

et al. 2021

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A unified approach is presented for constructing explicit solutions to the plane elasticity and thermoelasticity problems for orthotropic half-planes. The solutions are constructed in forms which decrease the distance from the loaded segments of the boundary for any feasible relationship between the elastic moduli of orthotropic materials. For the construction, the direct integration method was employed to reduce the formulated problems to a governing equation for a key function. In turn, the governing equation was reduced to an integral equation of the second kind, whose explicit analytical solution was constructed by using the resolvent-kernel algorithm.

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Direct and Inverse Problems of Thermomechanics Concerning the Optimization and Identification of the Thermal Stressed State of Deformed Solids

Cited by 17 publications

References 19 publications

Inverse Thermoelastic Analysis of a Cylindrical Tribo-Couple

Inverse Thermoelastic Analysis of a Cylindrical Tribo-Couple

Определение Трехмерных Напряжений В Полубесконечном Упругом Трансверсально-Изотропном Композите

Elastic and Thermoelastic Responses of Orthotropic Half-Planes

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