Thermo-elastic mismatch in nonhomogeneous beams

Розробляються та досліджуються лінійні та нелінійні математичні моде-лі процесу теплопровідності в однорідних і шаруватих середовищах із включення-ми. Наведені неоднорідні системи нагріва-ються зосередженим тепловим потоком у локальній області межових поверхонь кон-струкцій. Висвітлено підходи до розв'я-зування відповідних лінійних та неліній-них крайових задач теплопровідності. Створено алгоритми та розрахункові програми, які дають змогу аналізувати температурні поля в кусково-однорідних середовищах Ключові слова: теплопровідність, тем-пературне поле, чужорідне наскрізне вклю-чення, термочутлива система, тепловий потік Разрабатываются и исследуются ли-нейные и нелинейные математические модели процесса теплопроводности в одно-родных и слоистых средах с включения-ми. Приведенные неоднородные системы нагреваются сосредоточенным тепловым потоком в локальной области граничных поверхностей конструкций. Изложеноы подходы к решению соответствующих линейных и нелинейных граничных задач теплопроводности. Созданы алгоритмы и расчетные программы, с помощью кото-рых можно анализировать температур-ные поля в кусочно-однородных средах Ключевые слова: теплопроводность, температурное поле, инородное сквозное включение, термочувствительная систе-ма, тепловой поток UDC 536.24

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“…Determining the temperature regimes in both uniform and non-uniform designs attracts attention of many researchers [4,5].…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

“…Let us apply the integral Fourier transform by the x coordinate to equation (8) and boundary conditions (2) taking into consideration relation (4). Upon solving the obtained boundary problem relative to the representation…”

Section: Fig 2 Approximation Of Function T (±Hy)mentioning

confidence: 99%

Examining the temperature fields in flat piecewise- uniform structures

Havrysh

Ivasyk

Kolyasa

et al. 2017

EEJET

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“…(16). Then, from the remaining roots, we choose the one for which the temperature calculated according to (15) belongs to the temperature range on which the dependence of the coefficients of heat conductivity is defined.…”

Section: Solution Of the Heat Conduction Problemmentioning

confidence: 99%

“…Here, using the constructed exact solution of an auxiliary problem, we have reduced the heat conduction problems, irrespective of the number of layers, to the solution of one or a system of two nonlinear algebraic equations. We have also studied the temperature fields and stresses in four-layer plates under conditions of complex heat exchange.The determination of the thermoelastic state of both homogeneous and inhomogeneous bodies, in particular, those with plane-parallel boundaries, with regard for their thermal sensitivity (the dependence of physicomechanical characteristics on temperature) has attracted the attention of numerous researchers [4,[15][16][17][18][19][20]. Even in the case of uncoupled thermoelasticity problems, the corresponding heat conduction problems remain nonlinear.…”

mentioning

confidence: 99%

“…The determination of the thermoelastic state of both homogeneous and inhomogeneous bodies, in particular, those with plane-parallel boundaries, with regard for their thermal sensitivity (the dependence of physicomechanical characteristics on temperature) has attracted the attention of numerous researchers [4,[15][16][17][18][19][20]. Even in the case of uncoupled thermoelasticity problems, the corresponding heat conduction problems remain nonlinear.…”

mentioning

confidence: 99%

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Static thermoelasticity problems for layered thermosensitive plates with cubic dependence of the coefficients of heat conductivity on temperature

Protsyuk

2012

J Math Sci

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We describe an analytic-numerical method of solution of one-dimensional static thermoelasticity problems for layered plates, heated in different ways. We take into account the cubic dependence of the coefficients of heat conductivity and arbitrary nature of the dependence of other physicomechanical parameters on temperature. Here, using the constructed exact solution of an auxiliary problem, we have reduced the heat conduction problems, irrespective of the number of layers, to the solution of one or a system of two nonlinear algebraic equations. We have also studied the temperature fields and stresses in four-layer plates under conditions of complex heat exchange.The determination of the thermoelastic state of both homogeneous and inhomogeneous bodies, in particular, those with plane-parallel boundaries, with regard for their thermal sensitivity (the dependence of physicomechanical characteristics on temperature) has attracted the attention of numerous researchers [4,[15][16][17][18][19][20]. Even in the case of uncoupled thermoelasticity problems, the corresponding heat conduction problems remain nonlinear. For their solution, it is customary to apply the Kirchhoff substitution [1, 2, 5, 6, 9-12, 14, 16]. This technique enables one to linearize the problems under study partially or even completely and, correspondingly, to simplify their solution or, in some cases, to obtain an exact solution. However, for layered bodies, one does not succeed in completely linearizing heat conduction problems, including the simplest, one-dimensional, because nonlinearity is preserved in one of the conditions of thermal contact. Obviously, the solution of heat conduction problems and, hence, of the corresponding thermoelasticity problems becomes more difficult both in the case of convective or convective-radiative heat exchange with the environment and taking into account more complex temperature dependence of the coefficients of heat conductivity than linear. Therefore, such problems are solved, as a rule, by numerical and approximate analytic methods or by their combination.In the present work, we describe an analytic-numerical procedure, based on using the approach [7], of the solution of one-dimensional static thermoelasticity problems for layered plates, heated in different ways, with regard for the cubic dependence of the coefficients of heat conductivity and arbitrary character of the dependence of other physicomechanical characteristics on temperature. Using the exact solutions of the corresponding equations under special boundary conditions, constructed with the help of the Kirchhoff substitution and generalized functions, we reduce the heat conduction problems under study, irrespective of the quantity of layers, to the solution of one or a system of two nonlinear algebraic equations. The thermoelasticity problem is solved in terms of stresses. The boundary conditions on the cylindrical surface are satisfied integrally. We also analyze numerically the temperature fields and thermostressed state in four-layer plates under ...

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