Modeling and optimization in the thermomechanics of inhomogeneous solids

Кушнір, Р. М.

doi:10.15407/visn2014.10.010

Cited by 5 publications

(9 citation statements)

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“…The numerical analysis of the problems of lowering the level of thermal stresses by the proper choice of dependences of the characteristics of composite materials on two coordinates was carried out in [11]. The problems of determination of the speed-optimal modes of heating of bodies with constrains imposed either on temperature or on stresses were considered in [4,18]. In addition, the problem of identification of the thermal stressed state of bodies with incomplete information about the conditions of heating was also analyzed in these works.…”

Section: Introductionmentioning

confidence: 99%

Stationary Temperature Field Ensuring the Absence of Thermal Stresses in an Inhomogeneous Rectangular Beam

Kalynyak

2022

J Math Sci

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We consider the inverse problem of thermoelasticity for a long inhomogeneous rectangular beam under the conditions of constant axial strains in the presence of a stationary temperature field and convective heat exchange with ambient media. The elastic and thermal characteristics of the beam material in its cross section are arbitrary functions of coordinates. We establish the formulas for the temperature distributions on the lateral surfaces of the beam, heat-transfer coefficients, and densities of the internal heat sources guaranteeing the absence of thermal stresses in the beam. We also deduce analytic dependences of the thermal conductivity and the coefficients of linear thermal expansion on the coordinates corresponding to the absence of stresses in the beam without internal heat sources.

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Section: Introductionmentioning

confidence: 99%

Stationary Temperature Field Ensuring the Absence of Thermal Stresses in an Inhomogeneous Rectangular Beam

Kalynyak

2022

J Math Sci

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“…It is clear that the adequacy of theoretical investigations of the thermoelastic behavior of these structural elements is strongly affected by neglecting inhomogeneities, including, in particular, their functionally graded nature (the presence of layers in elements) and the temperature dependences (thermal sensitivity) of physicomechanical characteristics (PMC) of materials. The analysis of the state of investigations of the thermomechanical behavior of bodies of this kind shows that taking into account the entire collection of important factors (including the geometry of body, inhomogeneity of its structure, thermal sensitivity of the PMC of materials, and thermal and force actions) leads to mathematical problems whose solution, even with the help of numerical methods, is connected with significant difficulties and requires specially developed algorithms or substantial adaptation of the existing procedures [2,4,5,12,13,15]. However, in the engineering practice, it is preferable to use relatively simple numerical-analytic relations and algorithms, which enable one to study the thermomechanical behavior of the object with predicted reliability.…”

Section: Introductionmentioning

confidence: 99%

Numerical-Analytic Determination of the Static Thermoelastic State of Plane Multilayer Thermosensitive Structures

Кушнір

Makhorkin

2022

J Math Sci

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We propose a numerical-analytic method for the determination of one-dimensional static thermoelastic states of plane multilayer structures with arbitrary types of temperature dependences of the physical and mechanical characteristics of the materials of their components. The proposed method is based on the use of the theory of generalized functions, approximation of temperature dependences of the physical and mechanical characteristics of materials by piecewise-constant functions, and introduction of an analog of the Kirchhoff function. The method is verified by analyzing the static thermoelastic states of twoand three-layer plates.

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“…In this case, the mathematical model for the determination of the unknown thermal state of a solid calls for the formulation of an inverse thermoelasticity problem. [27][28][29] A problem on the identification of the heat flux on the inner circumference of a long hollow cylinder was considered by Blanc and Raynaud [26] under the supplementary information about the temperature and strains on the outer periphery. Comparing the experimental and numerical results, the efficiency of the presented technique was illustrated and the advantages of such formulation over the one based on the inverse heat-conduction problem were clearly shown.…”

Section: Introductionmentioning

confidence: 99%

“…In this case, the mathematical model for the determination of the unknown thermal state of a solid calls for the formulation of an inverse thermoelasticity problem. [ 27–29 ]…”

Section: Introductionmentioning

confidence: 99%

Effect of Material Properties in the Direct and Inverse Thermomechanical Analyses of Multilayer Functionally Graded Solids

2021

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Herein, the effect of material inhomogeneity on the temperature and stress distributions in functionally graded solids is analyzed. Assuming the inaccessibility of the inner surface of a multilayer functionally graded hollow sphere for the direct monitoring of the temperature in real time, the problem on identifying the temperature on this surface is formulated by implementing the temperature and circumferential strain given on the outer surface. The material properties within each sphere layer are assumed to be arbitrary functions of the radial coordinate. By representing the material properties of the sphere in the form of stepwise‐variable functions and implementing the generalized derivative technique, a method for the reduction of the formulated problem to an inverse thermoelasticity problem is developed. Using the finite difference method, a numerical algorithm for solving the inverse problem is suggested. The stability of the proposed numerical algorithm concerning the input perturbation is verified.

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Modeling and optimization in the thermomechanics of inhomogeneous solids

Cited by 5 publications

References 0 publications

Stationary Temperature Field Ensuring the Absence of Thermal Stresses in an Inhomogeneous Rectangular Beam

Stationary Temperature Field Ensuring the Absence of Thermal Stresses in an Inhomogeneous Rectangular Beam

Numerical-Analytic Determination of the Static Thermoelastic State of Plane Multilayer Thermosensitive Structures

Effect of Material Properties in the Direct and Inverse Thermomechanical Analyses of Multilayer Functionally Graded Solids

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