Application of the Variational Method of Homogeneous Solutions for the Optimal Control of the Axisymmetric Thermoelastic State of a Cylinder

We study a two-dimensional stationary problem of control over the vertical thermal displacements of a plane-deformed half space heated by internal heat sources. As the control function, we choose the distribution of temperature of the environment. The half space participates in the convective heat exchange with the environment according the Newton law. The formulated control problem is reduced to the solution of the inverse problem of thermoelasticity whose solution is constructed in the space of continuous functions. For some specific cases of thermal loading of the half space, we analyze the behavior of the constructed solution.

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“…Substituting the temperature field (8) in the expression for displacements (9) and using condition ( 7), we arrive at an integral equation…”

Section: Construction Of the Solution Of Control Problemmentioning

confidence: 99%

“…The problems of control of the thermal stressed state of homogeneous, inhomogeneous, and thermally sensitive bodies and the approaches used for their solution were studied, in particular, in the works [1,2,4,8,9,12,13,15].…”

Section: Introductionmentioning

confidence: 99%

Optimization of the Steady-State Thermal Displacements of a Plane-Deformed Half Space by Means of External Thermal Loading

Yasinskyy

Tokova

2021

J Math Sci

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“…The axisymmetric stressed state of the body is caused by structural inhomogeneity of the material. One can take it into account through representation of the total strain tensor e ij as the sum of elastic strain e e ij and eigenstrainê ij [9]: e ij = e e ij +ê ij , ij ∈ {ρρ, zz, ϕϕ, ρz} .…”

Section: A Mathematical Model For Axisymmetric Residual Stresses In Tmentioning

confidence: 99%

“…In the direct problem, we assume the eigenstrain componentsê ρρ (ρ) =ê ϕϕ (ρ),ê zz (ρ) to be known functions. Solving the boundary value problem (8), (9), one can determine the components u ρ and u z of the displacement vector, and then, using the relations 3and 7, calculate the stress components…”

Section: A Solution Presentationmentioning

confidence: 99%

See 1 more Smart Citation

Residual stresses in a finite cylinder. Direct and inverse problems and their solving using the variational method of homogeneous solutions

Чекурін¹,

Постолакі²

2018

Math. Model. Comput.

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Mathematical models and methods for determination of axisymmetric residual stresses in a finite cylinder are considered. The model of residual stresses is built using the conception of incompatible eigenstrain tensor. Within the frame of this model, a direct problem for residual stresses determination is formulated. A method based on the variational method of homogeneous solutions is developed for solving the direct problem. Using the obtained solution, features of residual stresses, caused by continuous and piece-wise homogeneous distributions of eigenstrain components are studied. A variational formulation of the inverse problem for residual stresses determination on the base of empirical data obtained by a photoelasticity method is suggested. The inverse problem is solved numerically with the use of iterative calculations of values of the criterion functional. The results presented in the paper can be used for the development of methods and means for nondestructive testing and engineering characterization of materials and structural elements.

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Control of Two-Dimensional Stationary Thermal Stresses in a Half Space with the Help of External Thermal Loading

Yasinskyy

Tokovyy

2022

J Math Sci

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Application of the Variational Method of Homogeneous Solutions for the Optimal Control of the Axisymmetric Thermoelastic State of a Cylinder

Cited by 7 publications

References 8 publications

Optimization of the Steady-State Thermal Displacements of a Plane-Deformed Half Space by Means of External Thermal Loading

Optimization of the Steady-State Thermal Displacements of a Plane-Deformed Half Space by Means of External Thermal Loading

Residual stresses in a finite cylinder. Direct and inverse problems and their solving using the variational method of homogeneous solutions

Control of Two-Dimensional Stationary Thermal Stresses in a Half Space with the Help of External Thermal Loading

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