Green tensor and regular solutions of equations of rods thermodynamics and their properties

Alexeyeva, L. A.; Dadayeva, Assyat; Ainakeyeva, Nursaule

doi:10.15632/jtam-pl/133233

Cited by 2 publications

(2 citation statements)

References 6 publications

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“…where is the singular generalized function -a simple layer on S [13], we get the their partial derivatives: , , Then Eqs (2.1) in take the form:…”

Section: Using Generalized Derivatives Of Functionsmentioning

confidence: 99%

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Method of Generalized Functions in Plane Boundary Value Problems of Uncoupled Thermoelastodynamics

Dadayeva¹,

Alexeyeva²

2021

Preprint

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Nonstationary boundary value problems of uncoupled thermoelasticity are considered. A method of boundary integral equations in the initial space-time has been developed for solving boundary value problems of thermoelasticity by plane deformation. According to generalized functions method the generalized solutions of boundary value problems are constructed and their regular integral representations are obtained. These solutions allow, using known boundary values and initial conditions (displacements, temperature, stresses and heat flux), to determine the thermally stressed state of the medium under the influence of various forces and thermal loads. Resolving singular boundary integral equations are constructed to determine the unknown boundary functions.

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“…where is the singular generalized function -a simple layer on S [13], we get the their partial derivatives: , , Then Eqs (2.1) in take the form:…”

Section: Using Generalized Derivatives Of Functionsmentioning

confidence: 99%

“…To solve problems, we use the method of generalized functions (GFM), the main ideas of which are presented in [10][11][12][13].…”

mentioning

confidence: 99%

Method of Generalized Functions in Plane Boundary Value Problems of Uncoupled Thermoelastodynamics

Dadayeva¹,

Alexeyeva²

2021

Preprint

Self Cite

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Dynamics of a Thermoelastic Rod Under Unsteady Thermal and Force Influences

Ainakeyeva

2024

jour

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Rod elements are extensively utilized in various technological fields. An unsteady temperature field induces a time-varying stress field within the rod structure, impacting its strength and reliability during operation. Determining the thermally stressed state of rod structures, considering their mechanical properties (especially elasticity), is a significant scientific and technical challenge. The application of mathematical modeling methods enables the study of thermodynamic processes occurring within a structure and its elements, allowing for the determination of their dynamic and strength characteristics during the design phase. This paper addresses the Cauchy problem for the dynamics of a thermoelastic rod under arbitrary initial conditions and subjected to force and thermal influences. By employing the Green’s tensor for thermoelasticity equations, an analytical solution is derived, which determines deformations, stresses, and temperatures at any point along the rod at any given time, provided the initial state and the acting force and heat sources are known. Numerical calculations of temperature and displacement are presented for cases involving pulsed concentrated force and heat sources. Additionally, solutions to Cauchy problems under the influence of regular force and heat sources distributed along the rod are computed. The developed program allows for the investigation of thermodynamic processes in rods with various physical and mechanical properties, under the influence of both distributed and concentrated pulsed thermal and force sources, described by singular generalized functions.

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Green tensor and regular solutions of equations of rods thermodynamics and their properties

Cited by 2 publications

References 6 publications

Method of Generalized Functions in Plane Boundary Value Problems of Uncoupled Thermoelastodynamics

Method of Generalized Functions in Plane Boundary Value Problems of Uncoupled Thermoelastodynamics

Dynamics of a Thermoelastic Rod Under Unsteady Thermal and Force Influences

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