Mathematical models of thermomechanics of a relaxing solid

Zarubin, V. S.; Кувыркин, Г. Н.

doi:10.3103/s0025654412020124

Cited by 8 publications

(9 citation statements)

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“…Large number of studies is devoted to the theory of temperature stresses and engineering methods for their calculation [1][2][3][4]. Mathematical model of thermal stresses of metal structures is reduced to calculation of non-stationary behavior of thermal fields by solving a non-stationary initial-boundary value problem of thermal conductivity, and calculation of temperature stresses by solving stationary boundary problem of elasticity [1,2].…”

Section: Introductionmentioning

confidence: 99%

Application of the Method of Boundary Integral Equations for Non-Stationary Problem of Thermal Conductivity in Axially Symmetric Domain

Zrazhevsky

Zrazhevska

2017

EUREKA: Physics and Engineering

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The article considers the non-stationary initial-boundary problem of thermal conductivity in axially symmetric domain in Minkowski space, formulated as equivalent boundary integral equation. Using the representation of the solution in the form of a Fourier series expansion, the problem is reformulated as an infinite system of two-dimensional singular integral equations regarding expansion coefficients. The paper presents and investigates the explicit form for fundamental solutions used in the integral representation of the solution in the domain and on the border. The obtained results can be used in the construction of efficient numerical boundary element method for estimation of structures behavior under the influence of intense thermal loads in real-time.

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Section: Introductionmentioning

confidence: 99%

Application of the Method of Boundary Integral Equations for Non-Stationary Problem of Thermal Conductivity in Axially Symmetric Domain

Zrazhevsky

Zrazhevska

2017

EUREKA: Physics and Engineering

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“…Analytical solutions of basic model problems for canonical domains are obtained [1][2][3][4]. At the same time, calculations and control of real constructions require the development of efficient numerical methods that allow to evaluate the behavior of structures under the influence of intense thermal loads in real time.…”

Section: Introductionmentioning

confidence: 99%

“…Since cylindrical structures, such as pipelines, reactor vessel, constitute a substantial part of the production elements, calculation of critical temperature modes of their operation is important. Theory of temperature stress and engineering methods of their calculation is widely represented in the literature [1][2][3][4]. Mathematical model of thermal stress of metal constructions can be reduced to investigation of the non-stationary behavior of thermal fields by solving non-stationary initial-boundary problem of thermal conductivity and calculating of temperature stress by solving stationary boundary problem of elasticity [1].…”

mentioning

confidence: 99%

“…Theory of temperature stress and engineering methods of their calculation is widely represented in the literature [1][2][3][4]. Mathematical model of thermal stress of metal constructions can be reduced to investigation of the non-stationary behavior of thermal fields by solving non-stationary initial-boundary problem of thermal conductivity and calculating of temperature stress by solving stationary boundary problem of elasticity [1].Analytical solutions of basic model problems for canonical domains are obtained [1][2][3][4]. At the same time, calculations and control of real constructions require the development of efficient numerical methods that allow to evaluate the behavior of structures under the influence of intense thermal loads in real time.…”

mentioning

confidence: 99%

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Obtaining and Investigation of the Integral Representation of Solution and Boundary Integral Equation for the Non-Stationary Problem of Thermal Conductivity

Zrazhevsky

Zrazhevska

2016

EUREKA: Physics and Engineering

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Technological processes in the energy sector and engineering require the calculation of temperature regime of functioning of different constructions. Mathematical model of thermal loading of constructions is reduced to a non-stationary initial-boundary value problem of thermal conductivity. The article examines the formulation of the non-stationary initial-boundary value problem of thermal conductivity in the form of a boundary integral equation, analyzes the singular equation and builds the fundamental solution. To build the integral representation of the solution the method of weighted residuals is used. The correctness of the obtained integral representation of the solution in Minkowski space is confirmed. Singularity of the fundamental solution is investigated. The boundary integral equation and fundamental solution for axially symmetric domain for internal problem is built. The results of the article can be useful for numerical implementation of boundary element method.

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“…To this end, three types of model materials are considered, according to [4]: materials with internal state parameters, materials with memory, and materials with rate-dependent behavior.…”

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confidence: 99%

A Mathematical Model Describing the Variation in Material Properties

Kuzin

2015

Int Appl Mech

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A mathematical model that describes the variation in material properties with time under a load is proposed. The material properties are considered at thermodynamic and structural levels. At the thermodynamical level, the free energy function is additively decomposed in the time parameter into terms that describe the history of loading of the body and its current parameters. At the structural level, damage as a scalar internal variable is used. The relations derived are analyzed for modeling and practical applications Keywords: mathematical model, damage, variation in material properties Introduction.To analyze the behavior of highly stressed structural members after failure, it is necessary to use fracture mechanics [10,11,16] or damage mechanics [2,12,18].Currently, the service life of engineering objects is estimated taking into account the evolution of the internal structure of the material. This structure changes its parameters under the action of external mechanical, thermal, and chemical factors [2]. This circumstance is one of the physical factors restricting the application of engineering models of delayed fracture (fatigue) in which the kinetics of fracture is determined by the variation of external factors with time.The accumulation of structural changes in a material under external loads is a multiscale and multistage kinetic process. It develops at different scales: atomic, dislocation, substructural, and structural. This necessitates combining micro-, meso-, and macroscopical model descriptions of the process, taking into account wave effects that may occur during dynamic changes of the structure [2,15,20]. The process is multistage in the sense that as structural changes occur, the material goes through sequential states, each characterized by its individual regularities and nonlinearly depending on the history of service of the object.All these phenomena cause variation of the rheology of the materials of parts and assemblies with time, i.e., change of the effective properties of the materials. Therefore, reliable prediction of the service life of parts and assemblies, assessment of the remaining service life, and revealing of the cause of failure of structural members are impossible without adequate mathematical models that describe the dominating structural processes occurring in individual service conditions of the object. Analysis of Alternative Descriptions of the Change of the Service Properties of an Object.External loads change the internal structure and the behavior of the material in service conditions, i.e., the response of the object. It is of importance to allow for the time-dependent rheological parameters of the materials (chronorheological properties) of parts and assemblies.There are three lines of study into the kinetics of structural changes and their effect on the chronorheological properties of metal systems: (i) study of the physical aspects of the structural changes in materials under external loads [2]; (ii) experimental study and description of metal systems in the context...

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Mathematical models of thermomechanics of a relaxing solid

Cited by 8 publications

References 1 publication

Application of the Method of Boundary Integral Equations for Non-Stationary Problem of Thermal Conductivity in Axially Symmetric Domain

Application of the Method of Boundary Integral Equations for Non-Stationary Problem of Thermal Conductivity in Axially Symmetric Domain

Obtaining and Investigation of the Integral Representation of Solution and Boundary Integral Equation for the Non-Stationary Problem of Thermal Conductivity

A Mathematical Model Describing the Variation in Material Properties

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