Identification of inhomogeneous characteristics of prestressed pyromaterials
https://doi.org/10.22405/2226-8383-2018-19-2-183-198
Abstract
Functional gradient pyromaterials are found
wide application in the creation of various diagnostic instruments. For
correct calculation of devices using pyroeffect, you need knowledge
material characteristics. In the case of inhomogeneous pre-stressed
bodies, direct measurements of material characteristics are impossible, since they
represent some functions of the coordinates. Finding characteristics
heterogeneous pyromaterials is possible only on the basis of apparatus
coefficient inverse problems of thermoelectroelasticity (KOZT), which
practically not developed. The paper presents the formulation of the inverse problem
thermoelectroelasticity for prestressed
functional gradient rod. For this, based on the approach,
proposed by Guzem AN, the equations of thermoelectroelasticity for
prestressed rod. The problem is dimensioned.
A weak formulation of the direct problem of thermoelectroelasticity is obtained. Based
weak formulation and the linearization method, the operator equations for
solution of the inverse problem on the basis of the iterative process. During the course of
Iteration process correction to recoverable characteristics
thermoelectroelastic rod were determined from the solution of integral equations
Fredholm of the first kind. A direct problem was solved on the basis of the method of reduction to
system of Fredholm integral equations of the second kind in transformants in
Laplace and the use of the treatment procedure implemented in accordance with
The theory of residues A series of computational experiments on
The restoration of characteristics, the change of which has an essential
influence on additional information. In computational experiments
one of the characteristics of a thermoelectroelastic rod under
known others. Practical recommendations for choosing the most
informative time intervals for measuring the input information.
It was found that the appearance of initial stresses significantly affects
results of reconstruction of the characteristics of the rod.
About the Authors
Alexander Ovanesovich Vatulyan
Institute of mathematics, mechanics and computer sciences I.I. Vorovich Southern Federal University.
Russian Federation
doctor of physical and mathematical sciences, professor, head of the chair of elasticity theory
Russian Federation
doctor of physical and mathematical sciences, professor, head of the chair of elasticity theory
Sergey Anatolyevich Nesterov
Mathematical Institute, a branch of the Vladikavkaz Scientific Center of the Russian Academy of Sciences.
Russian Federation
Candidate of Physical and Mathematical Sciences, Senior Researcher of the Department of Differential Equations
Russian Federation
Candidate of Physical and Mathematical Sciences, Senior Researcher of the Department of Differential Equations
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Review
For citations:
Vatulyan A.O., Nesterov S.A. Identification of inhomogeneous characteristics of prestressed pyromaterials. Chebyshevskii Sbornik. 2018;19(2):183-198. (In Russ.) https://doi.org/10.22405/2226-8383-2018-19-2-183-198
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