Identification of inhomogeneous characteristics of prestressed pyromaterials

A. O. Vatulyan ; S. A. Nesterov

Čebyševskij sbornik, Tome 19 (2018) no. 2, pp. 183-198.

Résumé

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.

Détail

Keywords: prestressing, thermoelectroelasticity, identification, inverse problem, rod.

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