Vladikavkazskii Matematicheskii Zhurnal
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Vladikavkaz. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Vladikavkazskii Matematicheskii Zhurnal, 2022, Volume 24, Number 2, Pages 75–84
DOI: https://doi.org/10.46698/v3482-0047-3223-o
(Mi vmj815)
 

This article is cited in 1 scientific paper (total in 1 paper)

Study of inverse problem of thermoelasticity for inhomogeneous materials

A. O. Vatulyanab, S. A. Nesterovb

a Southern Federal University, 8 a Milchakova St., Rostov-on-Don 344090, Russia
b Southern Mathematical Institute VSC RAS, 53 Vatutina St., Vladikavkaz 362025, Russia
Full-text PDF (237 kB) Citations (1)
References:
Abstract: The formulation of the coefficient inverse problem of thermoelasticity for finite inhomogeneous bodies is given. Operator equations of the first kind in Laplace transforms are obtained to solve a nonlinear inverse problem on the basis of an iterative process. The solution of inverse problems of thermoelasticity in the originals is based on the inversion of operator relations in transformants using theorems of operational calculus on the convolution and differentiation of the original. The procedure for reconstruction of thermomechanical characteristics of a rod, layer, cylinder is considered. The initial approximation for the iterative process is found on the basis of two approaches. In the first approach, the initial approximation is found in the class of positive bounded linear functions. The coefficients of linear functions are determined from the condition of minimizing the residual functional. The second approach to finding the initial approximation is based on the method of algebraization. Computational experiments were carried out to recover both monotone and non-monotonic functions. One characteristic was restored while the others were known. Monotonic functions are restored better than non-monotonic ones. In the case of reconstructing the characteristics of layered materials, the greatest error occurred in the vicinity of the points of conjugate. The reconstruction procedure turned out to be resistant to noise in the input information.
Key words: inverse problem of thermoelasticity, functionally graded materials, operator equations, iterative process, algebraization method.
Received: 26.10.2021
Bibliographic databases:
Document Type: Article
UDC: 539.3
MSC: 74B05, 80A20, 80A23
Language: Russian
Citation: A. O. Vatulyan, S. A. Nesterov, “Study of inverse problem of thermoelasticity for inhomogeneous materials”, Vladikavkaz. Mat. Zh., 24:2 (2022), 75–84
Citation in format AMSBIB
\Bibitem{VatNes22}
\by A.~O.~Vatulyan, S.~A.~Nesterov
\paper Study of inverse problem of thermoelasticity for inhomogeneous materials
\jour Vladikavkaz. Mat. Zh.
\yr 2022
\vol 24
\issue 2
\pages 75--84
\mathnet{http://mi.mathnet.ru/vmj815}
\crossref{https://doi.org/10.46698/v3482-0047-3223-o}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4448045}
Linking options:
  • https://www.mathnet.ru/eng/vmj815
  • https://www.mathnet.ru/eng/vmj/v24/i2/p75
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Владикавказский математический журнал
    Statistics & downloads:
    Abstract page:88
    Full-text PDF :31
    References:13
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024