LOGIN TO YOUR ACCOUNT

Username
Password
Remember Me
Or use your Academic/Social account:

CREATE AN ACCOUNT

Or use your Academic/Social account:

Congratulations!

You have just completed your registration at OpenAire.

Before you can login to the site, you will need to activate your account. An e-mail will be sent to you with the proper instructions.

Important!

Please note that this site is currently undergoing Beta testing.
Any new content you create is not guaranteed to be present to the final version of the site upon release.

Thank you for your patience,
OpenAire Dev Team.

Close This Message

CREATE AN ACCOUNT

Name:
Username:
Password:
Verify Password:
E-mail:
Verify E-mail:
*All Fields Are Required.
Please Verify You Are Human:
fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Marin, L; Karageorghis, A; Lesnic, D; Johansson, BT (2017)
Publisher: Taylor & Francis
Languages: English
Types: Article
Subjects:
An inverse problem in static thermo-elasticity is investigated. The aim is to reconstruct the unspecified boundary data, as well as the temperature and displacement inside a body from over-specified boundary data measured on an accessible portion of its boundary. The problem is linear but ill-posed. The uniqueness of the solution is established but the continuous dependence on the input data is violated. In order to reconstruct a stable and accurate solution, the method of fundamental solutions is combined with Tikhonov regularization where the regularization parameter is selected based on the L-curve criterion. Numerical results are presented in both two and three dimensions showing the feasibility and ease of implementation of the proposed technique.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • [1] G. Alessandrini, L. Rondi, E. Rosset and S. Vessella, The stability for the Cauchy problem foe elliptic equations, Inverse Problems 25 (2009), 123004 (47 pp).
    • [2] M. H. Aliabadi, The Boundary Element Method. Applications in Solids and Structures, John Wiley and Sons, London, 2002, Volume 2.
    • [3] A. Bakushinski, Remark on choosing a regularization parameter using the quasioptimality and ratio criterion, U.S.S.R. Comput. Math. Math. Phys. 24 (1984), 181-182.
    • [4] A. H. Barnett and T. Betcke, Stability and convergence of the method of fundamental solutions for Helmholtz problems on analytic domains, J. Comput. Phys. 227 (2008), 7003-7026.
    • [5] M. Belge, M. Kilmer and E. L. Miller, Efficient determination of multiple regularization parameters in a generalized L-curve framework, Inverse Problems 18 (2002), 1161-1183.
    • [6] C. S. Chen, A. Karageorghis and Y. Li, On choosing the location of the sources in the MFS, Numer. Algor., to appear DOI 10.1007/s11075-015-0036-0.
    • [7] R. Dautray and J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, Vol.3, Spectral Theory and Applications, Springer-Verlag, Berlin, 1990.
    • [8] B. H. Dennis and G. S. Dulikravich, Simultaneous determination of temperatures, heat fluxes, deformations and tractions on inaccesible boundaries, ASME J. Heat Transfer 121 (1999), 537-545.
    • [9] B. H. Dennis, G. S. Dulikravich and S. Yoshimura, A finite element formulation for the determination of unknown boundary conditions for three-dimensional steady thermoelastic problems, ASME J. Heat Transfer 126 (2004), 110-118.
    • [10] B. H. Dennis, W. Jin, G. S. Dulikravich and J. Jaric, Application of the finite element method to inverse problems in solid mechanics, Int. J. Structural Changes in Solids 3 (2011), 11-21.
    • [11] P. Di Barba and A. Lorenzi, A magneto-thermo-elastic identification problem with a moving boundary in a micro-device, Milan J. Math. 81 (2013), 347-383.
    • [12] G. Fichera, Existence Theorems in Elasticity, Springer, Berlin, 1973.
    • [13] X. W. Gao, Boundary element analysis in thermoelasticity with and without internal cells, Int. J. Numer. Meth. Eng. 57 (2003), 975-990.
    • [14] P. C. Hansen, Discrete Inverse Problems: Insight and Algorithms, SIAM, Philadelphia, 2010.
    • [15] T. I. Ishankulov and O. I. Makhmudov, The Cauchy problem for a system of thermoelasticity equations in a space, Mat. Zametki 64 (1998), 212-217.
    • [16] A. Karageorghis, D. Lesnic, and L. Marin, The method of fundamental solutions for an inverse boundary value problem in static thermo-elasticity, Comput. & Structures 135 (2014), 32-39.
    • [17] A. Karageorghis and Y.-S. Smyrlis, Matrix decomposition MFS algorithms for elasticity and thermo-elasticity problems in axisymmetric domains, J. Comput. Appl. Math. 206 (2007), 774-795.
    • [18] S. Khajehpour and M. R. Hematiyan, Inverse reconstruction of thermal and mechanical boundary conditions in coupled nonlinear thermo-elastic problems, Internat. J. Appl. Mech. 6 (2014), 1450014 (33 pages).
    • [19] V. A. Kozlov, V. G. Maz'ya, and A. V. Fomin, The inverse problem of coupled thermo-elasticity, Inverse Problems 10 (1994), 153-160.
    • [20] J.-L. Lee and Y.-C. Yang, Inverse problem of coupled thermoelasticity for prediction of heat flux and thermal stresses in an annular cylinder, Int. Commun. Heat Mass Transfer 28 (2001), 661-670.
    • [21] L. Marin and A. Karageorghis, The MFS-MPS for two-dimensional steady-state thermoelasticity problems, Eng. Anal. Bound. Elem. 37 (2013), 1004-1020.
    • [22] L. Marin and A. Karageorghis, The MFS for the Cauchy problem in two-dimensional steady-state linear thermoelasticity, Int. J. Solids Struct. 50 (2013), 3387-3398.
    • [23] L. Marin, L., A. Karageorghis and D. Lesnic, A numerical study of the SVD-MFS solution of inverse boundary value problems in two-dimensional steady-state linear thermoelasticity, Numer. Methods Partial Differential Equations 31 (2015), 168-201.
    • [24] L. Marin, A. Karageorghis. and D. Lesnic, Regularized MFS solution inverse boundary value problems in three-dimensional steadystate linear thermoelasticity, Int. J. Solids Struct., to appear DOI:10.1016/j.ijsolstr.2016.03.013.
    • [25] P. L. Mueller and S. Siltanen, Linear and Nonlinear Inverse Problems with Practical Applications, SIAM, Philadelphia, 2012.
    • [26] N. Noda, An inverse problem of coupled thermal stress in a long circular cylinder, JSME Int. J. Ser. 1 32 (1989), 348-354.
    • [27] N. Noda, F. Ashida and T. Tsuji, An inverse transient thermoelastic for a transversely-isotropic body, J. Appl. Mech. 56 (1989), 791-797.
    • [28] N. Noda, R. B. Hetnarski and Y. Tanigawa, Thermal Stresses, Taylor & Francis, New York, 2003.
    • [29] W. Nowacki, Thermoelasticity, second ed., Pergamon Press, Oxford; PWN-Polish Scientific Publishers, Warsaw, 1986.
    • [30] M. Tanaka, A. Guzik, T. Matsumoto and R. A. BiaƂecki, An inverse estimation of multi-dimensional load distributions in thermoelasticity problems via dual reciprocity BEM, Comput. Mech. 37 (2005), 86-95.
    • [31] Y.-C. Yang, U.C. Chen, and W.-J. Chang, A inverse problem of coupled thermoelasticity in predicting heat flux and thermal stresses by strain measurement, J. Ther. Stresses. 25 (2002), 265-281.
  • No related research data.
  • Discovered through pilot similarity algorithms. Send us your feedback.

Share - Bookmark

Cite this article