A linear uncoupling numerical scheme for the nonlinear coupled thermoelastodynamics equations

  • Carlos A. de Moura
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1005)


A numerical scheme for computing approximate solutions to the non-linear equations of coupled thermoelastodynamics is proposed. The discretization is made in such a way that the algebraic system to be solved at each time level is a linear one, the displacement and temperature fields being uncoupled for the calculations.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    C.M. DAFERMOS, "Can dissipation prevent the breaking of waves?", Transactions of the 26th Conference of Army Mathematicians, U.S. Dep. of Defense ARO Report 81-1, pp. 187–198, 1981.Google Scholar
  2. [2]
    M. SLEMROD, "Global existence, uniqueness and asymptotic stability of classical smooth solutions in one-dimensional non-linear thermoelasticity", Arch. Rat. Mech. Anal., vol. 76, no 2, pp. 97–134, 1981.MathSciNetCrossRefMATHGoogle Scholar
  3. [3]
    C.M. DAFERMOS, "Conservation laws with dissipation", Preprint, Div. of Appl. Mathematics, Brown University, July 1980.Google Scholar
  4. [4]
    C.A. de MOURA & R.A. FEIJÓO, "An uncoupling strategy for numerically solving the dynamic thermoelasticity equations", Rev. Br. C. Mec., vol. 111, no 1, pp. 41–47, 1981.Google Scholar
  5. [5]
    Z. da FONSECA, "Soluciones numéricas via métodos variacionales de problemas en termoelasticidad dinámica acoplada", M.Sc. Thesis, COPPE/UFRJ, R. de Janeiro, 1977.Google Scholar
  6. [6]
    C.A. de MOURA, R.A. FEIJÓO & Z. da FONSECA, "Estudo numérico de problemas lineares em termoelasticidade acoplada", VI Sem. Bras. de Anátise, IMPA, R. de Janeiro, pp. 209–220, 1977.Google Scholar
  7. [7]
    R.A. FEIJÓO, Z. da FONSECA & C.A. de MOURA, "Aplicación del método de elementos finitos en problemas dinámicos de termoelasticidad acoplada", XIX Jornadas Sudamericanas de Ing. Estnutural, Santiago do Chile, vol. II, paper F-3, pp. 1–13, 1978.Google Scholar
  8. [8]
    C.A. de MOURA & R.A. FEIJÓO, "An unconditionally convergent uncoupled algorithm for linear models in coupled thermoelasticity", Abstracts of the XV IUTAM Congress, Toronto, Canada, p. 234, 1980.Google Scholar
  9. [9]
    R.A. FEIJÓO & C.A. de MOURA, "Un método variacional en problemas de termoelasticidad acoplada", Rel. Pesq. Desenv. 09/81, LCC, R. de Janeiro, 1981.Google Scholar
  10. [10]
    S.I. CHOU & C.C. WANG, "Estimates of error in finite element approximate solutions to problems in linear thermoelasticity. Part 1. Computationally coupled numerical schemes", Arch. Rat. Mech. Anal., vol. 77, no 3, pp. 263–299, 1981.MathSciNetCrossRefMATHGoogle Scholar
  11. [11]
    S.I. CHOU & C.C. WANG, "Estimates of error in finite element approximate solutions to problems in linear thermoelasticity. Part 2. Computationally uncoupled numerical schemes", Ibidem (to appear).Google Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Carlos A. de Moura
    • 1
  1. 1.Laboratório de Computação Cientifica - CNPqRio de JaneiroBrasil

Personalised recommendations