A NEW MULTIFIELD FINITE ELEMENT METHOD IN STEADY STATE HEAT ANALYSIS

Abstract

A new original primal-mixed finite element approach and related hexahedral finite element for the analysis of behavior of solid bodies under thermal loading is presented. The essential contributions of the present approach is the treatment of temperature and heat flux as fundamental variables that are simultaneously calculated, as well as capability to introduce initial and prescribed temperature and heat flux. In order to minimize accuracy error and enable introductions of flux constraints, the tensorial character of the present finite element equations is fully respected. The proposed finite element is subjected to some standard benchmark tests in order to test convergence of the results, which enlighten the effectiveness and reliability of the approach proposed.

Keywords

Dates

  • Submission Date2004-07-14
  • Revision Date2005-05-05
  • Acceptance Date2005-05-10

References

  1. [1] Bathe KJ, The inf-sup condition and its evaluation for mixed finite element methods. Computers & Structures, 79 (2001),pp. 243-252
  2. [2] Arnold DN, Mixed finite element methods for elliptic problems. Comput. Meth. Appl. Mech. Eng., 82 (1990), pp. 281?300
  3. [3] Miranda S., Ubertini F., On the consistency of finite element models, Comput. Methods Appl. Mech. Engrg., 190 (2001), pp. 2411-2422
  4. [4] Cannarozzi AA, Ubertini F., A mixed variational method for linear coupled thermoelastic analysis, International Journal of Solids and Structures, 38 (2001), pp. 717-739
  5. [5] Mijuca D., On hexahedral finite element HC8/27 in elasticity, Computational Mechanics, 33 (2004), 6, pp. 466-480
  6. [6] Duff IS., Gould NI., Reid JK., Scott JA., and Turner K. Factorization of sparse symmetric indefinite matrices, IMA J. Numer. Anal., 11 (1991), pp. 181-204
  7. [7] G+DComputing, Straus7, Finite element analysis system software package ? Verification Manual, www.strand.aust.com, Australia
  8. [8] Hinton E., Campbell J.S., Local and global smoothing of discontinuous finite element functions using a least squares method, Int. J. Num. Meths. Eng., 8 (1974), pp. 461?480
  9. [9] Holman J.P., Heat Transfer, McGraw-Hill, New York, 1990
  10. [10] Zienkiewicz O.C., Zhu J.Z., Taylor R.L., Nakazawa S., The patch test for mixed formulations. Int. J. Numer. Meth. Eng., 23 (1986), pp. 1873?1883
  11. [11] Olson M.D., The mixed finite element method in elasticity and elastic contact problems. In: Atluri SN, Gallagher RH, Zienkiewicz OC (eds) Hybrid and mixed finite element methods, John Wiley & Sons, (1983), pp. 19?49
  12. [12] Kasper E.P., Taylor R.L., A mixed-enhanced strain method: linear problems. University of California, (1997), Report No.UCB/SEMM-97/02
  13. [13] Brezzi F., Fortin M., Mixed and hybrid finite element methods. Springer-Verlag, New York, (1991)
  14. [14] Berkovic M., Mijuca D., On the main properties of the primal-mixed finite element formulation. Facta Universitatis Series Mechanics, Automatic Control and Robotics., 2 (1999) , 9, pp. 903?920
  15. [15] Mijuca D., A new reliable 3D finite element in elasticity. In: Proceedings of the fifth world congress on computational mechanics (WCCM V), Mang HA, Rammerstorfer FG, Eberhardsteiner J (eds) Vienna University of Technology, Austria, 2002
  16. [16] Jaric J., Continuum mechanics, Gradjevinska knjiga (in Serbian) Beograd, 1988
  17. [17] Societe Francaise des Mecaniciens, Commission Validation des progiciels de calcul de Structures, groupe de travail Thermique (2D et 3D) et thermoelasticite: TPLA 01/89. Paris, (1989)
  18. [18] Societe Francaise des Mecaniciens, Commission Validation des progiciels de calcul de Structures, groupe de travail Thermique (2D et 3D) et thermoelasticite: TPLV 04/89. Paris, (1989)
Volume 9, Issue 1, Pages111 -130