Structural Engineering and Mechanics

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Non-conventional formulations for the finite element method

  • de Freitas, J.A. Teixeira (Departamento de Engenharia Civil, Instituto Superior Tecnico.) ;
  • de Almeida, J.P. Moitinho (Departamento de Engenharia Civil, Instituto Superior Tecnico.) ;
  • Peraira, E.M.B. Ribeiro (Departamento de Engenharia Civil, Instituto Superior Tecnico.)
  • Published : 1996.11.25
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Abstract

The paper reports on alternative hybrid/mixed formulations being developed by the Structural Analysis Research Group of Institute Superior T$\acute{e}$cnico. These formulations open the scope and increase the power of the finite element method by allowing different fields to be independently approximated, within certain consistency criteria, and by enhancing the use of a wide range of approximation functions. They have been applied to the analysis of 2-D problems, laminar structures and solids, using different constitutive relations, both in quasi-static and dynamic regimes. The fundamental properties of the formulations are identified and assessed and their performance is illustrated using simple, linear applications.

Keywords

References

  1. Almeida, J.P.M. (1991), "Modelos de elementos finitos para a anaise elastoplatica", Ph.D. Thesis, Universidade Tecnica de Lisboa.
  2. Almeida, J.P.M. (1991), "Alternative approach to the formulation of hybrid equilibrium finite elements", Comp. & Struct., 40,1043-1047. https://doi.org/10.1016/0045-7949(91)90336-K
  3. Almeida, J.P.M. (1992), "Janela: uma interface grafica destinada a aplicacao em problemas de Mecanica Computacional", Internal Report, IST, Lisbon.
  4. Almeida, J.P.M. and Freitas, J.A.T. (1995), "Equilibrated or compatible finite element solutions in the elastoplastic analysis of stretching plates", COMPLAS V, 2071-2080, Barcelona.
  5. Almeida, J.P.M. and Freitas, J.A.T. (1996), "On the parallel implementation of non-conventional finite element formulations", M. Papadrakakis, ed., Advanced Finite Element Solution Techniques, CIMNE, Barcelona, 39, 3175-3194.
  6. Almeida, J.P.M. and Pereira, O.J.B.A. (1996), "A set of hybrid equilibrium finite element models for the analysis of three-dimensional solids", Int. J. Num. Meth. Engng., 39, 2789-2802. https://doi.org/10.1002/(SICI)1097-0207(19960830)39:16<2789::AID-NME976>3.0.CO;2-J
  7. Castro, L.M.S.S. and Freitas, J.A.T. (1996)," Hybrid-mixed finite element elastoplastic analysis based on Walsh and wavelet interpolation", M. Papadrakskis, ed., Advanced Finite Element Solution Techniques, CIMNE, Barcelona, in press.
  8. Chudnovsky, A. and Kachanov, M. (1983), "Interaction of a crack with a field of microcracks", Int. J. Eng. Sci., 21, 1009-1018. https://doi.org/10.1016/0020-7225(83)90078-2
  9. Cottle, R.W. (1963), "Symmetric dual quadratic programs", Q. Appl. Maths., 21, 237-241. https://doi.org/10.1090/qam/156707
  10. Daubechies, I. (1988), "Orthonormal bases of compactly supported wavelets", Comm. on Pure & Appl. Mathematics, 41, 906-996.
  11. de Veubeke, B.F. (1965), "Displacement and equilibrium models in the finite element method", in Stress Analysis, ed. by O.C. Zienckiewicz and G.S. Holister, Wiley, London, 145-196.
  12. Dong, Y.F. and Freitas, J.A.T. (1993), "Alternative approach for hybrid stress elements with incompatible displacements", CIVILCOMP93, Edinburgh, 99-105.
  13. Freitas, J.A.T. (1989), "Duality and symmetry in mixed integral methods of elastostatics", Int. J. Num. Meth. Engng., 28, 1161-1179. https://doi.org/10.1002/nme.1620280512
  14. Freitas, J.A.T. and Pereira, E.M.B.R. (1991)," Application of the Mathieu series to the boundary integral method", Comp. & Struct., 40, 1307-1314. https://doi.org/10.1016/0045-7949(91)90400-G
  15. Freitas, J.A.T. and Castro, L.M.S.S. (1992), "Digital interpolation in mixed finite element structural analysis", Comp. & Struct., 44, 743-751. https://doi.org/10.1016/0045-7949(92)90458-C
  16. Freitas, J.A.T. and Ji, Z.Y. (1996), "Hybrid-Trefftz boundary integral formulation for simulation of singular stress fields", Int. J. Num. Meth. Engng., 39, 281-308. https://doi.org/10.1002/(SICI)1097-0207(19960130)39:2<281::AID-NME857>3.0.CO;2-X
  17. Freitas, J.A.T. and Ji, Z.Y. (1996), "Hybrid-Trefftz equilibrium model for crack problems", Int. J. Num. Meth. Engng., 39, 569-584. https://doi.org/10.1002/(SICI)1097-0207(19960229)39:4<569::AID-NME870>3.0.CO;2-8
  18. Freitas, J.A.T. and Castro, L.M.S.S. (1996), "Finite element solutions with Walsh series and wavelets", CAMES, in press.
  19. Freitas, J.A.T. (1996), "Hybrid-Trefftz displacement and stress elements for elastodynamic analysis in the frequency domain", CAMES, in press.
  20. Harwell Subroutine Library (1993), Release 11, Theoretical Studies Department, AEA Technology, Harwell.
  21. Kachanov, M. (1986), "On crack-microcrack interactions", Int. J. Fract., 30, R65-R72. https://doi.org/10.1007/BF00019712
  22. Karush, W. (1939), "Minima of functions of several variables with inequalities as side conditions", M.S. Thesis, University of Chicago.
  23. Kuhn, H.W. and Tucker, A.W. (1951), "Nonliear Programming", 2nd Berkeley Symp. on Mathematical Statistics and Probability, Berkeley.
  24. Kunzi, H.P., Krelle, W. and Tucker, A.W. (1966), "Nonlinear Programming", Blaisdel.
  25. Maier, G. and Munro, J. (1982), "Mathematical programming applications to engineering plastic analysis", AM update.
  26. Maier, G. and Smith, D.L. (1986), "Mathematical programming applications to engineering plastic analysis", AM Update.
  27. Maiti, S.K. (1992), "A multicorner variable order singularity triangle to model neighbouring singularities", Int. J. Numer. Meth. Engng., 35, 391-408. https://doi.org/10.1002/nme.1620350210
  28. Maunder, E.A.W., Almeida, J.P.M. and Ramsay, A.C.A. (1996), "A general formulation of equilibrium macro-elements with control of spurious kinematic modes - The exorcism of an old curse", Int. J. Num. Meth. Engng., 39, 3175-3194. https://doi.org/10.1002/(SICI)1097-0207(19960930)39:18<3175::AID-NME978>3.0.CO;2-3
  29. Pereira, E.M.B.R. (1993), "Elementos finitos de tensao aplicados a analise elastica de estruturas, Ph.D. Thesis, Universidade Tecnica de Lisboa.
  30. Pereira, E.M.B.R. and Freitas, J.A.T. (1996), "A mixed-hybrid finite element model based on orthogonal functions", Int. J. Num. Meth. Engng., 39, 1295-1312. https://doi.org/10.1002/(SICI)1097-0207(19960430)39:8<1295::AID-NME903>3.0.CO;2-H
  31. Pereira, E.M.B.R. and Freitas, J.A.T. (1996), "Hybrid-mixed finite element model based on Legendre polynomials for Reissner-Mindlin plates", Comp. Meth. Appl. Mech. Engng., in press.
  32. Pian, T.H.H. and Tong, P. (1969), "Basis of finite element methods for solid continua", Int. J. Num. Meth. Engng., 1, 3-28. https://doi.org/10.1002/nme.1620010103
  33. Pian, T.H.H. and Wu, C.C. (1988), "A rational approach for choosing stress terms elements with incompatible displacements", Int J Num Meth Engrng., 26, 2331-2343. https://doi.org/10.1002/nme.1620261014
  34. Pissanetzky, S. (1984), "Sparse matrix technology", Academic Press Inc.
  35. Ramsay, A.C.A. (1995), "Robust variable degree equilibrium elements: their formulation and application", Report for Human Capital and Mobility Network, ERB4050PL1930382.
  36. Rebelo, J.S. (1993), "Modelos de elementos finitos para a anaise elatica de lajes, PhD Thesis, Universidade Tecnica de Lisboa.
  37. Stolarski, H. and Belytschko, T. (1987), "Limitation principles for mixed finite elements based on the Hu-Wahizu variational formulation", Comp. Meth. Appl. Mech. & Eng., 60, 195-216. https://doi.org/10.1016/0045-7825(87)90109-5
  38. Walsh, J.L. (1923), "A closed set of orthogonal functions", Ann. J. Math., 55, 5-24.

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