An error calculation method for finite element analysis in large displacements

International Journal for Numerical Methods in Engineering

Volumn 40, Issue 20, 1997, Pages 3703-3728

  Bussy, Pascal ^a   Mosbah, Youcef ^a  

^a UNIVERSITÉ DE PICARDIE JULES VERNE   (France)

Author keywords

Damage; Elastoplasticity; Error indicators; Large time increment method; Mesh adaptation; Non linear geometric

Indexed keywords

ELASTOPLASTICITY; ERROR ANALYSIS; GEOMETRY; MATHEMATICAL MODELS; OPTIMIZATION; STRESSES;

DISPLACEMENT; EQUILIBRIUM EQUATION; LARGE TIME INCREMENT METHOD; MESH ADAPTATION;

FINITE ELEMENT METHOD;

EID: 0031248320     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(19971030)40:20<3703::AID-NME235>3.0.CO;2-V     Document Type: Article

References (31)

1. I. Babuska and A. Miller, The post-processing approach in the finite element method. Part 3: A posteriori error estimates and adaptive mesh selection', Int. J. Numer. Meth. Engng., 20, 2311-2324 (1984).
2. 1', Math. Comput., 33, 435-463 (1979).
3. P. Boisse, P. Bussy and P. Ladeveze, 'A new approach in non-linear mechanics: the large time increment method', Int. J. Numer. Meth. Engng., 29, 647-663 (1990).
4. I. Babuska and W. C. Rheinboldt, 'Error estimates for adaptative finite element computation', SIAM, J. Numer. Analysis, (4), 736-754 (1978).
5. J. Z. Zhu, O. C. Zienkiewicz, 'A simple error estimator and adaptative procedure for practical engineering analysis', Int. J. Numer. Meth. Enging., 24, 337-357 (1987).
6. O. C. Zienkiewicz and J. Z. Zhu, The superconvergent patch recovery and a posteriory error estimate. Part 1: The recovery technique, Part 2: Error estimate and adaptivity', Int. J. Numer. Meth. Engng., 33, 1331-1364 (1992).
7. J. Z. Zhu and O. C. Zienkiewicz 'Adaptative techniques in the finite element method' Commun. Appl. Numer. Meth., 4, 197-204 (1988).
8. O. C. Zienkiewicz, J. Z. Zhu and N. G. Gong, 'Effective and practical h-p version adaptive analysis procedures for the finite element method', Int. J. Numer. Meth. Engng., 28, 879-891 (1989).
9. P. Ladevèze and D. Leguillon, 'Error estimate procedure in finite element method and applications', SIAM J. Numer. Anal., 20, 485-509 (1983).
10. P. Ladevèze, G. Coffignal and J. P. Pelle, 'Accuracy of elastoplastic and dynamic analysis accuracy estimates and adaptivity for finite elements', Chap. 10, Wiley, New York, 1986, pp. 181-203.
11. P. Coorevits, P. Ladevèze, J. P. Pelle and P. Rougeot, 'Some new applications of a method for the control and optimization of finite elements computations', in P. Ladevèze, O. C. Zienkiewicz (eds.), New Advances in Computational Structural Mechanics, 1992, pp. 205-217.
12. J. Carnet, P. Ladeveze and D. Leguillon, 'An optimal mesh procedure in the finite element method', Third conf. on Mathematics of Finite Element and Applications, MAFELAP, England, 1981.
13. A. Abdali, K. Benkrid and P. Bussy, 'Numerical simulation of sheet cutting by the large time increment method', Metal Forming 96, J. Mater. Process. Technol, Krakovie, Pologne, 1996, pp. 155-260.
14. P. Bussy, G. Coffignal and P. Ladevèze, 'Reliability and optimization of non linear finite element analyses', Proc. numeta 85, Swansea, 1985, pp. 659-667.
15. P. Bussy, G. Coffignal and P. Ladevèze, 'Error control in elastoplasticity', Proc. smirt 8, Vol B, North-Holland, Amsterdam, 1985, pp. 417-422.
16. P. Bussy and Y. Mosbah, 'Optimisation des calculs linéaires par éléments finis', Proc. Congrés STRUCOME, Paris, 1993, pp. 277-289.
17. P. Ladeveze, J. P. Pelle and P. Rougeot, 'Error estimation and mesh optimisation for classical finite elements', Engng. Comput., 8, 69-80 (1991).
18. P. Bussy and Y. Mosbah, 'Optimization of finite element calculations in non-linear geometry', 4th Int. Conf. on Computational Plasticity: Fundamentals and Applications, Barcelona, 1995, pp. 383-394.
19. Y. Mosbah, 'Optimisation des calculs de structures par éléments finis en non linéaire géométrique', Thèse de Doctorat, de l'Université de Picardie Jules Verne, October 1995.
20. K. Benkrid, P. Bussy and A. Abdali, 'On the stable damage model for metal forming processes', Metal Forming 94, J. Mater. Process. Technol, 1996, pp. 521-526.
21. P. Bussy, P. Rougée and P. Vauchez, 'The large time increment method for numerical simulation of metal forming processes', Proc. NUMETA, Swansea, 1990.
22. D. C. Drucker, 'On the postulate of stability of materials in thermomechanics of continua', J. Méc., 3, 235-245 (1964).
23. P. Coorevits, P. Ladeveze, J. P. Pelle and P. Rougeot, 'Some new applications of a method for the control and optimisation of finite elements computations', In P. Ladeveze, O. C. Zienkiewicz (eds.), New Advances in Computational Structural Mechanics, 1992, pp. 205-217.
24. O. C. Zienkiewicz, D. W. Kelly and I. Babuska, in J. R. Whiteman (ed.), 'Hierrarchical finite element approaches error estimates and adaptative refinement', Proc. MAFELAP 81, Brunel University, 1982.
25. M. Ainswork, J. Z. Zhu, A. N. Craig and O. C. Zienkiewicz, 'Analysis of the Zienkiewicz-Zhu a posteriori error estimator in the finite element method', Int. J. Numer. Meth. Engng., 28, 2161-2174 (1989).
26. I. Babuska and W. C. Rheinboldt, 'Adaptative approaches and reliability estimation in finite element analysis', Comput. Appl. Mech. Engng., 519-540 (1979).
27. O. C. Zienkiewcz, J. R. Gago and D. W. Kelly, The hierarchical concept in finite element analysis', Comput. Struct., 16, 53-65 (1983).
28. J. R. Gago, D. W. Kelly, O. C. Zienkiewicz and I. Babuska, 'A posteriori error analysis and adaptative processes in finite element method. Part 2: adaptative mesh refinement', Int. J. Numer. Meth. Engng., 19, 1621-1656 (1983).
29. J. Z. Zhu and O. C. Zienkiewicz, 'A simple error estimator and adaptive procedure for practical engineering analysis', Int. J. Numer. Meth. Engng., 24, 337-357 (1987).
30. P. Ladeveze, 'Nouvelle procedure d'estimation d'erreur relative à la méthode des éléments finis et applications', Proc. J. Elements Finis, Rennes 1977.
31. A. Abdali, K. Benkrid and P. Bussy, 'Numerical simulation of sheet cutting', NUMIFORM 95, 1995, pp. 807-813, Ithaca, New York, U.S.A.