Superconvergent patch recovery for plate problems using statically admissible stress resultant fields

International Journal for Numerical Methods in Engineering

Volumn 44, Issue 5, 1999, Pages 697-727

  Okstad, Knut Morten ^a,b   Kvamsdal, Trond ^a,b   Mathisen, Kjell Magne ^a  

^a NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Norway)

^b SINTEF   (Norway)

Author keywords

Finite element method; Plate bending problems; Stress recovery

Indexed keywords

BENDING (DEFORMATION); BOUNDARY CONDITIONS; CONVERGENCE OF NUMERICAL METHODS; ERROR ANALYSIS; FUNCTIONS; LEAST SQUARES APPROXIMATIONS; PLATES (STRUCTURAL COMPONENTS); POLYNOMIALS; STRESS ANALYSIS; STRUCTURAL ANALYSIS;

STRESS RECOVERY; SUPERCONVERGENT PATCH RECOVERY (SPR) METHOD;

FINITE ELEMENT METHOD;

EID: 0033079759     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(19990220)44:5<697::AID-NME526>3.0.CO;2-L     Document Type: Article

References (24)

1. E. Hinton and J. S. Campbell, 'Local and global smoothing of discontinuous finite element functions using a least squares method', Int. J. Numer. Meth. Engng., 8, 461-480 (1974).
2. J. T. Oden and H. J. Brauchli, 'On the calculation of consistent stress distributions in finite element approximations', Int. J. Numer. Meth. Engng., 3, 317-325 (1971).
3. O. C. Zienkiewicz and J. Z. Zhu, 'A simple error estimator and adaptive procedures for practical engineering analysis', Int. J. Numer. Meth. Engng., 24, 337-357 (1987).
4. O. C. Zienkiewicz and J. Z. Zhu, 'Error estimates and adaptive refinement for plate bending problems', Int. J. Numer. Meth. Engng., 28, 2839-2853 (1989).
5. O. C. Zienkiewicz and J. Z. Zhu, 'The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique', Int. J. Numer. Meth. Engng., 33, 1331-1364 (1992).
6. O. C. Zienkiewicz and J. Z. Zhu, 'The superconvergent patch recovery and a posteriori error estimates. Part 2: Error estimates and adaptivity', Int. J. Numer. Meth. Engng., 33, 1365-1382 (1992).
7. M. Tabbara, T. Blacker and T. Belytschko, 'Finite element derivative recovery by moving least square interpolants', Comput. Meth. Appl. Mech. Engng., 117, 211-223 (1994).
8. N.-E. Wiberg and F. Abdulwahab, 'Patch recovery based on superconvergent derivatives and equilibrium', Int. J. Numer. Meth. Engng., 36, 2703-2724 (1993).
9. N.-E. Wiberg, F. Abdulwahab and S. Ziukas, 'Enhanced superconvergent patch recovery incorporating equilibrium and boundary conditions', Int. J. Numer. Meth. Engng., 37, 3417-3440 (1994).
10. T. Blacker and T. Belytschko, 'Superconvergent patch recovery with equilibrium and conjoint interpolant enhancements', Int. J. Numer. Meth. Engng., 37, 517-536 (1994).
11. A. Tessler, H. R. Riggs and S. C. Macy, 'A variational method for finite element stress recovery and error estimation', Comput. Meth. Appl. Mech. Engng., 111, 369-382 (1994).
12. 1-continuous stress recovery in finite element analysis', Comput. Meth. Appl. Mech. Engng., 143, 299-316 (1997).
13. T. Lee, H. C. Park and S. W. Lee, 'A superconvergent stress recovery technique with equilibrium constraint', Int. J. Numer. Meth. Engng., 40, 1139-1160 (1997).
14. T. Kvamsdal and K. M. Okstad, 'Error estimation based on superconvergent patch recovery using statically admissible stress fields', Int. J. Numer. Meth. Engng., 42, 443-472 (1998).
15. 0 plate problems', Engng. Comput., 11, 495-512 (1994).
16. N.-E. Wiberg and F. Abdulwahab, 'Superconvergent patch recovery in problems of mixed form', Commun. Numer. Meth. Engng., 13, 207-217 (1997).
17. M. S. Shephard and M. K. Georges, Automatic three-dimensional mesh generation by the finite octree technique', Int. J. Numer. Meth. Engng., 32, 709-749 (1991).
18. E. Rank, M. Schweingruber and M. Sommer, 'Adaptive mesh generation and transformation of triangular to quadrilateral meshes', Commun. Numer. Meth. Engng., 9, 121-129 (1993).
19. K.-J. Bathe and E. N. Dvorkin, 'A four-noded plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation', Int. J. Numer. Meth. Engng., 21, 367-383 (1985).
20. E. N. Dvorkin and K.-J. Bathe, 'A continuum mechanics based four-node shell element for general non-linear analysis', Engng. Comput., 1, 77-88 (1984).
21. J. C. Simo and T. J. R. Hughes, 'On the variational foundations of assumed strain methods', J. Appl. Mech., 53, 51-54 (1986).
22. J. C. Simo and M. S. Rifai, 'A class of mixed assumed strain methods and the method of incompatible modes', Int. J. Numer. Meth. Engng., 29, 1595-1638 (1990).
23. Z. Zhang and S. Zhang, 'Derivative superconvergence of rectangular finite elements for the Reissner-Mindlin plate', Comput. Meth. Appl. Mech. Engng., 134, 1-16 (1995).
24. S. P. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells. McGraw-Hill, New York, 1970.