×

zbMATH — the first resource for mathematics

On using different recovery procedures for the construction of smoothed stress in finite element method. (English) Zbl 0940.74064
Summary: We review the performance of three different stress recovery procedures, namely, the superconvergent patch recovery technique (SPR), the recovery by equilibrium in patches (REP) and a combined method known as the LP procedure [see the foregoing entry]. Different order of polynomials and various patch formation strategies have been employed in the numerical studies for the construction of smoothed stress fields. Two two-dimensional elastostatic problems with different characteristics are used to assess the behaviour of the stress recovery procedures. The numerical results obtained indicate that when the order of polynomial used in the recovery procedure is equal to that of the finite element analysis, the properties of all three recovery procedures are very similar, and each of them can provide a reliable recovered stress field for error estimation. In the case when the order of polynomial of the recovered stress is increased, the LP procedure seems to give a more stable recovery matrix and a more reliable recovered stress field than the REP procedure.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74K20 Plates
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Niu, Int. J. Numer. Meth. Engng. 36 pp 811– (1993)
[2] and , Finite Element Analysis, Wiley, New York, 1991.
[3] Cantin, INt. J. Numer. Meth. Engng. 12 pp 1493– (1978)
[4] Cook, Int. J. Numer. Meth. Engng. 22 pp 229– (1986)
[5] Cornwell, Finite Elements Anal. Des. 4 pp 203– (1988)
[6] Cook, Int. J. Numer. Meth. Engng. 18 pp 67– (1982)
[7] Loubignac, AIAA J. 15 pp 1645– (1977)
[8] Zienkiewicz, Int. J. Numer. Meth. Engng. 33 pp 1331– (1992)
[9] Zienkiewicz, Int. J. Numer. Meth. Engng. 33 pp 1365– (1992)
[10] Zienkiewicz, Int. J. Numer. Meth. Engng. 24 pp 337– (1987)
[11] Blacker, Int. J. Numer. Meth. Engng. 37 pp 517– (1994)
[12] Wiberg, Int. J. Numer. Meth. Engng. 36 pp 2703– (1993)
[13] Zhu, Int. J. Numer. Meth. Engng. 30 pp 1321– (1990)
[14] Hinton, Int. J. Numer. Meth. Engng. 8 pp 461– (1974)
[15] Li, Comput. Struct. 53 pp 907– (1994)
[16] Zienkiewicz, Finite Elements Anal. Des. 19 pp 11– (1995)
[17] Tabbara, Comput. Meth. Appl. Mech. Engng. 117 pp 211– (1994)
[18] and , ’Robust implementation of the superconvergent patch recovery technique’, in and (eds.), Proc. 2nd Asian-Pac. Conf. Computations. Mech., Sydney, Australia, A. A. Balkema, Rotterdam, pp. 1275-1280, 1993.
[19] Boroomand, Int. J. Numer. Meth. Engng. 40 pp 137– (1997)
[20] Lee, Int. J. Numer. Meth. Engng. 40 pp 1139– (1997)
[21] Lee, Int. J. Numer. Meth. Engng. 40 pp 3621– (1997)
[22] and , ’A model study of the quality of a posteriori error estimators for finite element solutions of linear elliptic problems, with particular reference to the behavior near the boundary’. · Zbl 0883.65080
[23] Szabo, Comput. Meth. Appl. Mech. Engng. 55 pp 181– (1986)
[24] Babuska, Comput. Meth. Appl. Mech. Engng. 80 pp 5– (1990)
[25] Boroomand, Int. J. Numer. Meth. Engng. 40 pp 2521– (1997)
[26] Computational Methods in the Mechanics of Fracture, North-Holland, Amsterdam, 1986.
[27] Barlow, Int. J. Numer. Meth. Engng. 10 pp 243– (1976)
[28] Lee, Int. J. Numer. Meth. Engng. 40 pp 4547– (1997)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.