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A new hybrid-mixed variational approach for Reissner-Mindlin plates. The MiSP model. (English) Zbl 0912.73051
Summary: We present a variational approach for plate problems based on the Reissner-Mindlin theory. The new MiSP (mixed shear projected) approach is based on the Hellinger-Reissner variational principle, with a particular representation of transversal shear forces and transversal shear strains. We derive the approximations of shear forces from those of the bending moments using the corresponding equilibrium relations, and define the shear strains in terms of edge tangential strains that are projected on the element degrees-of-freedom. Two finite elements are developed on the MiSP basis: 3-node triangular element MiSP3, and 4-node quadrilateral element MiSP4. We present also a modified MiSP model with a derived 4-node element. Numerical experiments show that the MiSP elements do not exhibit shear locking and give excellent results for thick and thin plates. They also pass the patch test for general triangles and quadrilaterals.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
74K20 Plates
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[1] Hrabok, Comp. Struct. 19 pp 479– (1984) · doi:10.1016/0045-7949(84)90055-5
[2] ’A review of recent developments in plate and shells elements’, Comp. Mech. Adv. and Trends AMD-75 ASME, New York, 1986.
[3] Kerber, La Recherche Aérospatiale 3 pp 45– (1990)
[4] ’Eléments Finis de Plaque et Coque en Formulation Mixte avec Projection en Cisaillement’, Thèse de Doctorat, UTC, 1993.
[5] Stricklin, AIAA J. 7 pp 180– (1969) · Zbl 0175.22703 · doi:10.2514/3.5068
[6] ’Numerical analysis of thin shells by curved triangular elements based discrete Kirchhoff hypothesis’, ASCE Symposium, Nashville, November 1969, pp. 255-278.
[7] Dhatt, Int. Conf. on Structural Mechanics, in Reactor Technology, Berlin 5 pp 257– (1971)
[8] Batoz, Int. J. Numer. Meth. Engng. 18 pp 1771– (1980) · Zbl 0463.73071 · doi:10.1002/nme.1620151205
[9] Batoz, Int. J. Numer. Meth. Engng. 18 pp 1655– (1982) · Zbl 0489.73080 · doi:10.1002/nme.1620181106
[10] and , ’Revue et bilan des éléments de plaque de type Kirchhoff discret’, in Fouetet al. (eds.), Calcul des Structures et Intelligence Artificielle, Vol. 2, Pluralis, 1988, pp. 137-160.
[11] Macneal, Nucl. Engng. Des. 70 pp 3– (1982) · doi:10.1016/0029-5493(82)90262-X
[12] Hughes, J. Appl. Mech. 48 pp 587– (1981) · Zbl 0459.73069 · doi:10.1115/1.3157679
[13] and , ’The linear triangle bending elements’, in The Mathematics of Finite Element and Application IV, MAFELAP 1981, Academic Press, London, 1982, pp. 127-142.
[14] Dvorkin, Engng. Comput. 1 pp 77– (1984) · doi:10.1108/eb023562
[15] Bathe, Int. J. Numer. Meth. Engng. 21 pp 367– (1985) · Zbl 0551.73072 · doi:10.1002/nme.1620210213
[16] Prathap, Int. J. Numer Meth. Engng. 26 pp 1693– (1988) · Zbl 0663.73045 · doi:10.1002/nme.1620260803
[17] Donea, Comp. Meth. Appl. Mech. Engng. 63 pp 183– (1987) · Zbl 0607.73081 · doi:10.1016/0045-7825(87)90171-X
[18] and , Modélisation des Structures par Eléménts Finis, Vol. 2, Poutres et Plaques, Editions Hermès, Paris, 1990.
[19] Zienkiewicz, Comp. Struct. 35 pp 505– (1990) · Zbl 0729.73227 · doi:10.1016/0045-7949(90)90072-A
[20] Papadopoulos, Int. J. Numer. Meth. Engng. 30 pp 1029– (1990) · Zbl 0728.73073 · doi:10.1002/nme.1620300506
[21] Onate, Int. J. Numer. Meth. Engng. 33 pp 345– (1992) · Zbl 0761.73111 · doi:10.1002/nme.1620330208
[22] and , ’Derivation of plate based on assumed shear strain fields’, in and (eds.), New Advances in Computational Structural Mechanics, Elsevier, Amsterdam, 1992, pp. 237-288.
[23] Aalto, Comm. Appl. Numer. Meth. 4 pp 231– (1988) · Zbl 0633.73079 · doi:10.1002/cnm.1630040215
[24] Batoz, Int. J. Numer. Meth. Engng. 28 pp 533– (1989) · Zbl 0675.73042 · doi:10.1002/nme.1620280305
[25] Lardeur, Int. J. Numer. Meth. Engng. 27 pp 343– (1989) · Zbl 0724.73239 · doi:10.1002/nme.1620270209
[26] Pinsky, Int. J. Numer. Meth. Engng. 28 pp 1677– (1989) · Zbl 0717.73069 · doi:10.1002/nme.1620280715
[27] Saleeb, Int. J. Numer. Meth. Engng. 24 pp 1123– (1987) · Zbl 0613.73065 · doi:10.1002/nme.1620240607
[28] Saleeb, Int. J. Numer. Meth. Engng. 26 pp 1101– (1988) · Zbl 0634.73070 · doi:10.1002/nme.1620260508
[29] Batoz, Int. J. Numer. Meth. Engng. 35 pp 1603– (1992) · Zbl 0775.73236 · doi:10.1002/nme.1620350805
[30] Arnold, SIAM J. Numer. Anal. 26 pp 1276– (1989) · Zbl 0696.73040 · doi:10.1137/0726074
[31] Zienkiewicz, Int. J. Numer. Meth. Engng. 26 pp 1169– (1988) · Zbl 0634.73064 · doi:10.1002/nme.1620260511
[32] ’Dévelopement et evaluation de deux nouveaux eléments finis de plaques et coques composites avec influence du cisaillement transverse’, Thèse de Doctorat, UTC, 1990.
[33] Reissner, J. Appl. Mech. 12 pp a69– (1945)
[34] Ayad, Revue Européenne des Eléments Finis 4 pp 415– (1995) · Zbl 0924.73118 · doi:10.1080/12506559.1995.10511191
[35] Irons, Int. J. Numer. Meth. Engng. 19 pp 1391– (1983) · Zbl 0516.73080 · doi:10.1002/nme.1620190908
[36] Taylor, Int. J. Numer. Meth. Engng. 22 pp 39– (1986) · Zbl 0593.73072 · doi:10.1002/nme.1620220105
[37] Skew Plates and Structures, Pergamon, Oxford, 1963. · Zbl 0124.17704
[38] Babuska, Int. J. Numer. Meth. Engng. 28 pp 155– (1989) · Zbl 0675.73041 · doi:10.1002/nme.1620280112
[39] Razzaque, Int. J. Numer. Meth. Engng. 6 pp 333– (1973) · doi:10.1002/nme.1620060305
[40] and , The Finite Element Method, Vol. 2: Plates, Shells, Fluids and Non-Linear Problems, 4th Ed., McGraw-Hill, London, 1991.
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