# zbMATH — the first resource for mathematics

Refined 9-dof triangular Mindlin plate elements. (English) Zbl 1065.74606
Summary: Based on the Mindlin-Reissner plate theory, two refined triangular thin/thick plate elements, the conforming displacement element DKTM with one point quadrature for the part of shear strain and the element RDKTM with the re-constitution of the shear strain, are proposed. In the formulations the exact displacement function of the Timoshenko’s beam is used to derive the element displacements of the refined elements. Numerical examples are presented to show that the present models indeed possess properties of high accuracy for thin and thick plates, is capable of passing the patch test required for Kirchhoff thin plate elements, and does not exhibits extra zero energy modes. The element RDKTM is free of locking for very thin plate analysis and its convergence can be ensured theoretically. However, the element DKTM is not free of shear locking when the thickness/span ratios less than $$10^{-2}$$.

##### MSC:
 74S05 Finite element methods applied to problems in solid mechanics 74K20 Plates
Full Text:
##### References:
 [1] Zienkiewicz, International Journal for Numerical Methods in Engineering 3 pp 275– (1971) · Zbl 0253.73048 · doi:10.1002/nme.1620030211 [2] Pugh, International Journal for Numerical Methods in Engineering 12 pp 1059– (1978) · Zbl 0377.73065 · doi:10.1002/nme.1620120702 [3] Malkus, Computer Methods in Applied Mechanics and Engineering 15 pp 63– (1978) · Zbl 0381.73075 · doi:10.1016/0045-7825(78)90005-1 [4] Hughes, Nuclear Engineering and Design 46 pp 203– (1978) · doi:10.1016/0029-5493(78)90184-X [5] Belytschko, International Journal for Numerical Methods in Engineering 20 pp 787– (1984) · Zbl 0528.73069 · doi:10.1002/nme.1620200502 [6] The linear triangle bending elements. The Mathematics of Finite Element and Application IV, MAFEAP 1981. Academic Press: London, 1982; 127-142. [7] Zienkiewicz, Computers and Structures 35 pp 505– (1990) · Zbl 0729.73227 · doi:10.1016/0045-7949(90)90072-A [8] Onate, International Journal for Numerical Methods in Engineering 33 pp 345– (1992) · Zbl 0761.73111 · doi:10.1002/nme.1620330208 [9] Alto, Communications in Applied Numerical Methods 4 pp 231– (1988) · Zbl 0633.73079 · doi:10.1002/cnm.1630040215 [10] Batoz, International Journal for Numerical Methods in Engineering 29 pp 533– (1989) · Zbl 0675.73042 · doi:10.1002/nme.1620280305 [11] Batoz, International Journal for Numerical Methods in Engineering 35 pp 1603– (1992) · Zbl 0775.73236 · doi:10.1002/nme.1620350805 [12] Katili, International Journal for Numerical Methods in Engineering 36 pp 1859– (1993) · Zbl 0775.73263 · doi:10.1002/nme.1620361106 [13] Lee, AIAA Journal 16 pp 29– (1978) · Zbl 0368.73067 · doi:10.2514/3.60853 [14] Salleb, International Journal for Numerical Methods in Engineering 26 pp 1101– (1988) · Zbl 0634.73070 · doi:10.1002/nme.1620260508 [15] Cheung, Computer and Structures 32 pp 327– (1989) · Zbl 0711.73241 · doi:10.1016/0045-7949(89)90044-8 [16] Ayad, International Journal for Numerical Methods in Engineering 42 pp 1149– (1998) · Zbl 0912.73051 · doi:10.1002/(SICI)1097-0207(19980815)42:7<1149::AID-NME391>3.0.CO;2-2 [17] Cheung, International Journal for Numerical Methods in Engineering 38 pp 283– (1995) · Zbl 0823.73062 · doi:10.1002/nme.1620380208 [18] Wanji, International Journal for Numerical Methods in Engineering 41 pp 1507– (1998) · Zbl 0915.73066 · doi:10.1002/(SICI)1097-0207(19980430)41:8<1507::AID-NME351>3.0.CO;2-T [19] Wanji, International Journal for Numerical Methods in Engineering 47 pp 605– (2000) · Zbl 0970.74072 · doi:10.1002/(SICI)1097-0207(20000110/30)47:1/3<605::AID-NME785>3.0.CO;2-E [20] Batoz, International Journal for Numerical Methods in Engineering 18 pp 1655– (1982) · Zbl 0489.73080 · doi:10.1002/nme.1620181106 [21] Razzaque, International Journal for Numerical Methods in Engineering 6 pp 333– (1973) · doi:10.1002/nme.1620060305 [22] Skew Plates and Structures. Pergamon Press: Oxford, 1963. · Zbl 0124.17704
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.