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A new and simple locking-free triangular thick plate element using independent shear degrees of freedom. (English) Zbl 1368.74038

Summary: In this paper, a new locking-free element triangular thick plate element with 9 standard kinematic degrees of freedom and 6 additional degrees of freedom for shear strains (TTK9S6) for analyzing plate/shell structures of thin or thick members is developed. With an appropriate use of independent shear degrees of freedom (DOF), the shear locking problem is completely removed without inducing any numerical expediency such as reduced integration, assumptions of strains/stresses, nor are additional efforts needed to stabilize spurious zero energy modes. Compared to existing triangular shear-deformable plate elements that pass patch tests for both thick and thin plates, the formulation of the present TTK9S6 element is very simple – and perhaps as simple as possible. A number of numerical examples are tested showing the convergence and accuracy of the TTK9S6 element.

MSC:

74K25 Shells
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[1] Zienkiewicz, O. C.; Taylor, R. L.; Too, J. M., Reduced integration technique in geneal analysis of plates and shells, Int. J. Numer. Methods Eng., 3, 275-290 (1971) · Zbl 0253.73048
[2] Pugh, E. D.L.; Hinton, E.; Zienkiewicz, O. C., A study of quadrilateral plate bending element with reduced integration, Int. J. Numer. Methods Eng., 12, 1059-1079 (1978) · Zbl 0377.73065
[3] Malkus, D. S.; Hughes, T. J.R., Mixed finite element methods-reduced and selective integration techniques: a unification of concepts, Comput. Methods Appl. Mech. Eng., 15, 63-81 (1978) · Zbl 0381.73075
[4] Hughes, T. J.R.; Cohen, M.; Haroun, M., Reduced and selective integration techniques in finite element analysis of plates, Nucl. Eng. Des., 46, 203-222 (1978)
[5] Bathe, K. J.; Dvorkin, E. N., A four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation, Int. J. Numer. Methods Eng., 21, 367-383 (1985) · Zbl 0551.73072
[6] Batoz, J. L.; Lardeur, P., A discrete shear triangular nine d.o.f. element for the analysis of thick to very thin plates, Int. J. Numer. Methods Eng., 29, 533-560 (1989) · Zbl 0675.73042
[7] Batoz, J. L.; Katili, I., On a simple triangular Reissner/Mindlin plate element based on incompatible modes and discrete constraints, Int. J. Numer. Methods Eng., 35, 1603-1632 (1992) · Zbl 0775.73236
[8] Zienkiewicz, O. C.; Taylor, R. L.; Papadopoulos, P.; Oñate, E., Plate bending elements with discrete constraints: new triangular elements, Comput. Struct., 35, 505-522 (1990) · Zbl 0729.73227
[9] Nguyen-Xuan, H.; Rabczuk, T.; Bordas, Stéphane; Debongnie, J. F., A smoothed finite element method for plate analysis, Comput. Methods Appl. Mech. Eng., 197, 1184-1203 (2008) · Zbl 1159.74434
[10] Chen, W. J.; Cheung, Y. K., Refined 9-Dof triangular Mindlin plate elements, Int. J. Numer. Methods Eng., 51, 1259-1281 (2001) · Zbl 1065.74606
[11] Choo, Y. S.; Choi, N.; Lee, B. C., A new hybrid-Trefftz triangular and quadrilateral plate elements, Appl. Math. Model., 34, 14-23 (2010) · Zbl 1185.90048
[12] Lee, S. W.; Pian, T. H.H., Improvement of plate and shell finite elements by mixed formulation, AIAA J., 16, 29-34 (1978) · Zbl 0368.73067
[13] Katili, I., A new discrete Kirchhoff-Mindlin element based on Mindlin-Reissner plate theory and assumed shear strain fields—part I: an extended DKT element for thick-plate bending analysis, Int. J. Numer. Methods Eng., 36, 1859-1883 (1993) · Zbl 0775.73263
[14] Brasile, S., An isostatic assumed stress triangular element for the Reissner-Mindlin plate-bending problem, Int. J. Numer. Methods Eng., 74, 971-995 (2008) · Zbl 1158.74480
[15] Bletzinger, K.-U.; Bischoff, M.; Rammb, E., A unified approach for shear-locking free triangular and rectangular shell finite elements, Comput. Struct., 75, 321-334 (2000)
[16] Thai-Hoang, C.; Nguyen-Thanh, N.; Nguyen-Xuan, H.; Rabczuk, T., An alternative alpha finite element method with discrete shear gap technique for analysis of laminated composite plates, Appl. Math. Comput., 217, 7324-7348 (2011) · Zbl 1415.74048
[17] Donning, B. M.; Liu, W. K., Meshless methods for shear-deformable beams and plates, Comput. Methods Appl. Mech. Eng., 152, 47-71 (1998) · Zbl 0959.74079
[18] Le, C.; Gilbert, M.; Askes, H., Limit analysis of plates using the EFG method and second-order cone programming, Int. J. Numer. Methods Eng., 78, 1532-1552 (2009) · Zbl 1171.74466
[19] Kanok-Nukulchai, W.; Barry, W.; Saran-Yasoontorn, K.; Bouillard, P. H., On elimination of shear locking in the element-free Galerkin method, Int. J. Numer. Methods Eng., 52, 705-725 (2001) · Zbl 1128.74347
[20] Li, Q.; Soric, J.; Jarak, T.; Atluri, S. N., A locking-free meshless local Petrov-Galerkin formulation for thick and thin plates, J. Comput. Phys., 208, 116-133 (2005) · Zbl 1115.74369
[21] Rabczuk, T.; Areias, P. M.A.; Belytschko, T., A meshfree thin shell method for nonlinear dynamic fracture, Int. J. Numer. Methods Eng., 72, 524-548 (2007) · Zbl 1194.74537
[22] Zhuang, X.; Heaney, C.; Augarde, C., On error control in the element-free Galerkin method, Eng. Anal. Boundary Elem., 36, 351-360 (2012) · Zbl 1245.65161
[23] Nguyen-Thanh, N.; Rabczuk, T.; Nguyen-Xuan, H.; Bordas, S., A smoothed finite element for shell analysis, Comput. Methods Appl. Mech. Eng., 198, 165-177 (2008) · Zbl 1194.74453
[24] Nguyen-Xuan, H.; Rabczuk, T.; Nguyen-Thanh, N.; Nguyen-Thoi, T.; Bordas, S., A node-based smoothed finite element method (NS-FEM) with stabilized discrete shear gap technique for analysis of Reissner-Mindlin plates, Comput. Mech., 46, 679-701 (2010) · Zbl 1260.74029
[25] Chau-Dinh, T.; Zi, G.; Lee, P. S.; Song, J. H.; Rabczuk, T., Phantom-node method for shell models with arbitrary cracks, Comput. Struct., 92-93, 242-256 (2012)
[26] Valizadeh, N.; Natarajan, S.; Gonzalez-Estrada, O. A.; Rabczuk, T.; Bui, T. Q.; Bordas, S. P.A., NURBS-based finite element analysis of functionally graded plates: static bending, vibration, buckling and flutter, Compos. Struct., 99, 309-326 (2012)
[27] Atluri, S. N., Methods of Computer Modeling in Engineering and Science (2005), Tech Science Press, Pennsylvania State University
[28] Cai, Y. C.; Tian, L. G.; Atluri, S. N., A simple locking-free discrete shear triangular plate element, Comput. Model. Eng. Sci., 77, 221-238 (2011) · Zbl 1356.74193
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