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The TRIC shell element: Theoretical and numerical investigation. (English) Zbl 1003.74071

Summary: The TRIC facet triangular shell element, which is based on the natural mode method, is seen under the light of the non-consistent formulation proposed by P. G. Bergan and co-workers [see, e.g., P. G. Bergan and M. K. Nygard, Plate bending elements based on orthogonal functions. In New concepts in finite element analysis, Appl. Mech. Conf., Boulder/Colo. 1981, AMD-Vol 44, 209-224 (1981; Zbl 0464.73084)]. In this formulation, the convergence requirements are fulfilled even with relaxed conditions on the conformity demands of displacement shape functions. Here we demonstrate an intrinsic connection between non-consistent formulation and natural mode method, establishing thus a rigorous theoretical foundation for TRIC element. By using the non-consistent formulation, TRIC’s convergence characteristics are established by satisfying a priori the patch test due to its inherent properties, and thus guaranteeing convergence to exact solution. Furthermore, the element’s accuracy, robustness and efficiency are tested on benchmark plate and shell problems, while a CPU time comparison with a pure displacement-based isoparametric shell element demonstrates its computational merits.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74K25 Shells

Citations:

Zbl 0464.73084

Software:

TRIC
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Full Text: DOI

References:

[1] Argyris, J. H.; Tenek, L.; Olofsson, L., TRIC: a simple but sophisticated 3-node triangular element based on six rigid-body and 12 straining modes for fast computational simulations of arbitrary isotropic and laminated composite shells, Comp. Meth. Appl. Mech. and Eng., 145, 11-85 (1997) · Zbl 0892.73051
[2] J.H. Argyris, L. Tenek, M. Papadrakakis, C. Apostolopoulou, Postbuckling performance of the TRIC natural mode triangular element for isotropic and laminated composite shells, Comp. Meth. Appl. Mech. and Engrg, 166 (1998) 211-231; J.H. Argyris, L. Tenek, M. Papadrakakis, C. Apostolopoulou, Postbuckling performance of the TRIC natural mode triangular element for isotropic and laminated composite shells, Comp. Meth. Appl. Mech. and Engrg, 166 (1998) 211-231 · Zbl 0945.74063
[3] Argyris, J. H.; Balmer, H.; Doltsinis, J. St.; Dunne, P. C.; Haase, M.; Muller, M.; Scharpf, D. W., Finite element method-the natural approach, Comp. Meth. Appl. Mech. and Eng., 17/18, 1-106 (1979) · Zbl 0407.73058
[4] Argyris, J. H.; Dunne, P. C.; Malejanakis, G. A.; Schekle, E., A simple triangular facet shell element with applications to linear and nonlinear equilibrium and inelastic stability problems, Comp. Meth. Appl. Mech. and Eng., 10, 371-403 (1977) · Zbl 0367.73073
[5] Argyris, J. H.; Haase, M.; Mlejnek, H.-P., On an unconventional but natural formation of a stiffness matrix, Comp. Meth. Appl. Mech. and Eng., 22, 1-22 (1980) · Zbl 0437.73054
[6] Argyris, J. H.; Tenek, L., An efficient and locking-free flat anisotropic plate and shell triangular element, Comp. Meth. Appl. Mech. and Eng., 118, 63-119 (1994) · Zbl 0851.73052
[7] Bergan, P. G.; Nygard, M. K., Finite elements with increased freedom in choosing shape functions, Num. Meth. Eng., 20, 643-663 (1984) · Zbl 0579.73077
[8] P.G. Bergan, L. Hanssen, A new approach for deriving “good” finite elements, in: Proceedings of the Conference on Mathematics of Finite Elements and Applications, Brunel University, 1975; P.G. Bergan, L. Hanssen, A new approach for deriving “good” finite elements, in: Proceedings of the Conference on Mathematics of Finite Elements and Applications, Brunel University, 1975
[9] Bergan, P. G., Finite elements based on energy orthogonal functions, Num. Meth. Eng., 15, 1541-1555 (1980) · Zbl 0438.73063
[10] Felippa, C. A.; Haugen, B.; Militello, C., From the individual element test to finite element templates: evolution of the patch test, Num. Meth. Eng., 38, 199-239 (1995) · Zbl 0822.73067
[11] Braun, M.; Bischoff, M.; Ramm, E., Nonlinear shell formulation for complete three-dimensional constistutive laws including composites and laminates, Comput. Mech., 15, 1-18 (1994) · Zbl 0819.73042
[12] Reddy, J. N.; Pandey, A. K., A first-ply failure analysis of composite laminates, Comput. and Struct., 25, 4, 371-393 (1987) · Zbl 0599.73055
[13] Pagano, N. J., Exact solutions for rectangular bidirectional composites and sandwich plates, Composite Materials, 4, 20-34 (1970)
[14] Hughes, T. J.R.; Liu, W. K., Nonlinear finite element analysis of shells, part II: two-dimensional shells, Comp. Meth. Appl. Mech. and Eng., 27, 167-182 (1981) · Zbl 0474.73093
[15] Lam, D.; Liu, K. K.; Law, E. S.; Belytschko, T., Resultant-stress degenerated-shell element, Comp. Meth. Appl. Mech. and Eng., 55, 259-300 (1986) · Zbl 0587.73113
[16] Bathe, K. J.; Dvorkin, E. N., A formulation of general shell elements-the use of mixed interpolation of tensorial components, Num. Meth. Eng., 22, 697-722 (1986) · Zbl 0585.73123
[17] Simo, J. C.; Fox, D. D., On a stress resultant geometrically exact shell element, part II: The linear theory; computational aspects, Comp. Meth. Appl. Mech. and Eng., 73, 53-92 (1989) · Zbl 0724.73138
[18] Belytschko, T.; Leviathan, I., Physical stabilization of the 4-node shell element with one-point quadrature, Comp. Meth. Appl. Mech. and Eng., 113, 321-350 (1994) · Zbl 0846.73058
[19] Scordelis, A. C.; Lo, U. S., Computer analysis of cylindrical shells, Amer. Concr. Inst., 61, 539-561 (1969)
[20] Rao, K. P., A rectangular laminated anisotropic shallow thin shell finite element, Comp. Meth. Appl. Mech. and Eng., 15, 13-33 (1978) · Zbl 0381.73080
[21] MacNeal, R. H.; Harder, R. L., A proposed standard set of problems to test finite element accuracy, Finite Elements in Analysis and Design, 1, 3-20 (1985)
[22] Wong, B. L.; Belytschko, T.; Stolarski, H., Assumed strain stabilization procedure for the 9-node Lagrange shell element, Num. Meth. Eng., 28, 385-414 (1989) · Zbl 0674.73054
[23] Morley, L. S.D.; Morris, A. J., Conflict between finite elements and shell theory (1978), Royal Aircraft Establishment Report: Royal Aircraft Establishment Report London
[24] Hinton, E.; Owen, D. R.J., Finite Element Software for Plates and Shells (1984), Pineridge Press: Pineridge Press Swansea, UK · Zbl 0568.73085
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