×

Extension of field consistence approach into developing plane stress elements. (English) Zbl 1161.74498

Summary: The possibilities for extending the field consistence approach [L. Yunhua, On shear locking in finite elements, Licentiate Thesis, Stockholm (1997); Comput. Methods Appl. Mech. Eng. 162, No. 1–4, 249–269 (1998; Zbl 0949.74069)], starting from different variational principles, to plane stress elements are investigated. In the extension, two main difficulties are: explicitly solving a set of coupled partial differential equations and satisfying inter-element compatibility. The first one is alleviated by constructing element interpolations from a set of quasi-general solutions, rather than the real general solutions, to the Euler-Lagrangian equations. The second one is solved by combining the field consistence approach with the iso-parametric interpolation technique. The traditional assumed stress method is improved and an efficient plane stress element is obtained. It seems that the relations between the three commonly used variational principles can be more reasonably established in the framework of the field consistence approach.

MSC:

74S05 Finite element methods applied to problems in solid mechanics

Citations:

Zbl 0949.74069

Software:

Maple; TRIC
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Yunhua, L., On shear locking in finite elements, Licentiate thesis, (1997), Stockholm
[2] Yunhua, L., Explanation and elimination of shear locking and membrane locking with field consistence approach, Comput. methods appl. mech. engrg., 162, 249-269, (1998) · Zbl 0949.74069
[3] Argyris, J.; Dunne, P.C.; Malejannakis, G.A.; Schelkle, E., A simple triangular facet shell element with applications to linear and non-linear equilibrium and elastic stability problem, Comput. methods appl. mech. engrg., 10, 371-403, (1977) · Zbl 0367.73073
[4] Argyris, J.; Tenek, L., Natural mode method: A practicable and novel approach to the global analysis of laminated composite plates and shells, Appl. mech. rev., 49, 381-399, (1996)
[5] Argyris, J.; Tenek, L.; Olofsson, L., TRIC: A simple but sophisticated 3-node triangular element based on 6 rigid-body and 12 straining modes for fast computational simulations of arbitrary isotropic and laminated composite shells, Comput. methods appl. mech. engrg., 145, 11-85, (1997) · Zbl 0892.73051
[6] Tenek, L.; Argyris, J., Computational aspects of the natural-mode finite element method, Comm. numer. methods engrg., 13, 705-713, (1997) · Zbl 0889.73071
[7] B. de Veubeke Fraeijs, Displacement and equilibrium models in the finite element method, in: O.C. Zienkiewicz and G.S. Holister, eds., Stress Analysis (Wiley, London) 145-196. · Zbl 0359.73007
[8] Stolarski, H.; Belytschko, T., Limitation principles for mixed finite elements based on the hu-washizu variational formulation, Comput. methods appl. mech. engrg., 60, 195-216, (1987) · Zbl 0613.73017
[9] Pian, T.H.H.; Sumihara, K., Rational approach for assumed stress finite elements, Int. J. numer. methods engrg., 20, 1685-1695, (1984) · Zbl 0544.73095
[10] Bathe, K.J., Finite element procedure, (1996), Prentice Hall Berkshire · Zbl 0511.73065
[11] Fröier, M.; Nilsson, L.; Samuelsson, A., The rectangular plane stress element by turner, Pian and Wilson, Int. J. numer. methods engrg., 8, 433-437, (1974)
[12] Feng, W.; Hoa, S.V.; Huang, Q., Classification of stress modes in assumed stress fields of hybrid finite elements, Int. J. numer. methods engrg., 40, 4313-4339, (1997) · Zbl 0893.73060
[13] Simo, J.C.; Rifai, M.S., A class of mixed assumed strain methods and the method of incompatible modes, Int. J. numer. methods engrg., 29, (1990) · Zbl 0724.73222
[14] Stolarski, H.; Belytschko, T., On the equivalence of mode decomposition and mixed finite elements based on the Hellinger-Reissner principle. part I: theory, Comput. methods appl. mech. engrg., 58, 249-263, (1986) · Zbl 0595.73076
[15] Stolarski, H.; Belytschko, T., On the equivalence of mode decomposition and mixed finite elements based on the Hellinger-Reissner principle. part II: application, Comput. methods appl. mech. engrg., 58, 265-284, (1986) · Zbl 0595.73077
[16] Zhao, P.-J.; Pian, T.H.H.; Yong, S., A new formulation of isoparametric finite elements and the relationship between hybrid stress element and incompatible element, Int. J. numer. methods engrg., 40, 15-27, (1997)
[17] Pian, T.H.H.; Tong, P., Relations between incompatible displacement model and hybrid stress model, Int. J. numer. methods engrg., 22, 173-181, (1986) · Zbl 0593.73068
[18] Simo, J.C.; Armero, F., Geometrically nonlinear enhanced mixed methods and the method of incompatible modes, Int. J. num. meth. engrg., 33, 1413-1449, (1992) · Zbl 0768.73082
[19] Crisfield, M.A., Incompatible modes, enhanced strains and substitute strains continuum elements, ()
[20] Zienkiewicz, O.C., The finite element method in engineering science, (1971), McGraw-Hill Barcelona · Zbl 0237.73071
[21] Maple, V., ()
[22] Eriksson, A.; Pacoste, C., Symbolic derivation of finite elements, ()
[23] Eriksson, A.; Pacoste, C., Symbolic software in linear and non-linear FEM development, ()
[24] Pian, T.H.H.; Chen, D.P., Alternative ways for formulation of hybrid stress elements, Int. J. numer. methods engrg., 18, 1679-1684, (1982) · Zbl 0497.73080
[25] Pian, T.H.H., On the equivalence of non-conforming element and hybrid stress element, Applied mathematics and mechanics, 3, 6, 773-776, (1982), (English edition) · Zbl 0519.73071
[26] Yuan, K.-Y.; Huang, Y.-S.; Pian, T.H.H., New strategy for assumed stress for 4-node hybrid stress membrane element, Int. J. numer. methods engrg., 36, 1747-1763, (1993) · Zbl 0772.73086
[27] Simo, J.C.; Hughes, T.J.R., On the variational foundations of assumed strain methods, ASME J. of appl. mech., 53, 51-54, (1986) · Zbl 0592.73019
[28] Simo, J.C.; Armero, F.; Taylor, R.L., Improved version of assumed enhanced strain tri-linear elements for 3D finite deformation problems, Comput. methods appl. mech. engrg., 110, 359-386, (1993) · Zbl 0846.73068
[29] Yuan, K.-Y.; Wen, J.-C.; Pian, T.H.H., A unified theory for formulation of hybrid stress membrane elements, Int. J. numer. methods engrg., 37, 457-474, (1994) · Zbl 0790.73070
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.