zbMATH — the first resource for mathematics

Further results for enhanced strain methods with isoparametric elements. (English) Zbl 0862.73056
The enhanced strain finite element method is investigated with particular attention given to the analysis of the method for isoparametric elements. It is shown that the results established earlier for affine-equivalent meshes carry over to the case of isoparametric elements. That is, the method is stable and convergent provided that a set of three criteria is satisfied and, for plane elements at least, convergence is at the same rate as in the standard method. A procedure for recovering the stress is shown to lead to an approximate stress which converges at the optimal rate of the actual stress. With regard to computations, a new basis for enhanced strains is introduced, and numerical results are presented.

74S05 Finite element methods applied to problems in solid mechanics
Full Text: DOI
[1] Simo, J.C.; Rifai, M.S., A class of assumed strain methods and the method of incompatible modes, Int. J. numer. methods engrg., 29, 1595-1638, (1990) · Zbl 0724.73222
[2] Wilson, E.L.; Taylor, R.L.; Docherty, W.P.; Ghaboussi, J., Incompatible displacement models, ()
[3] Taylor, R.L.; Beresford, P.J.; Wilson, E.L., A nonconforming element for stress analysis, Int. J. numer. methods engrg., 10, 1211-1219, (1976) · Zbl 0338.73041
[4] Reddy, B.D.; Simo, J.C., Stability and convergence of a class of enhanced strain methods, SIAM J. numer. anal., 32, (1995), in press · Zbl 0855.73073
[5] Andelfinger, U.; Ramm, E., EAS-elements for two-dimensional, three-dimensional, plate and shell structures and their equivalence to HR-elements, Int. J. numer. methods engrg., 36, 1311-1337, (1993) · Zbl 0772.73071
[6] Simo, J.C.; Armero, F., Geometrically nonlinear enhanced strain mixed methods and the method of incompatible modes, Int. J. numer. methods engrg., 33, 1413-1449, (1992) · Zbl 0768.73082
[7] Simo, J.C.; Armero, F.; Taylor, R.L., Improved versions of assumed enhanced strain tri-linear elements for 3D finite deformation problems, Comput. methods appl. mech. engrg., 110, 359-386, (1993) · Zbl 0846.73068
[8] 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
[9] Di, S.; Ramm, E., On alternative hybrid stress 2-D and 3-D elements, Engrg. comput., 11, 49-68, (1994)
[10] U. Hueck and P. Wriggers, A formulation for the four-node quadrilateral element, Int. J. Numer. Methods Engrg. in press. · Zbl 0845.73068
[11] Ciarlet, P.G.; Raviart, P.-A., Interpolation theory over curved elements, with applications to finite elements, Comput. methods appl. mech. engrg., 1, 217-249, (1972) · Zbl 0261.65079
[12] Ciarlet, P.G., The finite element method for elliptic problems, (1978), North-Holland Amsterdam · Zbl 0445.73043
[13] Bramble, J.H.; Hubert, S.H., Bounds for a class of linear functionals with applications to Hermite interpolation, Numer. math., 16, 362-369, (1971) · Zbl 0214.41405
[14] Arunakirinathar, K.; Reddy, B.D., Some geometrical results and estimates for quadrilateral finite elements, Comput. methods appl. mech. engrg., 122, 307-314, (1995) · Zbl 0846.65058
[15] Strang, G.; Fix, G.J., An analysis of the finite element method, (1973), Prentice-Hall Englewood Cliffs, NJ · Zbl 0278.65116
[16] Hughes, T.J.R., Introduction to the finite element method, (1987), Prentice-Hall Englewood Cliffs, NJ
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.