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Iterative solution of mixed problems and the stress recovery procedures.(English)Zbl 0586.73127

This note introduces certain stress smoothing procedures and the so called ”Loubignac-Cantin” iteration for restoration of momentum balance in the smoothed stress fields. It is shown that this iteration corresponds precisely to the solution of mixed formulations in which the stresses (or strains) and the displacements are used as primary variables. The procedure has a very wide field of application and promises to add considerable accuracy to FEM results by a small additional expenditure.

MSC:

74S05 Finite element methods applied to problems in solid mechanics

Cite

References:

[1]Oden, Int. j. numer. methods engg. 6 pp 55– (1973)
[2]Hinton, Int. j. numer. methods eng. 8 pp 461– (1974)
[3]and , ’The penalty function method and its application to the numerical solution of boundary value problems’, Penalty Finite Element Methods in Mechanics, (ed. J.N. Reddy), Am. Soc. Mech. Eng. AMD-51, 1982, pp. 157-179.
[4]The Finite Element Method, 3rd edition, McGraw-Hill, 1977.
[5]and , ’On nodal stress recovery in the displacement finite element method’, In preparation.
[6]Loubignac, AIAA J. 15 pp 1645– (1977)
[7]Cantin, Int. j. numer. methods eng. 12 pp 1493– (1978)
[8]and , ’Mixed finite elements and iterative solutions for nonlinear structural mechanics’, In preparation.
[9]and , ’Mixed and irreducible formulation in finite element analysis’, Ch. 21, pp. 405-432 of Hybrid and Mixed Finite Element Methods, (ed. and ), Wiley, Chichester, 1983.
[10]and , ’Mixed finite element solution of flow problems’, Ch. 1, pp. 1-20, Finite Elements in Fluids, Vol. 4 (ed. et al.), Wiley, Chichester, 1982.
[11]Yang, Int. j. numer. methods eng. 3 pp 377– (1983)
[12]and 4, 43-69 (1984)
[13]’The flow of a Maxwell fluid around a sphere’, pp. 537-458, Finite Elements in Fluids, Vol. 4 (ed. et al.), Wiley, Chichester, 1982.
[14], and , ’Constrained problems and their iterative solution’, to be published in Comp. Meth. in Appl. Mech. and Eng.
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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