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Dual finite element analysis for plasticity-friction torsion of composite bar. (English) Zbl 0822.73074

The quasi-static problem of torsion of an elastic-plastic, prismatic, composite bar is considered. The phenomenon of slip on the interfaces between the components of the bar is taken into account. The elastic- plastic behaviour of the material is described by the Prandtl-Reuss constitutive relation. The slip on the interface is governed by the Coulomb friction law – it is assumed that there is no cohesion between components of the bar. The stresses normal to the interfaces are considered to be caused by shrinkage of the matrix of the bar or by external forces acting perpendicularly to its longitudinal axis. The problem is set in the dual variational forms and solved with the help of the finite element method.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74E30 Composite and mixture properties
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74C99 Plastic materials, materials of stress-rate and internal-variable type
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[1] Annin, J. Appl. Math. Mech. 29 pp 1038– (1965)
[2] Lanchon, CR Acad. Sci. 263 pp 791– (1966)
[3] Lanchon, CR Acad. Sci. 270 pp 1137– (1970)
[4] Lanchon, J. de Mecanique 13 pp 267– (1974)
[5] Ting, Arch. Rat. Mech. Anal. 34 pp 228– (1969)
[6] Ting, J. Math. Mech. 19 pp 531– (1969)
[7] Ting, Ind. Univ. Math. J. 20 pp 1047– (1971)
[8] and , Les Inéquations en Mécanique et en Physique, Dunod, Paris, 1972.
[9] Glowinski, J. de Mécanique 12 pp 151– (1973)
[10] and , Analyse Numérique des Inéquations Variationelles, Dunod, Paris, 1976.
[11] Numerical Methods for Non-linear Variational Problems, Springer, New York, 1984.
[12] Inequality Problems in Mechanics and Applications. Convex and Non-convex Energy Functions, Birkhaäser, Boston, 1985.
[13] and , ’Homogenization for a quasi-static problem of torsion of a prismatic periodic fibrous bar with Coulomb friction on the fibre-matrix interface’, in and (eds.), Mechanical Behaviour of Composites and Laminates. Proceedings of the Euromech Colloquium 214, Kupari 1986, Elsevier, Amsterdam, 1988.
[14] Wriggers, Comput. Struct. 37 pp 319– (1990)
[15] Laursen, Int. j. numer. methods eng. 36 pp 3451– (1993)
[16] and , Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods, SIAM, Philadelphia, 1988.
[17] Wieckowski, J. Theoret. Appl. Mech. 30 pp 535– (1992)
[18] Hill, J. Appl. Mech. 17 pp 64– (1950)
[19] and , ’The saddle point of the differential program’, in (ed.), Energy Methods in Finite Element Analysis, Wiley, New York, 1979.
[20] and , Convex Analysis and Variational Problems, North-Holland, Amsterdam, 1976.
[21] ’Mathematical and numerical analysis of some problems of plasticity’, in Functional Analysis Methods in the Theory of Plasticity, Ossolineum, Wroclaw, 1981 (in Polish).
[22] Johnson, SIAM J. Numer. Anal. 14 pp 575– (1977)
[23] and , ’Finite elements in plasticity–a variational inequality approach’, in (ed.), MAFELAP 1978, Academic Press, London, 1979. · Zbl 0437.73058
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