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Theory and numerics of three-dimensional beams with elastoplastic material behaviour. (English) Zbl 0989.74069

Summary: We present a theory of space curved beams with arbitrary cross-sections, and an associated finite element formulation. Within the present beam theory the reference point, the centroid, the centre of shear and the loading point are arbitrary points of the cross-section. The beam strains are based on a kinematic assumption, where torsion-warping deformation is included. Each node of the derived finite element possesses seven degrees of freedom. The update of rotational parameters at finite element nodes is achieved in an additive way. Applying the isoparametric concept, the kinematic quantities are approximated using Lagrangian interpolation functions. Since the reference curve lies arbitrarily with respect to the centroid, the developed element can be used to discretize eccentric stiffener of shells. Due to the implemented constitutive equations for elastoplastic material behaviour, the element can be used to evaluate the load-carrying capacity of beam structures.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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[1] Argyris, Computer Methods in Applied Mechanics and Engineering 20 pp 105– (1979)
[2] Bathe, International Journal for Numerical Methods in Engineering 14 pp 961– (1979)
[3] Belytschko, International Journal for Numerical Methods in Engineering 7 pp 255– (1973)
[4] Crisfield, Computer Methods in Applied Mechanics and Engineering 81 pp 131– (1990)
[5] Nour-Omid, Computer Methods in Applied Mechanics and Engineering 93 pp 353– (1991)
[6] Reissner, Journal for Applied Mathematics 32 pp 734– (1981)
[7] Simo, Computer Methods in Applied Mechanics and Engineering 58 pp 79– (1986)
[8] Simo, International Journal for Solids and Structures 27 pp 371– (1991)
[9] Cardona, International Journal for Numerical Methods in Engineering 26 pp 2403– (1988)
[10] Ibrahimbegovi?, International Journal for Numerical Methods in Engineering 38 pp 3653– (1995)
[11] Reissner, International Journal for Solids Structures 15 pp 41– (1979)
[12] Reissner, Journal of Applied Mathematics 34 pp 642– (1983)
[13] G?radin, Revue europ?enne des ?l?ments finis 4 pp 497– (1995)
[14] Betsch, Computer Methods in Applied Mechanics and Engineering 155 pp 273– (1998)
[15] Theory of Elasticity, (3rd edn). McGraw-Hill: New York, 1984.
[16] Gruttmann, Bauingenieur 73 pp 138– (1998)
[17] Gruttmann, Computer Methods in Applied Mechanics and Engineering 160 pp 383– (1998)
[18] The Finite Element Method, (4th edn), vol. 1 McGraw Hill: London, 1988.
[19] Knicken, Biegedrillknicken, Kippen: Theorie und Berechnung von Knickst?ben: knickvorschriften (2nd edn). Springer: Berlin, 1961.
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