×

Finite element shakedown analysis of two-dimensional structures. (English) Zbl 1084.74052

Summary: The formulation proposed by R. Casciaro and G. Garcea [Comput. Meth. Appl. Mech. Eng. 191, No. 49–50, 5761-5792 (2002; Zbl 1083.74513)] and applied to the shakedown analysis of plane frames, is extended to the analysis of two-dimensional flat structures in both the cases of plane-stress and plane-strain. The discrete formulation is obtained using a mixed finite element in which both stress and displacement fields are interpolated. The material is assumed to be elasto-plastic, and a linearization of the elastic domain is performed. The result is a versatile iterative scheme well suited to implementation in general purpose FEM codes. An extensive series of numerical tests is presented showing the reliability of the proposed formulation.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
74R20 Anelastic fracture and damage

Citations:

Zbl 1083.74513
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Melan, Ingenieur Archiv 9 pp 116– (1938)
[2] General theorems for elastic-plastic solids. In Progress in Solids Mechanics, (eds). North-Holland: Amsterdam, 1960; 165-221.
[3] König, Journal of Nuclear Engineering Design 66 pp 81– (1981)
[4] Maier, European Journal of Mechanics - A/Solids 19 pp s79– (2000)
[5] Groß-Wedge, International Journal of Mechanical Sciences 39 pp 417– (1997)
[6] Casciaro, Computer Methods in Applied Mechanics and Engineering 191 pp 5761– (2002)
[7] Polizzotto, Journal of Applied Mechanics (ASME) 60 pp 20– (1993)
[8] Simo, International Journal for Numerical Methods in Engineering 26 pp 2161– (1998)
[9] Limit analysis by incremental iterative procedure. In Proceedings of the IUTAM Conference on Deformation and Failure of Granular Materials, Delft, 1982.
[10] Garcea, Computer Methods in Applied Mechanics and Engineering 165 pp 247– (1998)
[11] Riks, International Journal of Solids and Structures 15 pp 529– (1979) · Zbl 0408.73040
[12] Nonlinear Finite Elements for Continua and Structures. Wiley: New York, 2000. · Zbl 0959.74001
[13] Casciaro, International Journal for Numerical Methods in Engineering 18 pp 211– (1982)
[14] Practical Methods of Optimization. Wiley: New York, 1969.
[15] Goldfarb, Mathematical Programming 27 pp 1– (1983)
[16] Gill, Mathematical Programming 14 pp 349– (1978)
[17] Felippa, Computer Methods in Applied Mechanics and Engineering 190 pp 24– (2001)
[18] Zouanin, Computer Methods in Applied Mechanics and Engineering 191 pp 2463– (2002)
[19] Zhang, Engineering Analysis of Boundary Methods 28 pp 905– (2004)
[20] Belytschko, International Journal of Mechanical Sciences 14 pp 619– (1972)
[21] Shakedown analysis by displacement method and equilibrium finite element. Proceedings of the SMIRT 5, Berlin paper L3/3, 1979.
[22] Corradi, Computer Methods in Applied Mechanics and Engineering 3 pp 37– (1974)
[23] Genna, International Journal of Mechanical Sciences 30 pp 769– (1988) · Zbl 0669.73027
[24] Stein, International Journal of Plasticity 8 pp 1– (1992)
[25] Ponter, Computer Methods in Applied Mechanics and Engineering 140 pp 259– (1997)
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.