Abstract
In this paper one-point quadrature “assumed strain” mixed element formulation based on the Hu-Washizu variational principle is presented. Special care is taken to avoid hourglass modes and volumetric locking as well as shear locking. The assumed strain fields are constructed so that those portions of the fields which lead to volumetric and shear locking phenomena are eliminated by projection, while the implementation of the proposed URI scheme is straightforward to suppress hourglass modes. In order to treat geometric nonlinearities simply and efficiently, a corotational coordinate system is used. Several numerical examples are given to demonstrate the performance of the suggested formulation, including nonlinear static/dynamic mechanical problems.
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References
Flanagan DP, Belytschko T. A uniform strain hexahedron and quadrilateral with orthogonal hourglass control.Int J Numer Methods Engng, 1981, 17: 679–706.
Belytschko T, et al. Hourglass control in linear and nonlinear problems.Comput Methods Appl Mech Engng, 1984, 43: 251–276.
Belytschko T, et al. Efficient implemetation of quadrilaterals with high coarse—mesh accuracy.Comput Methods Appl Mech Engng, 1986, 54: 279–301
Belytschko T, Bindeman LP. Assumed strain stabilization of the 4-node quadrilateral with 1-point quadrature for nonlinear problems.Comput Methods Appl Mech Engng, 1991, 88: 311–340
Liu Wk, et al. Finite element stabilization matrices—a unification approach.Comput Methods Appl Mech Engng, 1985, 53: 13–46
Liu Wk, et al. Use of stabilization matrices in nonlinear analysis.Eng Comput, 1985, 2: 47–55
Koh BC, Kikuchi N. New improved hourglass control for bilinear and trilinear elements in anisotropic linear elasticity.Comput Methods Appl Mech Engng, 1987, 65: 1–46
Zhu YY, Cescotto S. Unified and mixed formulation of the 4-node quadrilateral elements by assumed strain method: application to thermomechanical problems.Int J Numer Methods Engng, 1995, 38: 685–716
Simo JC, et al. Variational and projection methods for the volume constraint in finite deformation elastoplasticity.Comput Methods Appl Mech Engng, 1985, 51: 177–208
Simo JC, Hughes TJR. On the variational foundations of assumed strain methods.J Appl Mech ASME, 1986, 53: 51–54
Simo JC, Rifai MS. A class of mixed assumed strain method and the method of incompatible modes.Int J Numer Methods Engng, 1990, 29: 1595–1638
Simo JC, Armero F. Geometrically nonlinear enhanced strain mixed methods and the method of incompatible modes.Int J Number Methods Engng, 1992, 33: 1413–1449
Fish J, Belytschko T. Elements with embedded localization zones for large deformation problems.Comput Struct, 1988, 30: 247–256
Hughes TJR, Liu WK. Nonlinear finite element analysis of shells: Part 1, Three-dimensional shells.Comput Methods Appl Mech Engng, 1981, 26: 331–362
Liu WK, et al. A multiple-quadrature eight-node hexahedral finite element for large deformation elastoplastic analysis.Comput Methods Appl Mech Engng, 1998, 154: 69–132
Belytschko T, et al. Nonlinear Finite Elements for Continua and Structures. Beijing: Tsinghua University Press, 2002
Belytschko T, et al. A fractal patch test.Int J Numer Methods Engng, 1988, 26: 2199–2210
Jacquotte OP, Oden JT. Analysis of hourglass instabilities and control in underintegrated finite element methods.Comput Methods Appl Mech Engng, 1984, 44: 339–363
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Jinyan, W., Jun, C. & Minghui, L. A URI 4-Node quadrilateral element by assumed strain. Acta Mech Sinica 20, 632–641 (2004). https://doi.org/10.1007/BF02485867
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DOI: https://doi.org/10.1007/BF02485867