A multiple-quadrature eight-node hexahedral finite element for large deformation elastoplastic analysis

Computer Methods in Applied Mechanics and Engineering

Volumn 154, Issue 1-2, 1998, Pages 69-132

  Liu, Wing Kam ^a   Guo, Yong ^a   Tang, Sing ^a   Belytschko, Ted ^a  

^a Northwestern University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; ELASTOPLASTICITY; ITERATIVE METHODS; KINEMATICS; MATHEMATICAL OPERATORS; NONLINEAR EQUATIONS; PLASTIC DEFORMATION; PROBLEM SOLVING;

MULTIPLE QUADRATURE EIGHT NODE HEXAHEDRAL FINITE ELEMENT METHOD; NEWTON'S ITERATION METHOD;

FINITE ELEMENT METHOD;

EID: 0031999714     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(97)00106-0     Document Type: Article

References (42)

1. T. Belytschko, Correction of article by D.P. Flanagan and T. Belytschko, Int. J. Numer. Methods Engrg. 19 (1983) 467-468.
2. T. Belytschko and L.P. Bindeman, Assumed strain stabilization of the 4-node quadrilateral with 1-point quadrature for nonlinear problems, Comput. Methods Appl. Mech. Engrg. 88 (1991) 311-340.
3. T. Belytschko and L.P. Binderman, Assumed strain stabilization of the eight node hexahedral element, Comput. Methods Appl. Mech. Engrg. 105 (1993) 225-260.
4. T. Belytschko and B.J. Hsieh, Nonlinear transient finite element analysis with convected coordinates, Int. J. Numer. Methods Engrg. 7 (1973) 225-271.
5. T. Belytschko, J.I. Lin and C.S. Tsay, Explicit algorithms for the nonlinear dynamics of shells, Comput. Methods Appl. Mech. Engrg. 42 (1984) 225-251.
6. T. Belytschko, J.S.-J. Ong, W.K. Liu and J.M. Kennedy, Hourglass control in linear and nonlinear problems, Comput. Methods Appl. Mech. Engrg. 43 (1984) 251-276.
7. 0 triangular plate element with one-point quadrature, Int. J. Numer. Methods Engrg. 20 (1984) 787-802.
8. T. Belytschko, B.L. Wong and H.Y. Chiang, Advances in one-point quadrature shell elements, Comput. Methods Appl. Mech. Engrg. 96 (1992) 93-107.
9. E.N. Dvorkin and K.J. Bathe, A continuum mechanics based four-node shell element for general nonlinear analysis, Int. J. Computer-Aided Engrg. and Software 1 (1984) 77-88.
10. J. Fish and T. Belytschko, Elements with embedded localization zones for large deformation problems, Comput. Struct. 30 (1988) 247-256.
11. D.P. Flanagan and T. Belytschko, A uniform strain hexahedron and quadrilateral with orthogonal hourglass control, Int. J. Numer. Methods Engrg. 17 (1981) 679-706.
12. Y.K. Hu and W.K. Liu, ALE finite element formulation of ring rolling analysis, Int. J. Numer. Methods Engrg. 33 (1992) 1217-1236.
13. Y.K. Hu and W.K. Liu, An ALE hydrodynamic lubrication finite element method with application to strip rolling, Int. J. Numer. Methods Engrg. 36 (1993) 855-880.
14. T.J.R. Hughes, Numerical implementation of constitutive models: rate-independent deviatoric plasticity, in: S. Nemat-Nasser, R.J. Asaro and G.A. Hegemier, eds., Theoretical Foundation for Large-scale Computations of Nonlinear Material Behavior (1984) 29-57.
15. T.J.R. Hughes and W.K. Liu, Nonlinear finite element analysis of shells: Part I. Three dimensional shells, Comput. Methods Appl. Mech. Engrg. 26 (1981) 331-362.
16. T.J.R. Hughes and W.K. Liu, Nonlinear finite element analysis of shells: Part II. Two-dimensional shells, Comput. Methods Appl. Mech. Engrg. 27 (1981) 167-181.
17. T.J.R. Hughes and T.E. Tezduyar, Finite elements based upon mindlin plate theory with particular reference to the four-node bilinear isoparametric element, J. Appl. Mech. 48 (1981) 587-596.
18. O.P. Jacquotte and O.T. Oden, Analysis of hourglass instabilities and control in underintegrated methods in finite element computations, Comput. Methods Appl. Mech. Engrg. 44 (1984) 339-363.
19. W.K. Liu, Lecture notes on nonlinear finite element methods, Northwestern University, 1983, revised in 1992.
20. W.K. Liu and T. Belytschko, Efficient linear and nonlinear heat conduction with a quadrilateral element, Int. J. Numer. Methods Engrg. 20 (1984) 931-948.
21. W.K. Liu, T. Belytschko and J.S. Chen, Nonlinear versions of flexurally superconvergent elements, Comput. Methods Appl. Mech. Engrg. 71 (1988) 241-258.
22. W.K. Liu, T. Belytschko, J.S.J. Ong and E. Law, Use of stabilization matrices in nonlinear finite element analysis, Engineering Computations 2 (1985) 47-55.
23. W.K. Liu, H. Chang, J.S. Chen and T. Belytschko, ALE Petrov-Galerkin finite elements for nonlinear continua, Comput. Methods Appl. Mech. Engrg. 68 (1988) 259-310.
24. W.K. Liu, J.S. Chen, T. Belytschko, and Y.F. Zhang, Adaptive ALE finite elements with particular reference to external work rate on frictional interface, Comput. Methods Appl. Mech. Engrg. 93 (1992) 189-216.
25. W.K. Liu and Y.K. Hu, Finite element hydrodynamic friction model for metal forming, Int. J. Numer. Methods Engrg. 37 (1994) 4015-4037.
26. W.K. Liu, Y.K. Hu and T. Belytschko, Multiple quadrature underintegrated finite elements, Int. J. Numer. Methods Engrg. 37 (1994) 3263-3289.
27. W.K. Liu, E.S. Law, D. Lam, and T. Belytschko, Resultant-stress degenerated-shell element, Comput. Methods Appl. Mech. Engrg. 55 (1986) 259-300.
28. W.K. Liu, J.S.-J. Ong and R.A. Uras, Finite element stabilization matrices - A unification approach, Comput. Methods Appl. Mech. Engrg. 53 (1985) 13-46.
29. B.C. Koh and N. Kikuchi, New improved hourglass control for bilinear and trilinear elements in anisotropic linear elasticity, Comput. Methods Appl. Mech. Engrg. 65 (1987) 1-46.
30. W.T. Koiter, A spherical shell under point loads at its poles, in: Progress in Applied Mechanics, The Prager Anniversary Volume (Macmillan, New York, 1963).
31. R.D. Krieg and S.W. Key, Implementation of a time independent plasticity theory into structural computer programs, in: J.A. Stricklin and K.J. Saczlski, eds., Constitutive Equations in Viscoplasticity: Computational and Engineering Aspects (AMD 20, ASME, New York, 1976) 125-137.
32. R.H. MacNeal, Derivative of element stiffness matrices by assumed strain distributions, Nuclear Engrg. Des. 70 (1982) 3-12.
33. R.H. MacNeal and R.L. Harder, A proposed standard set of problems to test finite element accuracy, Finite Elements Anal. Des. 11 (1985) 3-20.
34. D.S. Malkus and T.J.R. Hughes, Mixed finite element methods - Reduced and selective integration techniques: a unification of concepts, Comput. Methods Appl. Mech. Engrg. 15 (1978) 63-81.
35. K. Mattiasson, A. Bengtsson and A. Samuelsson, On the accuracy and efficiency of numerical algorithms for geometrically nonlinear structural analysis, in: P.G. Bergan, K.J. Bathe and W. Wunderlich, eds., Finite Element Methods for Nonlinear Problems (1985) 3-23.
36. J.C. Nagtegaal, D.M. Parks and J.R. Rice, On numerical accurate finite element solutions in the fully plastic range, Comput. Methods Appl. Mech. Engrg. 4 (1974) 153-177.
37. J.C. Schulz, Finite element hourglassing control, Int. J. Numer. Methods Engrg. 21 (1985) 1039-1048.
38. J.C. Simo and T.J.R. Hughes, On the variational foundational of assumed strain methods, J. Appl. Mech. 53 (1986) 51-54.
39. J.C. Simo and R.L. Taylor, Consistent tangent operators for rate-independent elastoplasticity, Comput. Methods Appl. Mech. Engrg. 48 (1985) 101-118.
40. 0 elements, Comput. Methods Appl. Mech. Engrg. 41 (1983) 279-296.
41. S.P. Timoshenko, and J.N. Goodier, Theory of Elasticity, 3rd edition (McGraw-Hill, New York, 1970) 41-46.
42. D.M. Woo, The stretch-forming test, The Engineering 26 (1965) 876-880.