Improved 4-node Hu-Washizu elements based on skew coordinates

Computers and Structures

Volumn 87, Issue 7-8, 2009, Pages 407-424

  Wisniewski, K ^a   Turska, E ^b  

^a POLISH ACADEMY OF SCIENCES   (Poland)

^b POLISH JAPANESE INSTITUTE OF INFORMATION TECHNOLOGY   (Poland)

Author keywords

4 Node finite elements; Incremental Hu Washizu functional; Mixed elements; Mixed enhanced elements; Plane stress; Skew coordinates

Indexed keywords

ELASTICITY; FINITE ELEMENT METHOD; FUNCTIONAL MATERIALS;

4-NODE FINITE ELEMENTS; INCREMENTAL HU-WASHIZU FUNCTIONAL; MIXED ELEMENTS; MIXED/ENHANCED ELEMENTS; PLANE STRESS; SKEW COORDINATES;

STRAIN;

EID: 61849088955     PISSN: 00457949     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruc.2009.01.011     Document Type: Article

References (42)

1. Babuška I. Error-bounds for the finite element method. Numer Math 16 (1971) 322-333
2. Babuška I. (edited and typed by Vardapetyan L, Yotow I.) On the inf-sup (Babuška-Brezzi) condition, TICAM Forum # 5; October 1996.
3. Bathe K.J. Finite element procedures (1996), Prentice-Hall, Englewood Cliffs
4. Bathe K.J. The inf-sup condition and its evaluation for mixed finite element methods. Comput Struct 79 (2001) 243-252
5. Belytschko T., Wong B.L., and Stolarski H. Assumed strain stabilization procedure for the 9-node Lagrange Shell element. Int J Numer Methods Eng 28 (1989) 385-414
6. Benzi M, Golub GH, Liesen J. Numerical solution of saddle point problems. Acta Numerica 2005;1-137. doi:10.1017/S0962492904000212.
7. Brezzi F., and Fortin M. Mixed and hybrid finite element methods. Springer series in comput ational mathematics vol. 15 (1991), Springer-Verlag, New-York
8. Brezzi F., and Bathe K.-J. A discourse on the stability conditions for FE formulations. Comput Methods Appl Mech Eng 82 (1990) 27-57
9. Chapelle D., and Bathe K.J. The inf-sup test. Comput Struct 47 4/5 (1993) 537-545
10. Cook R.D. A plane hybrid element with rotational dof and adjustable stiffness. Int J Numer Methods Eng 24 (1987) 1499-1508
11. Crisfield M.A., Moita G.F., Jelenic G., and Lyons L.P.R. Enhanced lower-order element formulation for large strains. Comput Mech 17 (1995) 62-73
12. Holzapfel G.A. Nonlinear solid mechanics. A continuum approach for engineering (2000), Wiley
13. Korelc J. Multi-language and multi-environment generation of nonlinear finite element codes. Eng Comput 18 (2002) 312-327
14. Korelc J., and Wriggers P. Improved enhanced strain four-node element with Taylor expansion of the shape functions. Int J Numer Methods Eng 40 3 (1997) 407-421
15. Liu W.K., Ong J.S.-J., and Uras R.A. Finite element stabilization matrices - a unification approach. Comput Methods Appl Mech Eng 53 (1985) 13-46
16. MacNeal R.H., and Harder R.L. A proposed standard set of problems to test finite element accuracy. Finite Elem Anal Des 1 (1985) 3-20
17. Panasz P., and Wisniewski K. Nine-node shell elements with 6 dofs/node based on two-level approximations. Finite Elem Anal Des 44 (2008) 784-796
18. Ogden R. Non-linear elastic deformations (1984), Ellis Horwood, Chichester, UK
19. Pantuso D., and Bathe K.J. A four-node quadrilateral mixed-interpolated element for solids and fluids. Math Models Methods Appl Sci 5 8 (1995) 1113-1128
20. Pian T.H.H. Derivation of element stiffness matrices by assumed stress distributions. AIAA 2 (1964) 1333-1336
21. Pian T.H.H., and Chen D.-P. Alternative ways for formulation of hybrid stress elements. Int J Numer Methods Eng 18 (1982) 1679-1684
22. Pian T.H.H., and Sumihara K. Rational approach for assumed stress finite elements. Int J Numer Methods Eng 20 (1984) 1685-1695
23. Pian T.H.H., and Tong P. Relations between incompatible displacement model and hybrid stress model. Int J Numer Methods Eng 22 (1986) 173-181
24. Pian T.H.H., and Wu C.C. A rational approach for choosing stress terms for hybrid finite element formulations. Int J Numer Methods Eng 26 (1988) 2331-2343
25. Piltner R., and Taylor R.L. A quadrilateral mixed finite element with two enhanced strain modes. Int J Numer Methods Eng 38 (1995) 1783-1808
26. Piltner R., and Taylor R.L. A systematic construction of B-bar functions for linear and non-linear mixed-enhanced finite elements for plane elasticity problems. Int J Numer Methods Eng 44 (1999) 615-639
27. Piltner R. An implementation of mixed enhanced finite elements with strains assumed in Cartesian and natural element coordinates using sparse over(B, ̄)-matrices. Eng Comput 17 8 (2000) 933-949
28. Roberts J.E., and Thomas J.M. Mixed and hybrid elements. In: Ciarlet P.G., and Lions J.L. (Eds). Handbook of numerical analysis vol. 2, part 2 (1991), Elsevier Science Publishers, North-Holland
29. Robinson J, Blackham S. An evaluation of lower order membranes as contained in MSC/NASTRAN ASA and PAFEC FEM systems. Dorset, England: Robinson and Associates; 1979.
30. Simo J.C., and Rifai M.S. A class of mixed assumed strain methods and the method of incompatible modes. Int J Numer Methods Eng 29 (1990) 1595-1638
31. Simo J.C., and Armero F. Geometrically non-linear enhanced strain mixed methods and the method of incompatible modes. Int J Numer Methods Eng 33 (1992) 1413-1449
32. Spilker R.L., Maskeri S.M., and Kania E. Plane isoparametric hybrid-stress elements: invariance and optimal sampling. Int J Numer Methods Eng 17 10 (1981) 1469-1496
33. Taylor R.L., Beresford P.J., and Wilson E.L. A non-conforming element for stress analysis. Int J Numer Methods Eng 10 (1976) 1211-1220
34. Wagner W., and Gruttmann F. A robust nonlinear mixed hybrid quadrilateral shell element. Int J Numer Methods Eng 64 5 (2005) 635-666
35. Wilson E.L., Taylor R.L., Doherty W.P., and Ghaboussi J. Incompatible displacement models. In: Fenves S.J., Perrone N., Robinson A.R., and Schnobrich W.C. (Eds). Numerical and computer methods in finite element analysis (1973), Academic Press, New York 43-57
36. Wisniewski K., and Turska E. Enhanced Allman quadrilateral for finite drilling rotations. Comput Methods Appl Mech Eng 195 (2006) 6086-6109
37. Wisniewski K., and Turska E. Improved four-node Hellinger-Reissner elements based on skew coordinates. Int J Numer Methods Eng 76 (2008) 798-836
38. Wriggers P., and Korelc J. On enhanced strain methods for small and finite deformations of solids. Comput Mech 18 6 (1996) 413-428
39. Wriggers P., and Reese S. A note on enhanced strain methods for large deformations. Comput Methods Appl Mech Eng 135 (1996) 201-209
40. Yuan K.-Y., Huang Y.-S., and Pian T.H.H. New strategy for assumed stress for 4-node hybrid stress membrane element. Int J Numer Methods Eng 36 (1993) 1747-1763
41. Zienkiewicz O.C., and Taylor R.L. The finite element method. Basic formulation and linear problems. 4th ed. vol. 1 (1989), McGraw-Hill, Berlin
42. Yamada T., and Kikuchi F. An arbitrary Lagrangian-Eulerian finite element method for incompressible hyperelasticity. Comput Methods Appl Mech Eng 102 (1993) 147-177