8- and 12-node plane hybrid stress-function elements immune to severely distorted mesh containing elements with concave shapes

Computer Methods in Applied Mechanics and Engineering

Volumn 200, Issue 29-32, 2011, Pages 2321-2336

  Cen, Song ^a   Fu, Xiang Rong ^b   Zhou, Ming Jue ^a  

^a TSINGHUA UNIVERSITY   (China)

^b CHINA AGRICULTURAL UNIVERSITY   (China)

Author keywords

Finite element; Fundamental analytical solutions; Hybrid stress function (HS F) element; Severely distorted mesh; Stress function; The principle of minimum complementary energy

Indexed keywords

FINITE ELEMENT; FUNDAMENTAL ANALYTICAL SOLUTIONS; HYBRID STRESS-FUNCTION (HS-F) ELEMENT; SEVERELY DISTORTED MESH; STRESS FUNCTION; THE PRINCIPLE OF MINIMUM COMPLEMENTARY ENERGY;

FINITE ELEMENT METHOD; STIFFNESS MATRIX; STRESSES;

FLUORINE;

EID: 79955812392     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2011.04.014     Document Type: Article

References (39)

1. Stricklin J.A., Ho W.S., Richardson E.Q., Haister W.E. On isoparametric vs linear strain triangular elements. Int. J. Numer. Methods Engrg. 1977, 11:1041-1043.
2. Lee N.S., Bathe K.J. Effects of element distortion on the performance of isoparametric elements. Int. J. Numer. Methods Engrg. 1993, 36:3553-3576.
3. Zienkiewicz O.C., Taylor R.L. The Finite Element Method. Basic Formulation and Linear Problems 1989, vol. 1. McGraw-Hill Book Company, London. fourth ed.
4. Pian T.H.H. Derivation of element stiffness matrices by assumed stress distributions. AIAA J. 1964, 2(7):1333-1336.
5. Pian T.H.H., Chen D.P. Alternative ways for formulation of hybrid stress elements. Int. J. Numer. Methods Engrg. 1982, 18:1679-1684.
6. Pian T.H.H., Sumihara K. Rational approach for assumed stress finite elements. Int. J. Numer. Methods Engrg. 1984, 20:1685-1695.
7. Zhang C.H., Wang D.D., Zhang J.L., Feng W., Huang Q. On the equivalence of various hybrid finite elements and a new orthogonalization method for explicit element stiffness formulation. Finite Elem. Anal. Des. 2007, 43:321-332.
8. Wilson E.L., Tayler R.L., Doherty W.P., Ghaboussi J. Incompatible displacement models. Numerical and Computational Methods in Structural Mechanics 1973, 43-57. Academic Press, New York. S.J. Fenves (Ed.).
9. Taylor R.L., Beresford P.J., Wilson E.L. A non-conforming element for stress analysis. Int. J. Numer. Methods Engrg. 1976, 10:1211-1219.
10. Simo J.C., Rifai M.S. A class of mixed assumed strain methods and the method of incompatible modes. Int. J. Numer. Methods Engrg. 1990, 29:1595-1638.
11. Belytschko T., Bachrach W.E. Efficient implementation of quadrilaterals with high coarse-mesh accuracy. Comput. Methods Appl. Mech. Engrg. 1986, 54:279-301.
12. Hughes T.J.R. Generalization of selective integration procedures to anisotropic and nonlinear media. Int. J. Numer. Methods Engrg. 1980, 16:1413-1418.
13. Macneal R.H. Derivation of element stiffness matrices by assumed strain distributions. Nucl. Engrg. Des. 1982, 70:3-12.
14. Piltner R., Taylor R.L. A systematic constructions of B-bar functions for linear and nonlinear mixed-enhanced finite elements for plane elasticity problems. Int. J. Numer. Methods Engrg. 1997, 44:615-639.
15. Tang L.M., Chen W.J., Liu Y.G. Formulation of quasi-conforming element and Hu-Washizu principle. Comput. Struct. 1984, 19(1-2):247-250.
16. Long Y.Q., Huang M.F. A generalized conforming isoparametric element. Appl. Math. Mech. 1988, 9(10):929-936.
17. Liu G.R., Nguyen-Thoi T., Lam K.Y. A novel FEM by scaling the gradient of strains with factor α (αFEM). Comput. Mech. 2009, 43:369-391.
18. Chen J., Li C.J., Chen W.J. A 17-node quadrilateral spline finite element using the triangular area coordinates. Appl. Math. Mech. 2010, 31(1):125-134.
19. Chen J., Li C.J., Chen W.J. A family of spline finite elements. Comput. Struct. 2010, 88(11-12):718-727.
20. Rajendran S., Liew K.M. A novel unsymmetric 8-node plane element immune to mesh distortion under a quadratic displacement field. Int. J. Numer. Methods Engrg. 2003, 58:1713-1748.
21. Rajendran S. A technique to develop mesh-distortion immune finite elements. Comput. Methods Appl. Mech. Engrg. 2010, 199(17-20):1044-1063.
22. Ooi E.T., Rajendran S., Yeo J.H. A 20-node hexahedron element with enhanced distortion tolerance. Int. J. Numer. Methods Engrg. 2004, 60:2501-2530.
23. Ooi E.T., Rajendran S., Yeo J.H. Remedies to rotational frame dependence and interpolation failure of US-QUAD8 element. Commun. Numer. Methods Engrg. 2008, 24(11):1203-1217.
24. Long Y.Q., Cen S., Long Z.F. Advanced Finite Element Method in Structural Engineering 2009, Springer-Verlag GmbH/Tsinghua University Press, Berlin, Heidelberg/Beijing.
25. Long Y.Q., Li J.X., Long Z.F., Cen S. Area coordinates used in quadrilateral elements. Commun. Numer. Methods Engrg. 1999, 15(8):533-545.
26. Long Z.F., Li J.X., Cen S., Long Y.Q. Some basic formulae for area coordinates used in quadrilateral elements. Commun. Numer. Methods Engrg. 1999, 15(12):841-852.
27. Long Z.F., Cen S., Wang L., Fu X.R., Long Y.Q. The third form of the quadrilateral area coordinate method (QACM-III): theory, application, and scheme of composite coordinate interpolation. Finite Elem. Anal. Des. 2010, 805-818.
28. Chen X.M., Cen S., Fu X.R., Long Y.Q. A new quadrilateral area coordinate method (QACM-II) for developing quadrilateral finite element models. Int. J. Numer. Methods Engrg. 2008, 73(13):1911-1941.
29. Li H.G., Cen S., Cen Z.Z. Hexahedral volume coordinate method (HVCM) and improvements on 3D Wilson hexahedral element. Comput. Methods Appl. Mech. Engrg. 2008, 197(51-52):4531-4548.
30. Chen X.M., Cen S., Long Y.Q., Yao Z.H. Membrane elements insensitive to distortion using the quadrilateral area coordinate method. Comput. Struct. 2004, 82(1):35-54.
31. Cheng A.H.D., Chen C.S., Golberg M.A., Rashed Y.F. BEM for theomoelasticity and elasticity with body forces - a revisit. Engrg. Anal. Bound. Elem. 2001, 25:377-387.
32. Timoshenko S.P., Goodier J.N. Theory of Elasticity 1934, McGraw-Hill, New York. third ed.
33. Cook R.D., Malkus D.S., Plesha M.E. Concepts and Applications of Finite Element Analysis 1989, John Wiley & Sons, Inc., New York. third ed.
34. Abaqus 6.9 HTML Documentation, Dassault Systèmes Simulia Corp., Providence, RI, USA, 2009.
35. Long Y.Q., Xu Y. Generalized conforming triangular membrane element with vertex rigid rotational freedom. Finite Elem. Anal. Des. 1994, 17:259-271.
36. Macneal R.H., Harder R.L. A proposed standard set of problems to test finite element accuracy. Finite Elem. Anal. Des. 1985, 1(1):3-20.
37. Spilker R.L., Maskeri S.M., Kania E. Plane isoparametric hybrid-stress elements: invariance and optimal sampling. Int. J. Numer. Methods Engrg. 1981, 17:1469-1496.
38. Fu X.R., Cen S., Long Y.Q., Jiang X.G., Ju J.S. The analytical trial function method (ATFM) for finite element analysis of plane crack/notch problems. Key Engrg. Mater. 2008, 385-387:617-620.
39. Fu X.R., Cen S., Li C.F., Chen X.M. Analytical trial function method for development of new 8-node plane element based on variational principle containing Airy stress function. Engrg. Comput. 2010, 27(4):442-463.