Shape-free finite element method: The plane hybrid stress-function (HS-F) element method for anisotropic materials

Science China: Physics, Mechanics and Astronomy

Volumn 54, Issue 4, 2011, Pages 653-665

  Cen, Song ^a   Fu, XianGrong ^b   Zhou, GuoHua ^a   Zhou, MingJue ^a   Li, ChenFeng ^c  

^a TSINGHUA UNIVERSITY   (China)

^b CHINA AGRICULTURAL UNIVERSITY   (China)

^c SWANSEA UNIVERSITY   (United Kingdom)

Author keywords

anisotropic materials; finite element; fundamental analytical solutions; hybrid stress function (HS F) element; shape free; stress function; the principle of minimum complementary energy

Indexed keywords

ANISOTROPIC MATERIAL; FINITE ELEMENT; FUNDAMENTAL ANALYTICAL SOLUTIONS; HYBRID STRESS-FUNCTION (HS-F) ELEMENT; SHAPE-FREE; STRESS FUNCTION; THE PRINCIPLE OF MINIMUM COMPLEMENTARY ENERGY;

FLUORINE; HYBRID MATERIALS; OPTICAL ANISOTROPY; STRESSES;

FINITE ELEMENT METHOD;

EID: 79956213534     PISSN: 16747348     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11433-011-4272-6     Document Type: Article

References (35)

1. Zienkiewicz O C, Taylor R L, Zhu J Z. The Finite Element Method: Its Basis & Fundamental. 6th ed. Butterworth Heinemann: Elsevier, 2005
2. Long Y Q, Cen S, Long Z F. Advanced Finite Element Method in Structural Engineering. Berlin, Heidelberg: Springer-Verlag GmbH; Beijing: Tsinghua University Press, 2009
3. N. S. Lee K. J. Bathe 1993 Effects of element distortion on the performance of isoparametric elements Int J Numer Methods Eng 36 3553 3576 10.1002/nme.1620362009 0800.73465
4. Wilson E L, Tayler R L, Doherty WP, et al. Incompatible displacement models. Fenves S J, et al, eds. Numerical and Computational Methods in Structural Mechanics, New York: Academic Press, 1973. 43-57
5. R. L. Taylor P. J. Beresford E. L. Wilson 1976 A non-conforming element for stress analysis Int J Numer Methods Eng 10 1211 1219 10.1002/nme.1620100602 0338.73041
6. A. Ibrahimbegovic E. L. Wilson 1991 A modified method of incompatible modes Commun Appl Numer Methods 7 187 194 10.1002/cnm.1630070303 0723.73097
7. J. C. Simo M. S. Rifai 1990 A class of mixed assumed strain methods and the method of incompatible modes Int J Numer Methods Eng 29 1595 1638 10.1002/nme.1620290802 0724.73222 1058742 (Pubitemid 20718675)
8. T. Belytschko W. E. Bachrach 1986 Efficient implementation of quadrilaterals with high coarse-mesh accuracy Comput Methods Appl Mech Eng 54 279 301 10.1016/0045-7825(86)90107-6 0579.73075 1986CMAME..54..279B 836187 (Pubitemid 16532310)
9. T. J. R. Hughes 1980 Generalization of selective integration procedures to anisotropic and nonlinear media Int J Numer Methods Eng 16 1413 1418 10.1002/nme.1620150914
10. R. H. Macneal 1982 Derivation of element stiffness matrices by assumed strain distributions Nucl Eng Des 70 3 12 10.1016/0029-5493(82)90262-X
11. R. Piltner R. L. Taylor 1999 A systematic construction of B-bar functions for linear and nonlinear mixed-enhanced finite elements for plane elasticity problems Int J Numer Methods Eng 44 615 639 10.1002/(SICI)1097-0207(19990220)44: 5<615::AID-NME518>3.0.CO;2-U 0947.74067 1670616
12. L. M. Tang W. J. Chen Y. G. Liu 1984 Formulation of quasi-conforming element and Hu-Washizu principle Comput Struct 19 247 250 10.1016/0045-7949(84) 90224-4 0548.73051
13. Y. Q. Long M. F. Huang 1988 A generalized conforming isoparametric element Appl Math Mech 9 929 936 10.1007/BF02014599 0729.73205
14. G. R. Liu T. Nguyen-Thoi K. Y. Lam 2009 A novel FEM by scaling the gradient of strains with factor α (αFEM) Comput Mech 43 369 391 10.1007/s00466-008-0311-1 1162.74469 2453545
15. J. Chen C. J. Li W. J. Chen 2010 A family of spline finite elements Comput Struct 88 718 727 10.1016/j.compstruc.2010.02.011
16. S. Rajendran K. M. Liew 2003 A novel unsymmetric 8-node plane element immune to mesh distortion under a quadratic displacement field Int J Numer Methods Eng 58 1713 1748 10.1002/nme.836 1032.74680 (Pubitemid 37453911)
17. E. T. Ooi S. Rajendran J. H. Yeo 2004 A 20-node hexahedron element with enhanced distortion tolerance Int J Numer Methods Eng 60 2501 2530 10.1002/nme.1056 1075.74665 (Pubitemid 39103409)
18. S. Rajendran 2010 A technique to develop mesh-distortion immune finite elements Comput Methods Appl Mech Eng 199 1044 1063 10.1016/j.cma.2009.11.017 2010CMAME.199.1044R 2594822
19. Y. Q. Long J. X. Li Z. F. Long, et al. 1999 Area coordinates used in quadrilateral elements Commun Numer Methods Eng 15 533 545 10.1002/(SICI)1099- 0887(199908)15:8<533::AID-CNM265>3.0.CO;2-D 0959.74068 1707165
20. Z. F. Long J. X. Li S. Cen, et al. 1999 Some basic formulae for area coordinates used in quadrilateral elements Commun Numer Methods Eng 15 841 852 10.1002/(SICI)1099-0887(199912)15:12<841::AID-CNM290>3.0.CO;2-A 0965.74070 1732069 (Pubitemid 30526327)
21. X. M. Chen S. Cen Y. Q. Long, et al. 2004 Membrane elements insensitive to distortion using the quadrilateral area coordinate method Comput Struct 82 35 54 10.1016/j.compstruc.2003.08.004
22. X. M. Chen S. Cen X. R. Fu, et al. 2008 A new quadrilateral area coordinate method (QACM-II) for developing quadrilateral finite element models Int J Numer Methods Eng 73 1911 1941 10.1002/nme.2159 1195.74168 (Pubitemid 351454755)
23. Z. F. Long S. Cen L. Wang, et al. 2010 The third form of the quadrilateral area coordinate method (QACM-III): theory, application, and scheme of composite coordinate interpolation Finite Elem Anal Des 46 805 818 10.1016/j.finel.2010.04.008
24. H. G. Li S. Cen Z. Z. Cen 2008 Hexahedral volume coordinate method (HVCM) and improvements on 3D Wilson hexahedral element Comput Methods Appl Mech Eng 197 4531 4548 10.1016/j.cma.2008.05.022 1194.74427 2008CMAME.197.4531L
25. T. Belytschko Y. Y. Lu L. Gu 1994 Element free Galerkin methods Int J Numer Methods Eng 37 229 256 10.1002/nme.1620370205 0796.73077 1256818
26. S. N. Atluri T. Zhu 1998 A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics Comput Mech 22 117 127 10.1007/s004660050346 0932.76067 1649420 (Pubitemid 128620889)
27. X. Zhang X. H. Liu K. Z. Song, et al. 2001 Least-squares collocation meshless method Int J Numer Methods Eng 51 1089 1100 10.1002/nme.200 1056.74064 1841338 (Pubitemid 32675966)
28. J. M. Zhang Z. H. Yao H. Li 2002 A hybrid boundary node method Int J Numer Methods Eng 53 751 763 10.1002/nme.313 1878406 (Pubitemid 34057170)
29. Y. C. Cai H. H. Zhu 2010 A PU-based meshless Shepard interpolation method satisfying delta property Eng Anal with Bound Elem 34 9 16 10.1016/j. enganabound.2009.07.007 2559252
30. T. H. H. Pian 1964 Derivation of element stiffness matrices by assumed stress distributions AIAA J 2 1333 1336 10.2514/3.2546
31. X. R. Fu S. Cen C. F. Li, et al. 2010 Analytical trial function method for development of new 8-node plane element based on the variational principle containing airy stress function Engineering Computations 27 442 463 10.1108/02644401011044568
32. S. Cen X. R. Fu M. J. Zhou 2010 A novel hybrid stress-function finite element method immune to severe mesh distortion IOP Conference Series: Materials Science and Engineering (Proceedings of WCCM/APCOM 2010) 10 012220 10.1088/1757-899X/10/1/012220 2010MS&E...10a2220C
33. J. A. Teixeira de Freitas 1998 Formulation of elastostatic hybrid-Trefftz stress elements Comput Methods Appl Mech Eng 153 127 151 10.1016/S0045-7825(97) 00042-X 0991.74077
34. J. A. T. Freitas Z. M. Wang 1998 Hybrid-Trefftz stress elements for elastoplasticity Int J Numer Methods Eng 43 655 683 10.1002/(SICI)1097- 0207(19981030)43:4<655::AID-NME416>3.0.CO;2-1 0951.74072 (Pubitemid 128448125)
35. J. A. T. Freitas F. L. S. Bussamra 2000 Three-dimensional hybrid - Trefftz stress elements Int J Numer Methods Eng 47 927 950 10.1002/(SICI)1097- 0207(20000220)47:5<927::AID-NME805>3.0.CO;2-B 0960.74069 (Pubitemid 32211182)