A new quadrilateral area coodinate method (QACM-II) for developing quadrilateral finite element models

International Journal for Numerical Methods in Engineering

Volumn 73, Issue 13, 2008, Pages 1911-1941

  Chen, Xiao Ming ^a   Cen, Song ^a   Fu, Xiang Rong ^b   Long, Yu Qiu ^a  

^a TSINGHUA UNIVERSITY   (China)

^b CHINA AGRICULTURAL UNIVERSITY   (China)

Author keywords

Finite element; QACII6; QACM I; QACM II; Quadrilateral element; Quadrilaterla area coordinate

Indexed keywords

BEAMS AND GIRDERS; BENCHMARKING; MATHEMATICAL MODELS;

QUADRILATERAL AREA COORDINATE METHOD; QUADRILATERAL ELEMENT;

FINITE ELEMENT METHOD;

BEAMS AND GIRDERS; BENCHMARKING; FINITE ELEMENT METHOD; MATHEMATICAL MODELS;

EID: 41449088147     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2159     Document Type: Article

References (40)

1. Taig IC. Structural analysis by the matrix displacement method. English Electric Aviation Report, 1961; S017.
2. Irons BM. Engineering application of numerical integration in stiffness method. Journal of the American Institute of Aeronautics and Astronautics 1966; 14:2035-2037.
3. Lee NS, Bathe KJ. Effects of element distortion on the performance of isoparametric elements. International Journal for Numerical Methods in Engineering 1993; 36:3553-3576.
4. Long YQ, Li JX, Long ZF, Cen S. Area coordinates used in quadrilateral elements. Communications in Numerical Methods in Engineering 1999; 15(8):533-545.
5. Long ZF, Li JX, Cen S, Long YQ. Some basic formulae for area coordinates used in quadrilateral elements. Communications in Numerical Methods in Engineering 1999; 15(12):841-852.
6. Wilson EL, Taylor RL, Doherty WP, Ghabussi T. Incompatible displacement models. In Numerical and Computer Methods in Structural Mechanics, Fenven ST et al. (eds). Academic Press~ New York, 1973; 43-57.
7. Chen XM, Cen S, Long YQ, Yao ZH. Membrane elements insensitive to distortion using the quadrilateral area coordinate method. Computers and Structures 2004; 82(1):35-54.
8. MacNeal RH, Harder RL. A proposed standard set of problems to test finite element accuracy. Finite Elements in Analysis and Design 1985; 1(1):3-20.
9. Cen S, Du Y, Chen XM, Fu XR. The analytical element stiffness matrix of a recent 4-node membrane element formulated by the quadrilateral area coordinate method. Communications in Numerical Methods in Engineering 2007; DOI: 10.1002/cnm.953.
10. Cardoso RPR, Yoon JW, Valente RAF. A new approach to reduce membrane and transverse shear locking for one-point quadrature shell elements: linear formulation. International Journal for Numerical Methods in Engineering 2006; 66(2):214-249.
11. Cardoso RPR, Yoon JW, Valente RAF. Enhanced one-point quadrature shell element for nonlinear applications. International Journal for Numerical Methods in Engineering 2007; 69(3):627-663.
12. Sob AK, Long YQ, Cen S. Development of eight-node quadrilateral membrane elements using the area coordinates method. Computational Mechanics 2000; 25(4):376-384.
13. Soh AK, Long ZF, Cen S. Development of a new quadrilateral thin plate element using area coordinates. Computer Methods in Applied Mechanics and Engineering 2000; 190(8-10):979-987.
14. Cen S, Long YQ, Yao ZH, Chiew SP. Application of the quadrilateral area coordinate method: a new element for Mindlin-Reissner plate. International Journal for Numerical Methods in Engineering 2006; 66(1):1-45.
15. Cen S, Fu XR, Long YQ, Li HG, Yao ZH. Application of the quadrilateral area coordinate method: a new element for laminated composite plate bending problems. Acta Mechanica Sinica 2007; DOI: 10.1007/ s10409-007-0088-z.
16. Zhu YQ, Lin ZQ, Zhang WG. A quadrilateral thin shell element based on area co-ordinate for explicit dynamic analysis. Communications in Numerical Methods in Engineering 2003; 19:169-178.
17. Zhu YQ, Wu CF. An improved area-coordinate based quadrilateral shell element in dynamic explicit FEA. International Journal of Modern Physics B 2005; 19(1-3):687-690.
18. Brunet M, Sabourin F. Analysis of a rotation-free 4-node shell element. International Journal for Numerical Methods in Engineering 2006; 66(9):1483-1510.
19. Long YQ, Long ZF, Cen S. Method of area coordinate - from triangular to quadrilateral elements. Advances in Structural Engineering 2001; 4(1):1-11.
20. Long YQ, Cen S, Long ZF. Generalized conforming element (GCE) and quadrilateral area coordinate method (QACM). In Proceedings of the Sixth World Congress on Computational Mechanics in Conjunction with the Second Asian-Pacific Congress on Computational Mechanics, Yao ZH, Yuan MW, Zhong WX (eds). Tsinghua University Press & Springer: Beijing, China, 2004; 462-467.
21. Taylor RL, Beresford PJ, Wilson EL. A non-conforming element for stress analysis. International Journal for Numerical Methods in Engineering 1976; 10:1211-1219.
22. Pian THH, Sumihara K. Rational approach for assumed stress finite elements. International Journal for Numerical Methods in Engineering 1984; 20: 1685-1695.
23. Pian THH, Wu CC. General formulation of incompatible shape function and an incompatible isoparametric element. Proceedings of the Invitational China - American Workshop on FEM, Chengde, China, 1986; 159-165.
24. Chen WJ, Cheung YK. Three dimensional 8-node and 20-node refined hybrid isoparametric elements. International Journal for Numerical Methods in Engineering 1992; 35: 1871-1889.
25. Chen WJ, Tang LM. Isoparametric quasi-conforming element. Journal of Dalian University of Technology 1981; 20(1):63-74 (in Chinese).
26. Andelfinger U, Ramm E. EAS-elements for two-dimensional, three-dimensional, plate and shell structures and their equivalence to HR-elements. International Journal for Numerical Methods in Engineering 1993; 36:1311-1337.
27. Piltner R, Taylor RL. A systematic constructions of B-bar functions for linear and nonlinear mixed-enhanced finite elements for plane elasticity problems. International Journal for Numerical Methods in Engineering 1997; 44:615-639.
28. Cook RD. Improved two-dimensional finite element. Journal of the Structural Division (ASCE) 1974; 100(9): 1851-1863.
29. Bassayya K, Bhattacharya K, Shrinivasa U. Eight-node brick, PN340, representing constant stress fields exactly. Computers and Structures 2000; 74:441-460.
30. Ibrahimgovic A, Taylor RL, Wilson EL. A robust quadrilateral membrane element with rotational degrees of freedom. International Journal for Numerical Methods in Engineering 1990; 30:445-457.
31. MacNeal RH, Harder RL. A refined four-noded membrane element with rotation degrees of freedom. Computers and Structures 1988; 28(1):75-84.
32. Cook RD, Malkus DS, Plesha ME. Concepts and Applications of Finite Element Analysis (3rd edn). Wiley: New York, 1989.
33. Long YQ, Xu Y. Generalized conforming triangular membrane element with vertex rigid rotational freedom. Finite Elements in Analysis and Design 1994; 17:259-271.
34. Irons BM, Razzaque A. Experience with patch test for convergence of finite element methods. In Mathematical Foundations of the Finite Element Methods, Aziz AK (ed.). Academic Press: New York, 1972; 557-587.
35. Bazeley GP, Cheung YK, Irons BM, Zienkiewicz OC. Triangular elements in bending, conforming and non-conforming solutions. Proceedings of Conference on Matrix Methods in Structural Mechanics, Ohio, 1965.
36. Zienkiewicz OC, Taylor RL. The Basis in the Finite Element Method, vol. 1 (5th edn). Butterworth-Heinnemann: Oxford, 2000.
37. Strang G, Fix GJ. An Analysis of the Finite Element Method. Prentice-Hall: Englewood Cliffs, NJ, 1973.
38. Stummel E. The limitation of the patch test. International Journal for Numerical Methods in Engineering 1980; 15:177-188.
39. Shi ZC. An explicit analysis of Stummel's patch test examples. International Journal for Numerical Methods in Engineering 1984; 20:1233-1246.
40. MacNeal RH. A theorem regarding the locking of tapered four-noded membrane elements. International Journal for Numerical Methods in Engineering 1987; 24:1793-1799.