A novel unsymmetric 8-node plane element immune to mesh distortion under a quadratic displacement field

International Journal for Numerical Methods in Engineering

Volumn 58, Issue 11, 2003, Pages 1713-1748

  Rajendran, S ^a   Liew, K M ^b  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

^b NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

Author keywords

Compatibility; Distortion sensitivity; Eight node quadrilateral plane element; Geometric distortion; Higher order completeness; Mesh distortion; US QUAD8 nsymmetric finite element formulation

Indexed keywords

FINITE ELEMENT METHOD; FUNCTIONS; INTEGRATION; NUMERICAL ANALYSIS; PROBLEM SOLVING;

MESH DISTORTION; QUADRATIC DISPLACEMENT FIELDS;

COMPUTATIONAL METHODS;

FINITE ELEMENT METHOD;

EID: 0345303889     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.836     Document Type: Article

References (28)

1. Zienkiewicz OC, Taylor RL. The Finite Element Method, vol. 1. Basic Formulation and Linear Problems (4th edn). McGraw-Hill Book Company: London, 1989.
2. Taig IC. Structural analysis by matrix displacement method. English Electric Aviation Report No. S017, 1961.
3. Taig IC, Ker RI. Some problems in the discrete element representation of aircraft structures. In Matrix Methods of Structural Analysis, Fraeijs de Veubeke BM (ed.). Pergamon Press: New York, 1964.
4. MacNeal RH. Toward a defect-free four-node membrane element. Finite Elements in Analysis and Design 1989; 5:31-37.
5. Prathap G. The Finite Element Method in Structural Mechanics. Kluwer Academic Press: Dordrecht, 1993.
6. MacNeal RH. Finite Elements: Their Design and Performance. Marcel Dekker: New York, 1994.
7. Babuska I, Suri M. On locking and robustness in the finite element method. SIAM Journal on Numerical Analysis 1992; 29:1261-1299.
8. Irons BM. Engineering application of numerical integration in stiffness methods. AIAA Journal 1966; 14:2035-2037.
9. Hughes TJR. Equivalence of finite elements for nearly incompressible elasticity. Journal of Applied Mechanics (ASME) 1977; 44:181-183.
10. Wilson EL, Taylor RL, Doherty WP, Ghaboussi J. Incompatible displacement models. In Numerical and Computational Methods in Structural Mechanics, Fenves ST et al. (eds). Academic Press: New York, 1973; 43-77.
11. Lee N-S, Bathe K-J. Effects of element distortions on the performance of isoparametric elements. International Journal for Numerical Methods in Engineering 1993; 36:3553-3576.
12. Stricklin JA, Ho WS, Richardson EQ, Haisler WE. On isoparametric vs linear strain triangular elements. International Journal for Numerical Methods in Engineering 1977; 11:1041-1043.
13. Backlund J. On isoparametric elements. International Journal for Numerical Methods in Engineering 1978; 12:731-732.
14. Gifford LN. More on distorted isoparametric elements. International Journal for Numerical Methods in Engineering 1979; 14:290-291.
15. MacNeal RH, Harder RL. Eight nodes or nine? International Journal for Numerical Methods in Engineering 1992; 33:1049-1058.
16. Kikuchi F, Okabe M, Fujio H. Modification of the 8-node serendipity element. Computer Methods in Applied Mechanics and Engineering 1999; 179:91-109.
17. Zhang J, Kikuchi F. Interpolation error estimates of a modified 8-node serendipity finite element. Numerische Mathematik 2000; 85:503-524.
18. Rajendran S, Liew KM. Completeness requirements of shape functions for higher order finite elements. Structural Engineering and Mechanics 2000; 10:93-110.
19. Hughes TJR. The Finite Element Method. Prentice-Hall: Englewood Cliffs, NJ, 1987; 78.
20. Timoshenko SP, Goodier JN. Theory of Elasticity (3rd edn). McGraw-Hill: New York, 1934.
21. Zienkiewicz OC, Zhu JZ. The superconvergent patch recovery and a posteriori error estimates. Part I: The recovery technique. International Journal for Numerical Methods in Engineering 1992; 33:1331-1364.
22. Babuska I. Error-bounds for finite element method. Numerische Mathematik 1971; 16:322-333.
23. Brezzi F. On the existence, uniqueness and approximation of saddle-point problems arising from Lagrange multiplier. Revue Francaise d'Automatique Informatique Recherche Operationnelle: Analyse Numérique 1974; 8(R-2):129-151.
24. Babuska I, Narasimhan R. The Babuska-Brezzi condition and the patch test: an example. Computer Methods in Applied Mechanics and Engineering 1997; 140:183-199.
25. Bathe KJ. Finite Element Procedures in Engineering Analysis (2nd edn). Prentice-Hall: Englewood Cliffs, NJ, 1996.
26. Chapelle D, Bathe KJ. The inf-sup test. Computers and Structures 1993; 47(4/5):537-545.
27. Gopalakrishnan S. Behaviour of isoparametric quadrilateral family of Lagrangian fluid finite elements. International Journal for Numerical Methods in Engineering 2002; 54:731-761.
28. Bathe KJ, Hendriana D, Brezzi F, Sangalli G. Inf-sup test of upwinding methods. International Journal for Numerical Methods in Engineering 2000; 48:745-760.