One point quadrature shell elements: A study on convergence and patch tests

Computational Mechanics

Volumn 40, Issue 5, 2007, Pages 871-883

  Cardoso, Rui P R ^a   Yoon, Jeong Whan ^b  

^a UNIVERSITY OF AVEIRO   (Portugal)

^b ALCOA TECHNICAL CENTER   (United States)

Author keywords

Bending patch test; Membrane patch test; Reduced integration; Shell elements

Indexed keywords

COMPUTATIONAL EFFICIENCY; COMPUTER SIMULATION; FORMING; SHEET METAL; STABILIZATION; STRAIN;

BENDING PATCH TEST; MEMBRANE PATCH TEST; REDUCED INTEGRATION; SHELL ELEMENTS;

COMPUTATIONAL MECHANICS;

EID: 34548226897     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-006-0148-4     Document Type: Article

References (26)

1. ABAQUS (2002) Theory manual, Version 6.3. Hibbitt, Karlsson & Sorensen, Inc. Rhode-Island USA
2. Andelfinger U, Ramm E (1993) EAS-Elements for two-dimensional, three-dimensional, plate and shells and their equivalence to HR-elements. Int J Numer Meth Eng 36: 1413-1449
3. Batoz JL, Dhatt G (1992) Modélisation des structures par Éléments Finis, Vol 3. Coques. Hermés, Paris
4. Bazeley GP, Cheung YK, Irons BM, Zienkiewicz OC (1965) Triangular elements in bending-conforming and non-conforming solutions. In: Conference of matrix methods in structural mechanics, Air Force Inst. Tech., Wright-Patterson AF base
5. Belytschko T, Bachrach WE (1986) Efficient implementation of quadrilaterals with high coarse-mesh accuracy. Comput Meth Appl Mech Eng 54:279
6. Belytschko T, Lin JI, Tsay CS (1984) Explicit algorithms for the nonlinear dynamics of shells. Comput Meth Appl Mech Eng 42:225
7. Belytschko T, Leviathan I (1994) Physical stabilization of the 4-node shell element with one point quadrature. Comput Meth Appl Mech Eng 113:321-350
8. Belytschko T, Leviathan I (1994) Projection schemes for one-point quadrature shell elements. Comput Meth Appl Mech Eng 115:277
9. Cardoso RPR, Yoon JW, Grácio JJA, Barlat F, César de Sá JMA (2002) Development of a one point quadrature shell element for nonlinear applications with contact and anisotropy. Comput Meth Appl Mech Eng 191:5177
10. Cardoso RPR, Yoon JW, Valente RAF (2006) A new approach to reduce membrane and transverse shear locking for one point quadrature shell elements: linear formulation. Int J Numer Meth Eng 66:214-249
11. Chen XM, Cen S, Long YQ, Yao ZH (2004) Membrane elements insensitive to distortion using the quadrilateral area coordinate method. Comput Struct 82:35-54
12. Dvorkin E, Bathe KJ (1984) A continuum mechanics based four-node shell element for general nonlinear analysis. Eng Comput 1:77
13. Hughes TJR (1987) The finite element method: linear static and dynamic analysis. Prentice-Hall, Englewood Cliffs
14. Ibrahimbegović A, Taylor RL, Wilson EL (1990) A robust quadrilateral membrane finite element with drilling degrees of freedom. Int J Numer Meth Eng 30:445-457
15. Kasper EP, Taylor RL (2000) A mixed-enhanced strain method. Part I: Geometrically linear problems. Comput Struct 75:237-250
16. Kemp BL, Cho C, Lee SW (1998) A four-node solid shell element formulation with assumed strain. Int J Numer Meth Eng 43:909-924
17. Knight NF (1997) The Raasch challenge for shell elements. AIAA J 35:375-381
18. MacNeal RH, Harder RL (1985) A proposed standard set of problems to test finite element accuracy. Finite Elem Anal Des 1:1-20
19. MacNeal RH (1994) Finite elements: their design and performance. Marcel Dekker New York
20. Parisch H (1991) An investigation of a finite rotation four node assumed strain shell element. Int J Numer Meth Eng 31:127-150
21. Simo JC, Fox DD, Rifai MS (1989) On a stress resultant geometrically exact shell model. Part I: Formulation and optimal parametrization. Comput Meth Appl Mech Eng 72: 267-304
22. Simo JC, Fox DD, Rifai MS (1989) On a stress resultant geometrically exact shell model. Part II: The linear theory-computational aspects. Comput Meth Appl Mech Eng 73: 53-92
23. Simo JC, Rifai MS (1990) A class of mixed assumed strain methods and the method of incompatible modes. Int J Numer Meth Eng 29:1595-1638
24. Slavković R, Miroslav Z, Kojić M (1994) Enhanced 8-node three-dimensional solid and 4-node shell elements with incompatible generalized displacements. Commun Numer Meth Eng 10:699-709
25. Taylor RL, Beresford PJ, Wilson EL (1976) A non-conforming element for stress analysis. Int J Numer Meth Eng 10:1211-1219
26. Wilson EL, Taylor RL, Doherty WP, Ghabussi T (1973) Incompatible displacement models. In: Fenven ST et al (eds) Numerical and Computer Methods in Structural Mechanics Academic, New York, pp 43-57