Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-18T19:02:14.075Z Has data issue: false hasContentIssue false
  • English
  • Français

A Parametric Study for Four Node Bilinear EAS Shell Elements

Published online by Cambridge University Press:  28 September 2011

Cengiz Polat
Cengiz Polat*
Affiliation:
Firat University, Faculty of Engineering, Department of Civil Engineering, 23279, Elazig, Turkey
*
* Assistant Professor, corresponding author
Get access

Abstract

A locking free formulation of 4-node bilinear shell element and its application to shell structures is demonstrated. The Enhanced Assumed Strain (EAS) method based on three-field variational principle of Hu-Washizu is used in the formulation. Transverse shear locking and membrane locking are circumvented by means of enhancing the displacement-dependent strain field with extra assumed strain field. Several benchmark shell problems are analyzed.

Keywords

Shell finite elementEAS methodShear and membrane locking
Type
Research Article
Information
Journal of Mechanics , Volume 26 , Issue 4 , December 2010 , pp. 431 - 438
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1. Ahmad, S., Irons, B. M. and Zienkiewicz, O. C., “Analysis of Thick and Thin Shell Structures by Curved Finite Elements,” International Journal for Numerical Methods in Engineering, 2, pp. 419–451 (1970).CrossRefGoogle Scholar
2. Wagner, W. and Gruttmann, F., “A Robust Non-Linear Mixed Hybrid Quadrilateral Shell Element,” International Journal for Numerical Methods in Engineering, 64, pp. 635–666 (2005).CrossRefGoogle Scholar
3. Zienkiewicz, O. C., Taylor, R. L. and Too, J. M., “Reduced Integration Techniques in Finite Element Method,” International Journal for Numerical Methods in Engineering, 3, pp. 275–290 (1971).CrossRefGoogle Scholar
4. Hughes, T. J. R., Taylor, R. L. and Kanoknukulchai, W., “A Simple and Efficient Finite Element for Plate Bending,” International Journal for Numerical Methods in Engineering, 11, pp. 1529–1543 (1977).CrossRefGoogle Scholar
5. Hughes, T. J. R., Cohen, M. and Haroun, M., Reduced and Selective Integration Techniques in the Finite Element Analysis of Plates,” Nuclear Engineering and Design, 46, pp. 203–222 (1978).CrossRefGoogle Scholar
6. Zhong, Z. H., “A Bilinear Shell Element with the Cross-Reduced Integration Technique,” International Journal for Numerical Methods in Engineering, 36, pp. 611–625 (1993).CrossRefGoogle Scholar
7. Hughes, T. R. J. and Tezduyar, T. E., “Finite Elements Based Upon Mindlin Plate Theory with Particular Reference to the Four Node Isoparametric Element,” Journal of Applied Mechanics, 58, pp. 587–596 (1981).CrossRefGoogle Scholar
8. MacNeal, R. H., “Derivation of Element Stiffness Matrices by Assumed Strain Distributions,” Nuclear Engineering and Design, 33, pp. 1049–1058 (1982).Google Scholar
9. Dvorkin, E. N. and Bathe, K. J., “A Continuum Mechanics Based Four-Node Shell Element for General Nonlinear Analysis,” Engineering Computations, 1, pp. 77–88 (1984).CrossRefGoogle Scholar
10. Bathe, K. J. and Dvorkin, E. N., “A Formulation of General Shell Elements- The Use of Mixed Interpolation of Tensorial Components,” International Journal for Numerical Methods in Engineering, 22, pp. 697–722 (1986).CrossRefGoogle Scholar
11. Bucalem, M. L. and Bathe, K. J., “Higher-Order MITC General Shell Elements,” International Journal for Numerical Methods in Engineering, 36, pp. 3729–3754 (1993).CrossRefGoogle Scholar
12. Lee, S. J. and Kanok-Nukulchai, W., “A Nine-Node Assumed Strain Finite Element for Large-Deformation Analysis of Laminated Shells,” International Journal for Numerical Methods in Engineering, 42, pp. 777–798 (1998).3.0.CO;2-P>CrossRefGoogle Scholar
13. Bischoff, M. and Ramm, E., “Shear Deformable Shell Elements for Large Strains and Rotations,” International Journal for Numerical Methods in Engineering, 40, pp. 4427–4449 (1997).3.0.CO;2-9>CrossRefGoogle Scholar
14. Kemp, B. I., Cho, C. and Lee, S. W., “A Four-Node Solid Shell Element Formulation with Assumed Strain,” International Journal for Numerical Methods in Engineering, 43, pp. 909–924 (1998).3.0.CO;2-X>CrossRefGoogle Scholar
15. Sze, K. Y. and Zhu, D., “A quadratic assumed natural strain curved triangular shell element,” Computer Methods in Applied Mechanics and Engineering, 174, pp. 57–71 (1999).CrossRefGoogle Scholar
16. Sze, K. Y. and Yao, L. Q., “A Hybrid Stress ANS Solid-Shell Element and its Generalization for Smart Structure Modelling. Part I: Solid-Shell Element Formulation,” International Journal for Numerical Methods in Engineering, 48, pp. 545–564 (2000).3.0.CO;2-6>CrossRefGoogle Scholar
17. Sze, K. Y., Yao, L. Q. and Yi, S., “A Hybrid Stress ANS Solid-Shell Element and its Generalization for Smart Structure Modelling. Part II: Smart Structure Modeling,” International Journal of Numerical Methods in Engineering, 48, pp. 565–582 (2000).3.0.CO;2-U>CrossRefGoogle Scholar
18. Chapelle, D., Oliveira, D. L. and Bucalem, M. L., “MITC Elements for a Classical Shell Model,” Computers and Structures, 81, pp. 523–533 (2003).CrossRefGoogle Scholar
19. Kim, K. D., Lomboy, G. R. and Han, S. C., “A Co Rotational 8-Node Assumed Strain Shell Element for Post-Buckling,” Computational Mechanics, 30, pp. 330–342 (2003).CrossRefGoogle Scholar
20. Tan, X. G. and Vu-Quoc, L., “Efficient and Accurate Multilayer Solid-Shell Element: Non-Linear Materials at Finite Strain,” International Journal of Numerical Methods in Engineering, 63, pp. 2124–2170 (2005).CrossRefGoogle Scholar
21. Kim, K. D., Lee, C. S. and Han, S. C., “A 4-Node Co-Rotational ANS Shell Element for Laminated Composite Structures,” Composite Structures, 80, pp. 234–252 (2007).CrossRefGoogle Scholar
22. Simo, J. C. and Rifai, M. S., “A Class of Mixed Assumed Strain Methods and the Method of Incompatible Modes,” International Journal for Numerical Methods in Engineering, 29, pp. 1595–1638 (1990)CrossRefGoogle Scholar
23. Andelfinger, U. and 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, 36, pp. 1311–1337 (1993).CrossRefGoogle Scholar
24. Sa, J. M. A. C., Jorge, R. M. N. and Valente, R. A. F. and Areias, P. M. A., “Development of Shear Locking-Free Shell Elements Using an Enhanced Assumed Strain Formulation,” International Journal for Numerical Methods in Engineering, 53, pp. 1721–1750 (2002).Google Scholar
25. Valente, R. A. F., Developments on Shell and Solid-Shell Finite Elements Technology in Nonlinear Continuum Mechanics,” Ph.D. Thesis, University of Porto, Portugal (2004).Google Scholar
26. Betsch, P., Gruttmann, F. and Stein, E., “A 4-Node Finite Shell Element for the Implementation of General Hyperelastic 3D-Elasticity at Finite Strains,” Computer Methods in Applied Mechanics and Engineering, 130, pp. 57–79 (1996).CrossRefGoogle Scholar
27. Sousa, R. J. A., Cardoso, R. P. R., Valente, R. A. F., Yoon, J. W., Gracio, J. J. and Jorge, R. M. N., “A New One-Point Quadrature Enhanced Assumed Strain (EAS) Solid-Shell Element with Multiple Integration Points Along Thickness: Part I-Geometrically Linear Applications,” International Journal of Numerical Methods in Engineering, 62, pp. 952–977 (2005).CrossRefGoogle Scholar
28. Sousa, R. J. A., Cardoso, R. P. R., Valente, R. A. F., Yoon, J. W., Gracio, J. J. and Jorge, R. M. N., “A New One-Point Quadrature Enhanced Assumed Strain Solid-Shell Element with Multiple Integration Points Along Thickness Part II – Nonlinear Applications,” International Journal of Numerical Methods in Engineering, 67, pp. 160–188 (2006).CrossRefGoogle Scholar
29. Bischoff, M. and Ramm, E., “Shear Deformable Shell Elements for Large Strains and Rotations,” International Journal of Numerical Methods in Engineering, 40, pp. 4427–4449 (1997).3.0.CO;2-9>CrossRefGoogle Scholar
30. Kim, K. D., Lomboy, G. R. and Voyiadjis, G. Z., “A 4-Node Assumed Strain Quasi-Conforming Shell Element with 6 Degrees of Freedom,” International Journal of Numerical Methods in Engineering, 58, pp. 2177–2200 (2003).CrossRefGoogle Scholar
31. MacNeal, R. H. and Harder, R. L., “A Proposed Standard Set of Problems to Test Finite Element Accuracy,” Finite Elements in Analysis and Design, 1, pp. 3–20 (1985).CrossRefGoogle Scholar
32. Hossain, S. J., Sinha, P. K. and Sheikh, A. H., “A Finite Element Formulation for the Analysis of Laminated Composite Shells,” Computers and Structures, 82, pp. 1623–1638 (2004).CrossRefGoogle Scholar
33. Liu, J., Riggs, H. R. and Tessler, A., “A Four-Node, Shear-Deformable Shell Element Developed Via Explicit Kirchhoff Constraints,” International Journal of Numerical Methods in Engineering, 49, pp. 1065–1086 (2000).3.0.CO;2-5>CrossRefGoogle Scholar
34. Simo, J. C., Fox, D. D. and Rifai, M. S., “On a Stress Resultant Geometrically Exact Shell Model. Part-II: The Linear Theory; Computational Aspects,” Computer Methods in Applied Mechanics and Engineering, 73, pp. 53–92 (1989).CrossRefGoogle Scholar