Refined Non-Conforming Five-Node Thin Flat Shell Element

Abstract

In this study, a new 5-node discrete Kirchhoff flat shell element with 30 degrees of freedom (dof), called DKP30, was proposed. This element was developed by superposing the15-dof membrane element and the 15-dof plate bending element at the element level. In developing procedure Allmansi interpolation function was utilized for drilling dof of the membrane element while the plate bending element was derived via discrete Kirchhoff plate formulation. In order to test its performance the patch test was first applied to the DKP30 element and it was then subjected to the standard test problems and compared with the shell elements available in the literature. The numerical results showed that the proposed 5-node thin flat shell element, DKP30, passed the patch test and presented moderate accuracy and high performance while its usage as a transition element with a 4-node DKQ24 thin flat shell element was also found to be possible

Keywords

• 5-node Membrane Element, 5-node Plate Bending Element, 5-node Flat Shell Element, Discrete Kirchhoff Formulation.

References

1. Gedikli, H. The Investigation of Flat Shell Elements by Using The Refined Finite Element Method, Ph.D. Thesis, Karadeniz Technical University, Turkey, 2005 (in Turkish).
2. Zhang, X.Y, Cheung Y.K., Chen, W.J. Two refined non-conforming quadrilateral flat shell elements, Int J Num Meth Engng, 49, 355-382, 2000.
3. Batoz, J.L., Hammadi, Zheng, F., Zhong, C. On the linear analysis of plates and shells using a new-16 degrees of fredom flat shell element, Computers and Structures, 78, 1120, 2000.
4. Dawe, D.J. Shell analysis using a simple facet element, J Strain Analysis, 7, 266-270, 1972.
5. Morley, L.S.D. The constant moment plate bending element, J Strain Analysis, 6, 2024, 1971.
6. Batoz, J.L, Zheng, C.L, Hammadi, F. Formulation and evaluation of new triangular, quadrilateral, pentagonal and hexagonal discrete Kirchhoff plate/shell elements, Int J Num Meth Engng, 52, 615-630, 2000.
7. Batoz, J,L, Dhatt, G., Development of two simple shell elements. American Institute of Aeronautics and Astronautics, 10, 237-238, 1972.
8. Bathe, K,J, Ho, L.W. A simple and effective element for the analysis of general shell structures”, Computers and Structures, 13, 673-681, 1981.

9. Carpenter, N., Stolarski, H., Belytschko, T. A flat triagular shell element with improved membrane interpolation”, Computer Methods in Applied Mechanics and Engineering, 1, 161-168, 1985.
10. 0] Dhatt, G., Marcotte, L., Matte, Y., Talbot M. Two new discrete Kirchhoff plate shell elements, 4th Symposium on Numerical Methods in Engineering, Atlanta, Georgia, 599604, 1986.
11. 1] Fafard, M., Dhatt, G., Batoz, J.L. A new discrete Kirchhoff plate/shell element with updated procedures, Computers and Structures, 31, 591-606, 1989.
12. 2] Talbot, M., Dhatt, G. Three discrete Kirchhoff elements for shell analysis, with large geometrical non linearities and bifurcations, Engineering Computations, 4,415-22, 1987.
13. 3] Poulsen, P.N, Damkilde, L. A flat triangular shell element with loof modes, Int J Num Meth Engng, 39, 3867-3887, 1996.
14. 4] Samuelson, A. The global constant strain condition and the patch test, Energy Methods in Finite Element Analysis, Wiley: New York, 47-52, 1979.
15. 5] Felippa, C.A, Haugen, B. Militello, C. From the individual element test to finite element templates: evolution of patch test, Int J Num Meth Engng, 38, 199-229, 1995.
16. 6] Noor, A.K. Bibliography of monographs and surveys on shells, Applied Mechanics Review, 43, 223-224, 1990.
17. 7] Argyris, J.H, Papadrakkakis, M, Apostolopoulou, C., Koutsourelakis, S. The TRIC shell element: theoretical and numerical investication”, Computer Methods in Applied Mechanics and Engineering, 182, 217-245, 2000.
18. 8] Zhong, W.X., Zeng, J. Rotational finite elements, J Comp Struct Mech Appl, 13, 1-8, 1996.
19. 9] Zienkiewicz, O.C, Taylor, R.L. The Finite Element Method, Vol.1-3, 5.ed. ButterworthHeinemann, Oxford, 2000.
20. 0] MacNeal, R.H., Harder, R.L. A proposed standard set of problems to test finite element accuracy, Finite Element Analysis and Design, 1, 3-20, 1985.
21. 1] Green, S, Turkiyyah, G. Second Order Accurate Constraint Formulation for Subdivision Finite Element Simulation of Thin Shells, Int J Num Meth Engng, 61(3), 380-405, 2004.
22. 2] Huges, T.J.R., Liu, W.K. Nonlinear finite element analysis of shells, part II: twodimensional shells, Comp Meth Appl Mech Eng, 27, 167-182, 1981.
23. 3] Bathe, K.J., Dvorkin, E.N. A formulation of general shell elements-the use of mixed interpolation of tensorial components, Num Meth Eng, 22, 697-722, 1986.
24. 4] Simo, J.C, Fox D.D. On a Stress Resultant Geometrically Exact Shell Model. Part II, The linear theory; computational aspects, Comp Meth Appl Mech Eng, 73, 53-92, 1989.
25. 5] Belytschko, T., Leviathan, I. Physical stabilization of the 4-node shell element with one point quadrature, Comp Meth Appl Mech Eng, 113, 321-350, 1994.