Finite Element Modeling of Crushing Behaviour of Thin Tubes with ...

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12/19 Paper: ASAT-13-ST-34 Figure (16) shows that the results of the fold depth formula coincide with the numerical data. This relation is valid for the polygonal tubes with number of sides greater than or equal four sides. Conclusion The non-linear finite element model simulations provide much more detailed information than other approaches. These are especially efficient in local folding and internal contact of structural elements. In this paper, a study on the quasi-static crushing collapse of multi-sided and round tubes was performed using a non-linear finite element program ABAQUS/Explicit. Based on the numerical data, simple empirical formulas were developed to predict the absorbed energy and the fold depth as a function of the side breadth-to-thickness ratio of the tubes. From the present study, the following conclusion can be drawn: - All the tube models were crushed in symmetric concertina modes. - The greatest number of folds was observed fourteen in the circular cylinder and minimum with three folds in the triangular tube. - The folds of the cylindrical tube were compact with short depth while the triangular tube terminated folding without contact between folds. - The initial peak load increases with the increasing of the no. of sides of the tube and decreases with the increasing of the side breadth. - The greatest energy absorption capacity was obtained by the circular cylinder while the square tube absorbed minimum energy. - The mean crushing load recorded lowest value in case of the square tube however the highest magnitude was noticed in the triangular tube. References [1] J. K. Paik, J. Y. Chung, and M. S. Chun, “On quasi-static crushing of a stiffened square tube”, J. Ship Res., Vol. 40, No. 3, pp. 258–267, 1996. [2] A. Zhang, and K. Suzuki, “A study on the effect of stiffeners on quasi-static crushing of stiffened square tube with non-linear finite element method”, Int. J. of Imp. Eng., Vol. 34, pp. 544–555, 2007. [3] Gupta N. K., Sekhon G. S. and Gupta P. K., “A Study of Formation in Axi-symmetric Axial Collapse of Round Tubes”, Int. J. Impact. Eng., Vol. 27, pp. 87-117, 2002. [4] Gupta N. K. and Gupta S. K., “Effect of Annealing, Size and Cutouts on Axial Collapse Behaviour of Circular Tubes”, Int. J. of Mech. Sci., Vol. 35, pp. 519-613, 1993. [5] Wierzbicki T. and Abramowicz W., “On the Crushing Mechanics of Thin-Walled Structures”, J. Appl. Mech., Vol. 50, No. 4a, pp. 727–34, 1983. [6] Abramowicz W. and Jones N., “Dynamic Axial Crushing of Square Tubes”, Int. J. Impact Eng., Vol. 2, No. 2, pp. 179–208, 1984. [7] Abramowicz W. and Jones N., “Dynamic Progressive Buckling of Circular and Square Tubes”, Int. J. Impact Eng., Vol. 4, No. 4, pp. 243–70, 1986. [8] Grzebeita R. H., “An Alternate Method for Determining the Behaviour of Round Stocky Tubes Subjected to an Axial Crush Load”, Thin Wall Struct., Vol., 9, pp. 61-89, 1990. [9] Gupta N. K., Velmurugan R., “Consideration of Internal Folding and non Symmetric Fold Formation in Axi-symmetric Axial Collapse of Round Tubes”, Int. J. Solids Struct., Vol. 34, No. 20, pp. 2611-40, 1997.
13/19 Paper: ASAT-13-ST-34 [10] Wierzbicki T., Bhat S. U., Abramowicz W. and Brodikin D., “A Two Folding Elements Model of Progressive Crushing of Tubes”, Int. J. Solids Struct., Vol. 29, No. 24, pp. 3269-88, 1992. [11] Singace A. A. and EI-Sobky H., “Further Experimental Investigation on the Eccentricity Factor in the Progressive Crushing of Tubes”, Int. J. Solids Struct., Vol. 33, No. 24, pp. 3517-38, 1996. [12] Singace A. A, EI-Sobky H. and Reddy T. Y., “On the Eccentricity Factor in the Progressive Crushing of Tubes”, Int. J. Solids Struct., Vol. 32, No. 24, pp. 3589-602, 1995. [13] Singace A. A., “Axial Crushing Analysis of Tubes Deforming in the Multi-Lobe Mode”, Int. J. Mech. Sci., Vol. 41, pp. 865-90, 1999. [14] Hull D., “A Unified Approach to Progressive Crushing of Fiber-Reinforced Composite Tubes”, Comp. Sci. Technol., Vol. 40, pp. 377-421, 1991. [15] Farley G. L., “Effects of Specimen Geometry on the Energy Absorption Capability of Composite Materials”, J. Comp. Mater., Vol. 20, pp. 390-400, 1986. [16] Mamalis A. G., Manolakos D. E., Demosthenous G. A. and Ioannidis M. B., “The Deformation Mechanism of Thin-Walled Non-circular Composite Tubes Subjected to Bending”, Comp. Struct., Vol. 30, pp. 131-146, 1995. [17] Mamalis A. G., Manolakos D. E., Demosthenous G. A. and Ioannidis M. B., “Analysis of Failure Mechanisms Observed in Axial Collapse of Thin-Walled Circular Fiberglass Composite Tubes”, Thin-Walled Struct., Vol. 24, pp. 335-352, 1996. [18] Mamalis A. G., Manolakos D. E., Demosthenous G. A. and Ioannidis M. B., “Analytical Modeling of the Static and Dynamic Axial Collapse of Thin-Walled Fiberglass Composite Conical Shells”, Int. J. Impact Eng., Vol. 19, No. 5-6, pp. 477- 492, 1997. 75 mm 100 mm 95.49 mm 60 mm 50 100 mm Fig. (1) Different shapes of uniform cross-sections used in the F.E. analysis of a 300 mm perimeter tube. 50 mm
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