Theoretical Investigation of the Instantaneous Folding Force during the First Fold Creation in a Square Column
In this paper, a theoretical formula is presented to
predict the instantaneous folding force of the first fold creation in a
square column under axial loading. Calculations are based on analysis
of “Basic Folding Mechanism" introduced by Wierzbicki and
Abramowicz. For this purpose, the sum of dissipated energy rate under
bending around horizontal and inclined hinge lines and dissipated
energy rate under extensional deformations are equated to the work rate
of the external force on the structure. Final formula obtained in this
research, reasonably predicts the instantaneous folding force of the first
fold creation versus folding distance and folding angle and also predicts
the instantaneous folding force instead of the average value. Finally,
according to the calculated theoretical relation, instantaneous folding
force of the first fold creation in a square column was sketched
versus folding distance and was compared to the experimental results
which showed a good correlation.
[1] T. Wierzbicki, W. Abramowicz, "On the Crushing Mechanics of Thin-
Walled Structures", Journal of Applied Mechanics; Vol. 50, pp. 727-
734, 1983.
[2] R. J. Hayduk, and T. Wierzbicki, "Extensional Collapse Modes of
Structural Members", Computers and Structures, vol. 18, pp. 447-458,
1984.
[3] W. Abramowicz, "The Effective Crushing Distance in Axially
Compressed Thin-Walled Metal Columns", International Journal of
Impact Engineering, vol.1, No.3, pp. 309-317, 1983.
[4] W. Abramowicz, and N. Jones, "Dynamic Axial Crushing of Square
Tubes", International Journal of Impact Engineering, vol. 2, No. 2, pp.
179-208, 1984.
[5] W. Abramowicz, and T. Wierzbicki, "Axial Crushing of Foam-Filled
Columns", International Journal of Mechanical Sciences, vol. 30, No.
3/4, pp. 263-271, 1988.
[6] W. Abramowicz, and T. Wierzbicki, "Axial Crushing of Multi-corner
Sheet Metal Columns", Journal of Applied Mechanics, vol. 56, pp. 113-
120, 1989.
[7] G. H. Liaghat, and A. Alavinia, "A Comment on the Axial Crush of
Metallic Honeycombs by Wu and Jiang", International Journal of
Impact Engineering, vol. 28, pp. 1143-1146, 2003.
[8] G. H. Liaghat, H. R. Daghiani, M. Sedighi, and A. Alavinia, "Dynamic
Crushing of Honeycomb panel under Impact of Cylindrical Projectile
(Persian)", Amirkabir Journal, vol.53, pp. 68-79, 2002.
[9] G. H. Liaghat, M. Sedighi, H. R. Daghiani, and A. Alavinia, "Crushing
of Metal honeycomb structures under Quasi-static Loads (Persian)",
Tehran University Journal, vol. 37, No. 1, pp. 145-156, 2003.
[10] J. Zamani, M. Soleimani, A. Darvizeh, and G. H. Liaghat, "Numerical
Analysis of Full Folding of Thin-Walled Structures with Square Crosssection
by LS-DYNA", Fourteenth International Conference of
Mechanical Engineering, Iran, 2006.
[11] A. Alavinia, and G. H. Liaghat, "Investigation of Properties and Quasistatic
Analysis of Honeycombs", Twelfth International Conference of
Mechanical Engineering, Tehran, Iran, 2004.
[12] A. Alavinia, and G. H. Liaghat, "Dynamic Crushing of Thin-Walled
Columns under Impact of Projectile", Twelfth International Conference
of Mechanical Engineering, Tehran, Iran, 2004.
[13] J. Zamani, and G. H. Liaghat, "Effect of Honeycomb Main Properties
under Impact Loads", Tenth International Conference of Mechanical
Engineering, Iran, 2002, pp. 687-689.
[14] S. Santosa, and T. Wierzbicki, "Effect of Ultra light Metal Filler on the
Bending Collapse Behavior of Thin-Walled Prismatic Columns",
International Journal of Mechanical Sciences, vol. 41, pp. 995-1019,
1999.
[15] S. Santosa, T. Wierzbicki, A. G. Hanssen, and M. Langseth,
"Experimental and Numerical Studies of Foam-Filled Sections",
International Journal of Impact Engineering, vol. 24, pp. 509-534,
2000.
[16] W. Chen, and T. Wierzbicki, "Relative Merits of Single-Cell, Multi-Cell
and Foam-Filled Thin-Walled Structures in Energy Absorption", Thin-
Walled Structures, vol. 39, pp. 287-306, 2001.
[17] Xiong Zhang, G. Cheng, and Hui Zhang, "Theoretical Prediction and
Numerical Simulation of Multi-Cell Square Thin-Walled Structures",
Thin-Walled Structures, vol. 44, pp. 1185-1191, 2006.
[18] S. R. Reid, T. Y. Reddy, and M. D. Gray, "Static and Dynamic Axial
Crushing of Foam-Filled Sheet Metal Tubes", International Journal of
Mechanical Sciences, vol. 28, No.5, pp. 295-322, 1986.
[1] T. Wierzbicki, W. Abramowicz, "On the Crushing Mechanics of Thin-
Walled Structures", Journal of Applied Mechanics; Vol. 50, pp. 727-
734, 1983.
[2] R. J. Hayduk, and T. Wierzbicki, "Extensional Collapse Modes of
Structural Members", Computers and Structures, vol. 18, pp. 447-458,
1984.
[3] W. Abramowicz, "The Effective Crushing Distance in Axially
Compressed Thin-Walled Metal Columns", International Journal of
Impact Engineering, vol.1, No.3, pp. 309-317, 1983.
[4] W. Abramowicz, and N. Jones, "Dynamic Axial Crushing of Square
Tubes", International Journal of Impact Engineering, vol. 2, No. 2, pp.
179-208, 1984.
[5] W. Abramowicz, and T. Wierzbicki, "Axial Crushing of Foam-Filled
Columns", International Journal of Mechanical Sciences, vol. 30, No.
3/4, pp. 263-271, 1988.
[6] W. Abramowicz, and T. Wierzbicki, "Axial Crushing of Multi-corner
Sheet Metal Columns", Journal of Applied Mechanics, vol. 56, pp. 113-
120, 1989.
[7] G. H. Liaghat, and A. Alavinia, "A Comment on the Axial Crush of
Metallic Honeycombs by Wu and Jiang", International Journal of
Impact Engineering, vol. 28, pp. 1143-1146, 2003.
[8] G. H. Liaghat, H. R. Daghiani, M. Sedighi, and A. Alavinia, "Dynamic
Crushing of Honeycomb panel under Impact of Cylindrical Projectile
(Persian)", Amirkabir Journal, vol.53, pp. 68-79, 2002.
[9] G. H. Liaghat, M. Sedighi, H. R. Daghiani, and A. Alavinia, "Crushing
of Metal honeycomb structures under Quasi-static Loads (Persian)",
Tehran University Journal, vol. 37, No. 1, pp. 145-156, 2003.
[10] J. Zamani, M. Soleimani, A. Darvizeh, and G. H. Liaghat, "Numerical
Analysis of Full Folding of Thin-Walled Structures with Square Crosssection
by LS-DYNA", Fourteenth International Conference of
Mechanical Engineering, Iran, 2006.
[11] A. Alavinia, and G. H. Liaghat, "Investigation of Properties and Quasistatic
Analysis of Honeycombs", Twelfth International Conference of
Mechanical Engineering, Tehran, Iran, 2004.
[12] A. Alavinia, and G. H. Liaghat, "Dynamic Crushing of Thin-Walled
Columns under Impact of Projectile", Twelfth International Conference
of Mechanical Engineering, Tehran, Iran, 2004.
[13] J. Zamani, and G. H. Liaghat, "Effect of Honeycomb Main Properties
under Impact Loads", Tenth International Conference of Mechanical
Engineering, Iran, 2002, pp. 687-689.
[14] S. Santosa, and T. Wierzbicki, "Effect of Ultra light Metal Filler on the
Bending Collapse Behavior of Thin-Walled Prismatic Columns",
International Journal of Mechanical Sciences, vol. 41, pp. 995-1019,
1999.
[15] S. Santosa, T. Wierzbicki, A. G. Hanssen, and M. Langseth,
"Experimental and Numerical Studies of Foam-Filled Sections",
International Journal of Impact Engineering, vol. 24, pp. 509-534,
2000.
[16] W. Chen, and T. Wierzbicki, "Relative Merits of Single-Cell, Multi-Cell
and Foam-Filled Thin-Walled Structures in Energy Absorption", Thin-
Walled Structures, vol. 39, pp. 287-306, 2001.
[17] Xiong Zhang, G. Cheng, and Hui Zhang, "Theoretical Prediction and
Numerical Simulation of Multi-Cell Square Thin-Walled Structures",
Thin-Walled Structures, vol. 44, pp. 1185-1191, 2006.
[18] S. R. Reid, T. Y. Reddy, and M. D. Gray, "Static and Dynamic Axial
Crushing of Foam-Filled Sheet Metal Tubes", International Journal of
Mechanical Sciences, vol. 28, No.5, pp. 295-322, 1986.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:55438", author = "A. Niknejad and G. H. Liaghat and A. H. Behravesh and H. Moslemi Naeini", title = "Theoretical Investigation of the Instantaneous Folding Force during the First Fold Creation in a Square Column", abstract = "In this paper, a theoretical formula is presented to
predict the instantaneous folding force of the first fold creation in a
square column under axial loading. Calculations are based on analysis
of “Basic Folding Mechanism" introduced by Wierzbicki and
Abramowicz. For this purpose, the sum of dissipated energy rate under
bending around horizontal and inclined hinge lines and dissipated
energy rate under extensional deformations are equated to the work rate
of the external force on the structure. Final formula obtained in this
research, reasonably predicts the instantaneous folding force of the first
fold creation versus folding distance and folding angle and also predicts
the instantaneous folding force instead of the average value. Finally,
according to the calculated theoretical relation, instantaneous folding
force of the first fold creation in a square column was sketched
versus folding distance and was compared to the experimental results
which showed a good correlation.", keywords = "Instantaneous force, Folding force, Honeycomb,Square column.", volume = "2", number = "10", pages = "1128-6", }
