Multi-criteria Optimization of Square Beam using Linear Weighted Average Model
Increasing energy absorption is a significant parameter
in vehicle design. Absorbing more energy results in decreasing
occupant damage. Limitation of the deflection in a side impact results
in decreased energy absorption (SEA) and increased peak load (PL).
Hence a high crash force jeopardizes passenger safety and vehicle
integrity. The aims of this paper are to determine suitable dimensions
and material of a square beam subjected to side impact, in order to
maximize SEA and minimize PL. To achieve this novel goal, the
geometric parameters of a square beam are optimized using the
response surface method (RSM).multi-objective optimization is
performed, and the optimum design for different response features is
obtained.
[1] Dong G, Wang D, Zhang J, Huang S. Side structure sensitivity to
passenger car crashworthiness during pole side impact. Tsinghua
Science & Technology. 2007;12:290-5.
[2] Fildes B, Bostrom O, Haland Y, Sparke L. COUNTERMEASURES TO
ADDRESS FARSIDE CRASHES: FIRST RESULTS. 2003.
[3] Abramowicz W, Wierzbicki T. Axial crushing of foam-filled columns.
International Journal of Mechanical Sciences. 1988;30:263-71.
[4] Kecman D. Bending collapse of rectangular and square section tubes.
International Journal of Mechanical Sciences. 1983;25:623-36.
[5] Kim T, Reid S. Bending collapse of thin-walled rectangular section
columns. Computers & Structures. 2001;79:1897-911.
[6] Mamalis A, Manolakos D, Ioannidis M, Kostazos P. Bending of
cylindrical steel tubes: numerical modelling. International Journal of
Crashworthiness. 2006;11:37-47.
[7] Zhang Z, Liu S, Tang Z. Design optimization of cross-sectional
configuration of rib-reinforced thin-walled beam. Thin-Walled
Structures. 2009;47:868-78.
[8] Wierzbicki T, Abramowicz W. On the crushing mechanics of thinwalled
structures. Journal of Applied mechanics. 1983;50:727.
[9] Langseth M, Hopperstad O. Static and dynamic axial crushing of square
thin-walled aluminium extrusions. International Journal of Impact
Engineering. 1996;18:949-68.
[10] Wierzbicki T, Recke L, Abramowicz W, Gholami T, Huang J. Stress
profiles in thin-walled prismatic columns subjected to crush loading-II.
Bending. Computers & Structures. 1994;51:625-41.
[11] Niknejad A, Liaghat G, Naeini HM, Behravesh A. Experimental and
theoretical investigation of the first fold creation in thin walled columns.
Acta Mechanica Solida Sinica. 2010;23:353-60.
[12] Chan C, Khalid Y, Sahari B, Hamouda A. Finite element analysis of
corrugated web beams under bending. Journal of Constructional Steel
Research. 2002;58:1391-406.
[13] Langseth M, Hopperstad O, Hanssen A. Crash behaviour of thin-walled
aluminium members. Thin-Walled Structures. 1998;32:127-50.
[14] Langseth M, Hopperstad O. Local buckling of square thin-walled
aluminium extrusions. Thin-Walled Structures. 1997;27:117-26.
[15] Halquist J. LS-DYNA keyword user-s manual version 971. Livermore
Software Technology Corporation, Livermore, CA. 2007.
[16] Salehghaffari S, Rais-Rohani M, Najafi A. Analysis and optimization of
externally stiffened crush tubes. Thin-Walled Structures. 2011.
[17] Hou S, Li Q, Long S, Yang X, Li W. Design optimization of regular
hexagonal thin-walled columns with crashworthiness criteria. Finite
elements in analysis and design. 2007;43:555-65.
[18] Acar E, Rais-Rohani M. Ensemble of metamodels with optimized
weight factors. Structural and Multidisciplinary Optimization.
2009;37:279-94.
[19] Xiang Y, Wang Q, Fan Z, Fang H. Optimal crashworthiness design of a
spot-welded thin-walled hat section. Finite elements in analysis and
design. 2006;42:846-55.
[20] Yamazaki K, Han J. Maximization of the crushing energy absorption of
cylindrical shells. Advances in Engineering Software. 2000;31:425-34.
[21] Lee TH, Lee K. Multi-criteria shape optimization of a funnel in cathode
ray tubes using a response surface model. Structural and
Multidisciplinary Optimization. 2005;29:374-81.
[22] Allahbakhsh H, Saemi J. Design optimization of square and circular
aluminium extrusion damage columns with crashworthiness criteria.
Indian Journal of Engineering & Materials Sciences. 2011;18:341-50.
[23] Montgomery DC. Design and analysis of experiments: John Wiley &
Sons Inc; 2008.
[24] Fang H, Rais-Rohani M, Liu Z, Horstemeyer M. A comparative study of
metamodeling methods for multiobjective crashworthiness optimization.
Computers & Structures. 2005;83:2121-36.
[25] Zarei H, Kröger M. Multiobjective crashworthiness optimization of
circular aluminum tubes. Thin-Walled Structures. 2006;44:301-8.
[26] Hou S, Li Q, Long S, Yang X, Li W. Multiobjective optimization of
multi-cell sections for the crashworthiness design. International Journal
of Impact Engineering. 2008;35:1355-67.
[1] Dong G, Wang D, Zhang J, Huang S. Side structure sensitivity to
passenger car crashworthiness during pole side impact. Tsinghua
Science & Technology. 2007;12:290-5.
[2] Fildes B, Bostrom O, Haland Y, Sparke L. COUNTERMEASURES TO
ADDRESS FARSIDE CRASHES: FIRST RESULTS. 2003.
[3] Abramowicz W, Wierzbicki T. Axial crushing of foam-filled columns.
International Journal of Mechanical Sciences. 1988;30:263-71.
[4] Kecman D. Bending collapse of rectangular and square section tubes.
International Journal of Mechanical Sciences. 1983;25:623-36.
[5] Kim T, Reid S. Bending collapse of thin-walled rectangular section
columns. Computers & Structures. 2001;79:1897-911.
[6] Mamalis A, Manolakos D, Ioannidis M, Kostazos P. Bending of
cylindrical steel tubes: numerical modelling. International Journal of
Crashworthiness. 2006;11:37-47.
[7] Zhang Z, Liu S, Tang Z. Design optimization of cross-sectional
configuration of rib-reinforced thin-walled beam. Thin-Walled
Structures. 2009;47:868-78.
[8] Wierzbicki T, Abramowicz W. On the crushing mechanics of thinwalled
structures. Journal of Applied mechanics. 1983;50:727.
[9] Langseth M, Hopperstad O. Static and dynamic axial crushing of square
thin-walled aluminium extrusions. International Journal of Impact
Engineering. 1996;18:949-68.
[10] Wierzbicki T, Recke L, Abramowicz W, Gholami T, Huang J. Stress
profiles in thin-walled prismatic columns subjected to crush loading-II.
Bending. Computers & Structures. 1994;51:625-41.
[11] Niknejad A, Liaghat G, Naeini HM, Behravesh A. Experimental and
theoretical investigation of the first fold creation in thin walled columns.
Acta Mechanica Solida Sinica. 2010;23:353-60.
[12] Chan C, Khalid Y, Sahari B, Hamouda A. Finite element analysis of
corrugated web beams under bending. Journal of Constructional Steel
Research. 2002;58:1391-406.
[13] Langseth M, Hopperstad O, Hanssen A. Crash behaviour of thin-walled
aluminium members. Thin-Walled Structures. 1998;32:127-50.
[14] Langseth M, Hopperstad O. Local buckling of square thin-walled
aluminium extrusions. Thin-Walled Structures. 1997;27:117-26.
[15] Halquist J. LS-DYNA keyword user-s manual version 971. Livermore
Software Technology Corporation, Livermore, CA. 2007.
[16] Salehghaffari S, Rais-Rohani M, Najafi A. Analysis and optimization of
externally stiffened crush tubes. Thin-Walled Structures. 2011.
[17] Hou S, Li Q, Long S, Yang X, Li W. Design optimization of regular
hexagonal thin-walled columns with crashworthiness criteria. Finite
elements in analysis and design. 2007;43:555-65.
[18] Acar E, Rais-Rohani M. Ensemble of metamodels with optimized
weight factors. Structural and Multidisciplinary Optimization.
2009;37:279-94.
[19] Xiang Y, Wang Q, Fan Z, Fang H. Optimal crashworthiness design of a
spot-welded thin-walled hat section. Finite elements in analysis and
design. 2006;42:846-55.
[20] Yamazaki K, Han J. Maximization of the crushing energy absorption of
cylindrical shells. Advances in Engineering Software. 2000;31:425-34.
[21] Lee TH, Lee K. Multi-criteria shape optimization of a funnel in cathode
ray tubes using a response surface model. Structural and
Multidisciplinary Optimization. 2005;29:374-81.
[22] Allahbakhsh H, Saemi J. Design optimization of square and circular
aluminium extrusion damage columns with crashworthiness criteria.
Indian Journal of Engineering & Materials Sciences. 2011;18:341-50.
[23] Montgomery DC. Design and analysis of experiments: John Wiley &
Sons Inc; 2008.
[24] Fang H, Rais-Rohani M, Liu Z, Horstemeyer M. A comparative study of
metamodeling methods for multiobjective crashworthiness optimization.
Computers & Structures. 2005;83:2121-36.
[25] Zarei H, Kröger M. Multiobjective crashworthiness optimization of
circular aluminum tubes. Thin-Walled Structures. 2006;44:301-8.
[26] Hou S, Li Q, Long S, Yang X, Li W. Multiobjective optimization of
multi-cell sections for the crashworthiness design. International Journal
of Impact Engineering. 2008;35:1355-67.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:57560", author = "Ali Farhaninejad and Rizal Zahari and Ehsan Rasooliyazdi", title = "Multi-criteria Optimization of Square Beam using Linear Weighted Average Model", abstract = "Increasing energy absorption is a significant parameter
in vehicle design. Absorbing more energy results in decreasing
occupant damage. Limitation of the deflection in a side impact results
in decreased energy absorption (SEA) and increased peak load (PL).
Hence a high crash force jeopardizes passenger safety and vehicle
integrity. The aims of this paper are to determine suitable dimensions
and material of a square beam subjected to side impact, in order to
maximize SEA and minimize PL. To achieve this novel goal, the
geometric parameters of a square beam are optimized using the
response surface method (RSM).multi-objective optimization is
performed, and the optimum design for different response features is
obtained.", keywords = "Crashworthiness, side impact, energy absorption,
multi-objective optimization, Square beam, SEA", volume = "6", number = "8", pages = "1622-4", }
