Discrete variable optimization of structures subjected to dynamic loads using equivalent static loads and metaheuristic algorithms
This paper presents a new computational procedure for optimization of structures subjected to dynamic loads. The optimization problem is formulated with discrete design variables that represent the members from a table of commercially available members. Also, the requirements in the American Institu...
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| Published in | Optimization and engineering Vol. 23; no. 2; pp. 643 - 687 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.06.2022
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1389-4420 1573-2924 1573-2924 |
| DOI | 10.1007/s11081-021-09599-y |
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| Abstract | This paper presents a new computational procedure for optimization of structures subjected to dynamic loads. The optimization problem is formulated with discrete design variables that represent the members from a table of commercially available members. Also, the requirements in the American Institute of Steel Construction (AISC) manual are formulated as constraints. This results in a nondifferentiable optimization problem. In the new procedure, the dynamic load is transformed into equivalent static loads (ESLs). Then the static response optimization problem having discrete design variables is solved using a metaheuristic optimization algorithm. Three methods to calculate the ESLs are investigated. It is found that the ESL cycles cannot converge to the final design. Therefore after a few ESL cycles, the original dynamic loads need to be used in the optimization process. Four example problems are solved to analyze the procedure. Based on this analysis, it is concluded that the new procedure is more efficient compared to a procedure that does not use the ESL cycles because it reduces the total CPU effort to obtain the final design. Also, better final designs are found. The reason is that many more designs are analyzed very efficiently with the ESL procedure. |
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| AbstractList | This paper presents a new computational procedure for optimization of structures subjected to dynamic loads. The optimization problem is formulated with discrete design variables that represent the members from a table of commercially available members. Also, the requirements in the American Institute of Steel Construction (AISC) manual are formulated as constraints. This results in a nondifferentiable optimization problem. In the new procedure, the dynamic load is transformed into equivalent static loads (ESLs). Then the static response optimization problem having discrete design variables is solved using a metaheuristic optimization algorithm. Three methods to calculate the ESLs are investigated. It is found that the ESL cycles cannot converge to the final design. Therefore after a few ESL cycles, the original dynamic loads need to be used in the optimization process. Four example problems are solved to analyze the procedure. Based on this analysis, it is concluded that the new procedure is more efficient compared to a procedure that does not use the ESL cycles because it reduces the total CPU effort to obtain the final design. Also, better final designs are found. The reason is that many more designs are analyzed very efficiently with the ESL procedure. |
| Author | Al-Bazoon, Mustafa Arora, Jasbir S. |
| Author_xml | – sequence: 1 givenname: Mustafa surname: Al-Bazoon fullname: Al-Bazoon, Mustafa email: mustafa-jasim@uomisan.edu.iq organization: The Department of Civil Engineering, College of Engineering, The University of Misan – sequence: 2 givenname: Jasbir S. surname: Arora fullname: Arora, Jasbir S. organization: Iowa Technology Institute, The University of Iowa |
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| Cites_doi | 10.1016/j.compstruc.2014.04.006 10.1016/j.cma.2009.10.014 10.1007/s00158-014-1101-3 10.1016/S0045-7949(00)00127-9 10.1023/A:1024799727258 10.1007/s00158-010-0530-x 10.1007/s00158-005-0575-4 10.1016/j.compstruc.2014.04.005 10.1007/978-3-319-94743-3 10.1016/S0045-7825(01)00373-5 10.1007/s00158-018-2059-3 10.1007/978-3-319-19659-6 10.1007/s00158-017-1884-0 10.1002/9780470549070 10.1007/978-3-319-05549-7 10.1016/j.advengsoft.2014.01.002 10.1177/003754970107600201 |
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| Keywords | Dynamic loads Structural optimization Equivalent static loads method Metaheuristic algorithms Discrete variables |
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| References | Goldberg DE, Holland JH (1988) Genetic algorithms and machine learning KavehAGhazaanMComputer codes for colliding bodies optimization and its enhanced versionInt J Optim Civil Eng201443321332 BhattiMAAdvanced topics in finite element analysis of structures: with mathematica and matlab computations2006New YorkWiley1111.74001 Gilsanz R, Hamburger R, Barker J, Smith D, Rahimian A (2013) Design of blast resistant structures. steel design guide no. 26l. American Institute of Steel Construction ParkGLeeYDiscussion on the optimality condition of the equivalent static loads method for linear dynamic response structural optimizationStruct Multidiscip Optim2019591311316389538310.1007/s00158-018-2059-3 KangBParkG-JAroraJSA review of optimization of structures subjected to transient loadsStruct Multidiscip Optim20063128195219954410.1007/s00158-005-0575-4 KavehAMahdaviVColliding bodies optimization: a novel meta-heuristic methodComput Struct2014139182710.1016/j.compstruc.2014.04.005 AroraJOptimization of structures subjected to dynamic loadsStructural dynamic systems computational techniques and optimization199971731754754 KavehAAdvances in metaheuristic algorithms for optimal design of structures2014BerlinSpringer10.1007/978-3-319-05549-7 StolpeMVerbartARojas-LabandaSThe equivalent static loads method for structural optimization does not in general generate optimal designsStruct Multidiscip Optim2018581139154381699510.1007/s00158-017-1884-0 ParkGTechnical overview of the equivalent static loads method for non-linear static response structural optimizationStruct Multidiscip Optim201143331933710.1007/s00158-010-0530-x PazMKimYHStructural dynamics2019BerlinSpringer10.1007/978-3-319-94743-3 AroraJIntroduction to optimum design Introduction to optimum design20174AmsterdamElsevier Inc KangBChoiWParkG-JStructural optimization under equivalent static loads transformed from dynamic loads based on displacementComput Struct200179214515410.1016/S0045-7949(00)00127-9 ParkGKangBValidation of a structural optimization algorithm transforming dynamic loads into equivalent static loadsJ Optim Theory Appl20031181191200199570210.1023/A:1024799727258 EberhartRCShiYKennedyJSwarm intelligence2001AmsterdamElsevier StolpeMOn the equivalent static loads approach for dynamic response structural optimizationStruct Multidiscip Optim2014506921926331241010.1007/s00158-014-1101-3 GeemZWKimJ. HLoganathanG. VA new heuristic optimization algorithm: harmony searchSimulation2001762606810.1177/003754970107600201 ChoiW-SParkG-JStructural optimization using equivalent static loads at all time intervalsComput Methods Appl Mech Eng200219119–202105212210.1016/S0045-7825(01)00373-5 Dorigo M (1992) Optimization, learning and natural algorithms. PhD Thesis, Politecnico di Milano KimY-IParkG-JNonlinear dynamic response structural optimization using equivalent static loadsComput Methods Appl Mech Eng20101999–1266067610.1016/j.cma.2009.10.014 ASCE (2011) Blast protection of buildings Blast protection of buildings. ASCE/Structural Engineering Institute KavehAMahdaviVColliding bodies optimization: extensions and applications2015BerlinSpringer10.1007/978-3-319-19659-6 KavehAMahdaviVColliding bodies optimization method for optimum design of truss structures with continuous variablesAdv Eng Softw20147011210.1016/j.advengsoft.2014.01.002 ASCE (2010) Design of blast-resistant buildings in petrochemical facilities. American Society of Civil Engineers DoD (2008) Structures to resist the effects of accidental explosions. UFC 3-340-02 DusenberryDOHandbook for blast resistant design of buildings2010HobokenWiley10.1002/9780470549070 KavehAMahdaviVColliding bodies optimization method for optimum discrete design of truss structuresComput Struct2014139435310.1016/j.compstruc.2014.04.006 AISC (2017) Steel construction manual. American Institute of Steel Construction, Chicago Y-I Kim (9599_CR23) 2010; 199 G Park (9599_CR24) 2011; 43 9599_CR4 B Kang (9599_CR15) 2001; 79 9599_CR5 W-S Choi (9599_CR7) 2002; 191 9599_CR8 ZW Geem (9599_CR12) 2001; 76 9599_CR9 9599_CR13 9599_CR14 RC Eberhart (9599_CR11) 2001 M Stolpe (9599_CR29) 2018; 58 G Park (9599_CR26) 2019; 59 DO Dusenberry (9599_CR10) 2010 MA Bhatti (9599_CR6) 2006 J Arora (9599_CR3) 2017 M Paz (9599_CR27) 2019 A Kaveh (9599_CR17) 2014 A Kaveh (9599_CR21) 2014; 139 A Kaveh (9599_CR22) 2015 B Kang (9599_CR16) 2006; 31 G Park (9599_CR25) 2003; 118 A Kaveh (9599_CR20) 2014; 70 M Stolpe (9599_CR28) 2014; 50 A Kaveh (9599_CR19) 2014; 139 J Arora (9599_CR2) 1999; 7 A Kaveh (9599_CR18) 2014; 4 9599_CR1 |
| References_xml | – reference: AroraJIntroduction to optimum design Introduction to optimum design20174AmsterdamElsevier Inc – reference: ParkGKangBValidation of a structural optimization algorithm transforming dynamic loads into equivalent static loadsJ Optim Theory Appl20031181191200199570210.1023/A:1024799727258 – reference: StolpeMVerbartARojas-LabandaSThe equivalent static loads method for structural optimization does not in general generate optimal designsStruct Multidiscip Optim2018581139154381699510.1007/s00158-017-1884-0 – reference: GeemZWKimJ. HLoganathanG. VA new heuristic optimization algorithm: harmony searchSimulation2001762606810.1177/003754970107600201 – reference: AISC (2017) Steel construction manual. American Institute of Steel Construction, Chicago – reference: Dorigo M (1992) Optimization, learning and natural algorithms. PhD Thesis, Politecnico di Milano – reference: ASCE (2011) Blast protection of buildings Blast protection of buildings. ASCE/Structural Engineering Institute – reference: ASCE (2010) Design of blast-resistant buildings in petrochemical facilities. American Society of Civil Engineers – reference: AroraJOptimization of structures subjected to dynamic loadsStructural dynamic systems computational techniques and optimization199971731754754 – reference: KavehAGhazaanMComputer codes for colliding bodies optimization and its enhanced versionInt J Optim Civil Eng201443321332 – reference: KavehAMahdaviVColliding bodies optimization method for optimum discrete design of truss structuresComput Struct2014139435310.1016/j.compstruc.2014.04.006 – reference: KangBParkG-JAroraJSA review of optimization of structures subjected to transient loadsStruct Multidiscip Optim20063128195219954410.1007/s00158-005-0575-4 – reference: DusenberryDOHandbook for blast resistant design of buildings2010HobokenWiley10.1002/9780470549070 – reference: KavehAMahdaviVColliding bodies optimization: a novel meta-heuristic methodComput Struct2014139182710.1016/j.compstruc.2014.04.005 – reference: ChoiW-SParkG-JStructural optimization using equivalent static loads at all time intervalsComput Methods Appl Mech Eng200219119–202105212210.1016/S0045-7825(01)00373-5 – reference: DoD (2008) Structures to resist the effects of accidental explosions. UFC 3-340-02 – reference: ParkGTechnical overview of the equivalent static loads method for non-linear static response structural optimizationStruct Multidiscip Optim201143331933710.1007/s00158-010-0530-x – reference: PazMKimYHStructural dynamics2019BerlinSpringer10.1007/978-3-319-94743-3 – reference: ParkGLeeYDiscussion on the optimality condition of the equivalent static loads method for linear dynamic response structural optimizationStruct Multidiscip Optim2019591311316389538310.1007/s00158-018-2059-3 – reference: KangBChoiWParkG-JStructural optimization under equivalent static loads transformed from dynamic loads based on displacementComput Struct200179214515410.1016/S0045-7949(00)00127-9 – reference: KavehAAdvances in metaheuristic algorithms for optimal design of structures2014BerlinSpringer10.1007/978-3-319-05549-7 – reference: Goldberg DE, Holland JH (1988) Genetic algorithms and machine learning – reference: KimY-IParkG-JNonlinear dynamic response structural optimization using equivalent static loadsComput Methods Appl Mech Eng20101999–1266067610.1016/j.cma.2009.10.014 – reference: BhattiMAAdvanced topics in finite element analysis of structures: with mathematica and matlab computations2006New YorkWiley1111.74001 – reference: KavehAMahdaviVColliding bodies optimization method for optimum design of truss structures with continuous variablesAdv Eng Softw20147011210.1016/j.advengsoft.2014.01.002 – reference: StolpeMOn the equivalent static loads approach for dynamic response structural optimizationStruct Multidiscip Optim2014506921926331241010.1007/s00158-014-1101-3 – reference: KavehAMahdaviVColliding bodies optimization: extensions and applications2015BerlinSpringer10.1007/978-3-319-19659-6 – reference: EberhartRCShiYKennedyJSwarm intelligence2001AmsterdamElsevier – reference: Gilsanz R, Hamburger R, Barker J, Smith D, Rahimian A (2013) Design of blast resistant structures. steel design guide no. 26l. 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| Title | Discrete variable optimization of structures subjected to dynamic loads using equivalent static loads and metaheuristic algorithms |
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