Skip to main content
Erschienen in: Structural and Multidisciplinary Optimization 6/2015

20.07.2015 | RESEARCH PAPER

Multi-objective robust optimization of foam-filled tapered multi-cell thin-walled structures

verfasst von: Hanfeng Yin, Hongbing Fang, Youye Xiao, Guilin Wen, Qixiang Qing

Erschienen in: Structural and Multidisciplinary Optimization | Ausgabe 6/2015

Einloggen

Aktivieren Sie unsere intelligente Suche um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Foam-filled multi-cell thin-walled structure has recently gained attentions for its excellent energy absorption capacity. Tapered thin-walled structure is less likely to fail by global buckling, and is more capable of bearing oblique impact loads. Thus, foam-filled tapered multi-cell thin-walled structure (FTMTS) may be an extremely excellent energy absorber candidate in future vehicle body. This paper focuses on the crashworthiness of four kinds of axisymmetric FTMTSs with different cell numbers. According to our study, we find that FTMTSs have very excellent energy absorption capacity as well as strong capacity of avoiding global buckling. According to our investigation, it was found that the crashworthiness of FTMTS was largely affected by design parameters such as geometric sizes and foam density. In order to find optimal designs of FTMTSs, it is very essential to carry out crashworthiness optimization for FTMTSs. However, the conventional deterministic design is likely to become less meaningful or even unacceptable when considering the uncertainties of design parameters due to the manufacturing or installation deviation. In order to overcome this drawback, a multi-objective robust optimization procedure which employs Kriging metamodels, multi-objective particle swarm optimization (MOPSO) algorithm, “k-sigma” robust design theory and Monte Carlo simulation (MCS) was developed. The comparison of the Pareto fronts obtained by the developed multi-objective robust optimization procedure and the traditional multi-objective deterministic optimization algorithm shows that the robust optimization result is more reliable than the deterministic optimization result. The robust optimal design of FTMTS not only has very excellent crashworthiness but also has very high reliability when considering the uncertainty of design parameters.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
Zurück zum Zitat Abramowicz W, Jones N (1986) Dynamic progressive buckling of circular and square tubes. Int J Impact Eng 4(4):243–270CrossRef Abramowicz W, Jones N (1986) Dynamic progressive buckling of circular and square tubes. Int J Impact Eng 4(4):243–270CrossRef
Zurück zum Zitat Abramowicz W, Wierzbicki T (1988) Axial crushing of foam-filled columns. Int J Mech Sci 30(3/4):263–271CrossRef Abramowicz W, Wierzbicki T (1988) Axial crushing of foam-filled columns. Int J Mech Sci 30(3/4):263–271CrossRef
Zurück zum Zitat Ahmad Z, Thambiratnam DP (2009) Crushing response of foam-filled conical tubes under quasi-static axial loading. Mater Des 30(7):2393–2403CrossRef Ahmad Z, Thambiratnam DP (2009) Crushing response of foam-filled conical tubes under quasi-static axial loading. Mater Des 30(7):2393–2403CrossRef
Zurück zum Zitat Aktay L, Toksoy AK, Güden M (2006) Quasi-static axial crushing of extruded polystyrene foam-filled thin-walled aluminum tubes: experimental and numerical analysis. Mater Des 27(7):556–565CrossRef Aktay L, Toksoy AK, Güden M (2006) Quasi-static axial crushing of extruded polystyrene foam-filled thin-walled aluminum tubes: experimental and numerical analysis. Mater Des 27(7):556–565CrossRef
Zurück zum Zitat Aktay L, Kröplin BH, Toksoy AK, Güden M (2008) Finite element and coupled finite element/smooth particle hydrodynamics modeling of the quasi-static crushing of empty and foam-filled single, bitubular and constraint hexagonal- and square-packed aluminum tubes. Mater Des 29(5):952–962CrossRef Aktay L, Kröplin BH, Toksoy AK, Güden M (2008) Finite element and coupled finite element/smooth particle hydrodynamics modeling of the quasi-static crushing of empty and foam-filled single, bitubular and constraint hexagonal- and square-packed aluminum tubes. Mater Des 29(5):952–962CrossRef
Zurück zum Zitat Bi J, Fang HB, Wang QA, Ren XC (2010) Modeling and optimization of foam-filled thin-walled columns for crashworthiness designs. Finite Elem Anal Des 46(9):698–709CrossRef Bi J, Fang HB, Wang QA, Ren XC (2010) Modeling and optimization of foam-filled thin-walled columns for crashworthiness designs. Finite Elem Anal Des 46(9):698–709CrossRef
Zurück zum Zitat Chen WG, Wierzbicki T (2001) Relative merits of single-cell, multi-cell and foam-filled thin-walled structures in energy absorption. Thin Wall Struct 39(4):287–306CrossRef Chen WG, Wierzbicki T (2001) Relative merits of single-cell, multi-cell and foam-filled thin-walled structures in energy absorption. Thin Wall Struct 39(4):287–306CrossRef
Zurück zum Zitat Coello Coello C, Salazar Lechuga M (2002) MOPSO: A proposal for multiple objective particle swarm optimization. Congress on Evolutionary Computation (CEC), 1051–1056 Coello Coello C, Salazar Lechuga M (2002) MOPSO: A proposal for multiple objective particle swarm optimization. Congress on Evolutionary Computation (CEC), 1051–1056
Zurück zum Zitat Deshpande VS, Fleck NA (2000) Isotropic constitutive models for metallic foams. J Mech Phys Solids 48(6–7):1253–1283CrossRefMATH Deshpande VS, Fleck NA (2000) Isotropic constitutive models for metallic foams. J Mech Phys Solids 48(6–7):1253–1283CrossRefMATH
Zurück zum Zitat Gu XG, Sun GY, Li GY, Mao LC, Li Q (2013) A comparative study on multiobjective reliable and robust optimization for crashworthiness design of vehicle structure. Struct Multidisc Optim 48(3):669–684CrossRef Gu XG, Sun GY, Li GY, Mao LC, Li Q (2013) A comparative study on multiobjective reliable and robust optimization for crashworthiness design of vehicle structure. Struct Multidisc Optim 48(3):669–684CrossRef
Zurück zum Zitat Gümrük R, Karadeniz S (2008) A numerical study of the influence of bump type triggers on the axial crushing of top hat thin-walled sections. Thin Wall Struct 46(10):1094–1106CrossRef Gümrük R, Karadeniz S (2008) A numerical study of the influence of bump type triggers on the axial crushing of top hat thin-walled sections. Thin Wall Struct 46(10):1094–1106CrossRef
Zurück zum Zitat Hallquist JO (1998) LS-DYNA theoretical manual. Livemore Software Technology Corporation, California Hallquist JO (1998) LS-DYNA theoretical manual. Livemore Software Technology Corporation, California
Zurück zum Zitat Hallquist JO (2003) LS-DYNA keyword user’s manual. Livemore Software Technology Corporation, California Hallquist JO (2003) LS-DYNA keyword user’s manual. Livemore Software Technology Corporation, California
Zurück zum Zitat Hanssen AG, Langseth M, Hopperstad OS (2000a) Static and dynamic crushing of circular aluminium extrusions with aluminium foam filler. Int J Impact Eng 24(5):475–507CrossRef Hanssen AG, Langseth M, Hopperstad OS (2000a) Static and dynamic crushing of circular aluminium extrusions with aluminium foam filler. Int J Impact Eng 24(5):475–507CrossRef
Zurück zum Zitat Hanssen AG, Langseth M, Hopperstad OS (2000b) Static and dynamic crushing of square aluminium extrusions with aluminium foam filler. Int J Impact Eng 24(4):347–383CrossRef Hanssen AG, Langseth M, Hopperstad OS (2000b) Static and dynamic crushing of square aluminium extrusions with aluminium foam filler. Int J Impact Eng 24(4):347–383CrossRef
Zurück zum Zitat Hanssen AG, Hopperstad OS, Langseth M, IIstad H (2002) Validation of constitutive models applicable to aluminium foams. Int J Mech Sci 44(2):359–406CrossRef Hanssen AG, Hopperstad OS, Langseth M, IIstad H (2002) Validation of constitutive models applicable to aluminium foams. Int J Mech Sci 44(2):359–406CrossRef
Zurück zum Zitat Hou SJ, Li Q, Long SY, Yang XJ, Li W (2008) Multiobjective optimization of multi-cell sections for the crashworthiness design. Int J Impact Eng 35(11):1355–1367CrossRef Hou SJ, Li Q, Long SY, Yang XJ, Li W (2008) Multiobjective optimization of multi-cell sections for the crashworthiness design. Int J Impact Eng 35(11):1355–1367CrossRef
Zurück zum Zitat Hou SJ, Li Q, Long SY, Yang XJ, Li W (2009) crashworthiness design for foam filled thin-walled structures. Mater Des 30(6):2024–2032CrossRef Hou SJ, Li Q, Long SY, Yang XJ, Li W (2009) crashworthiness design for foam filled thin-walled structures. Mater Des 30(6):2024–2032CrossRef
Zurück zum Zitat Hou SJ, Han X, Sun GY, Long SY, Li W, Yang XJ, Li Q (2011) Multiobjective optimization for tapered circular tubes. Thin Wall Struct 49(7):855–863CrossRef Hou SJ, Han X, Sun GY, Long SY, Li W, Yang XJ, Li Q (2011) Multiobjective optimization for tapered circular tubes. Thin Wall Struct 49(7):855–863CrossRef
Zurück zum Zitat Kavi H, Toksoy AK, Guden M (2006) Predicting energy absorption in a foam-filled thin-walled aluminum tube based on experimentally determined strengthening coefficient. Mater Des 27(4):263–269CrossRef Kavi H, Toksoy AK, Guden M (2006) Predicting energy absorption in a foam-filled thin-walled aluminum tube based on experimentally determined strengthening coefficient. Mater Des 27(4):263–269CrossRef
Zurück zum Zitat Kim HS (2002) New extruded multi-cell aluminum profile for maximum crash energy absorption and weight efficiency. Thin Wall Struct 40(4):311–327CrossRef Kim HS (2002) New extruded multi-cell aluminum profile for maximum crash energy absorption and weight efficiency. Thin Wall Struct 40(4):311–327CrossRef
Zurück zum Zitat Kleijnen JPC (2005) An overview of the design and analysis of simulation experiments for sensitivity analysis. Eur J Oper Res 164(2):287–300CrossRefMATH Kleijnen JPC (2005) An overview of the design and analysis of simulation experiments for sensitivity analysis. Eur J Oper Res 164(2):287–300CrossRefMATH
Zurück zum Zitat Langseth M, Hopperstand OS (1996) Static and dynamic axial crushing of square thin-walled aluminum extrusions. Int J Impact Eng 18(7/8):949–968CrossRef Langseth M, Hopperstand OS (1996) Static and dynamic axial crushing of square thin-walled aluminum extrusions. Int J Impact Eng 18(7/8):949–968CrossRef
Zurück zum Zitat Langseth M, Hopperstad OS, Hanssen AG (1998) Crash behaviour of thin-walled aluminium members. Thin Wall Struct 32(1–3):127–150CrossRef Langseth M, Hopperstad OS, Hanssen AG (1998) Crash behaviour of thin-walled aluminium members. Thin Wall Struct 32(1–3):127–150CrossRef
Zurück zum Zitat Liao XT, Li Q, Yang XJ, Zhang WG, Li W (2008) Multiobjective optimization for crash safety design of vehicles using stepwise regression model. Struct Multidisc Optim 35(6):561–569CrossRef Liao XT, Li Q, Yang XJ, Zhang WG, Li W (2008) Multiobjective optimization for crash safety design of vehicles using stepwise regression model. Struct Multidisc Optim 35(6):561–569CrossRef
Zurück zum Zitat Liu YC, Day ML (2008) Bending collapse of thin-walled circular tubes and computational application. Thin Wall Struct 46(4):442–450CrossRef Liu YC, Day ML (2008) Bending collapse of thin-walled circular tubes and computational application. Thin Wall Struct 46(4):442–450CrossRef
Zurück zum Zitat Liu DS, Tan KC, Goh CK, Ho WK (2007) A multiobjective memetic algorithm based on particle swarm optimization. IEEE T Syst Man Cy B 37(1):42–50CrossRef Liu DS, Tan KC, Goh CK, Ho WK (2007) A multiobjective memetic algorithm based on particle swarm optimization. IEEE T Syst Man Cy B 37(1):42–50CrossRef
Zurück zum Zitat Lu GX, Yu TX (2003) Energy absorption of structures and materials. CRC Press, Boca RatonCrossRef Lu GX, Yu TX (2003) Energy absorption of structures and materials. CRC Press, Boca RatonCrossRef
Zurück zum Zitat Mahmoudabadi MZ, Sadighi M (2011) A study on the static and dynamic loading of the foam filled metal hexagonal honeycomb—Theoretical and experimental. Mater Sci Eng A 530:333–343CrossRef Mahmoudabadi MZ, Sadighi M (2011) A study on the static and dynamic loading of the foam filled metal hexagonal honeycomb—Theoretical and experimental. Mater Sci Eng A 530:333–343CrossRef
Zurück zum Zitat Meguid SA, Attia MS, Monfort A (2004) On the crush behaviour of ultralight foam-filled structures. Mater Des 25(3):183–189CrossRef Meguid SA, Attia MS, Monfort A (2004) On the crush behaviour of ultralight foam-filled structures. Mater Des 25(3):183–189CrossRef
Zurück zum Zitat Mirfendereski L, Salimi M, Ziaei-Rad S (2008) Parametric study and numerical analysis of empty and foam-filled thin-walled tubes under static and dynamic loadings. Int J Mech Sci 50(6):1042–1057CrossRef Mirfendereski L, Salimi M, Ziaei-Rad S (2008) Parametric study and numerical analysis of empty and foam-filled thin-walled tubes under static and dynamic loadings. Int J Mech Sci 50(6):1042–1057CrossRef
Zurück zum Zitat Myers RH, Montgomery DC, Anderson-Cook CM (2009) Response surface methodology: Process and product optimization using designed experiments, 3rd edn. Wiley, Hoboken Myers RH, Montgomery DC, Anderson-Cook CM (2009) Response surface methodology: Process and product optimization using designed experiments, 3rd edn. Wiley, Hoboken
Zurück zum Zitat Paik JK, Kim BJ, Park DK, Jang BS (2011) On quasi-static crushing of thin-walled steel structures in cold temperature: experimental and numerical studies. Int J Impact Eng 38(1):13–28CrossRef Paik JK, Kim BJ, Park DK, Jang BS (2011) On quasi-static crushing of thin-walled steel structures in cold temperature: experimental and numerical studies. Int J Impact Eng 38(1):13–28CrossRef
Zurück zum Zitat Parsopoulos K, Vrahatis M (2002) Particle swarm optimization method in multiobjective problems. Proceedings of the ACM Symposium on Applied Computing (SAC), 603–607 Parsopoulos K, Vrahatis M (2002) Particle swarm optimization method in multiobjective problems. Proceedings of the ACM Symposium on Applied Computing (SAC), 603–607
Zurück zum Zitat Raquel C, Naval P (2005) An effective use of crowding distance in multiobjective particle swarm optimization. In: Proceedings of the 2005 conference on Genetic and evolutionary computation, Washington (DC), USA, 257–264 Raquel C, Naval P (2005) An effective use of crowding distance in multiobjective particle swarm optimization. In: Proceedings of the 2005 conference on Genetic and evolutionary computation, Washington (DC), USA, 257–264
Zurück zum Zitat Reddy TY, Wall RJ (1988) Axial compression of foam-filled thin-walled circular tubes. Int J Impact Eng 7(2):151–166CrossRef Reddy TY, Wall RJ (1988) Axial compression of foam-filled thin-walled circular tubes. Int J Impact Eng 7(2):151–166CrossRef
Zurück zum Zitat Reid SR, Reddy TY (1986) Axial crushing of foam-filled tapered sheet metal tubes. Int J Mech Sci 28(10):643–656CrossRef Reid SR, Reddy TY (1986) Axial crushing of foam-filled tapered sheet metal tubes. Int J Mech Sci 28(10):643–656CrossRef
Zurück zum Zitat Reid SR, Reddy TY, Gray MD (1986) Static and dynamic axial crushing of foam-filled sheet metal tubes. Int J Mech Sci 28(5):295–322CrossRef Reid SR, Reddy TY, Gray MD (1986) Static and dynamic axial crushing of foam-filled sheet metal tubes. Int J Mech Sci 28(5):295–322CrossRef
Zurück zum Zitat Reyes A, Langseth M, Hopperstad OS (2003a) Square aluminum tubes subjected to oblique loading. Int J Impact Eng 28(10):1077–1106CrossRef Reyes A, Langseth M, Hopperstad OS (2003a) Square aluminum tubes subjected to oblique loading. Int J Impact Eng 28(10):1077–1106CrossRef
Zurück zum Zitat Reyes A, Hopperstad OS, Berstad T, Hanssen AG, Langseth M (2003b) Constitutive modeling of aluminum foam including fracture and statistical variation of density. Eur J Mech A-Solid 22(6):815–835CrossRefMATH Reyes A, Hopperstad OS, Berstad T, Hanssen AG, Langseth M (2003b) Constitutive modeling of aluminum foam including fracture and statistical variation of density. Eur J Mech A-Solid 22(6):815–835CrossRefMATH
Zurück zum Zitat Rossi A, Fawaz Z, Behdinan K (2005) Numerical simulation of the axial collapse of thin-walled polygonal section tubes. Thin Wall Struct 43(10):1646–1661CrossRef Rossi A, Fawaz Z, Behdinan K (2005) Numerical simulation of the axial collapse of thin-walled polygonal section tubes. Thin Wall Struct 43(10):1646–1661CrossRef
Zurück zum Zitat Rust W, Schweizerhof K (2003) Finite element limit load analysis of thin-walled structures by ANSYS (implicit), LS-DYNA (explicit) and in combination. Thin Wall Struct 41(2–3):227–244CrossRef Rust W, Schweizerhof K (2003) Finite element limit load analysis of thin-walled structures by ANSYS (implicit), LS-DYNA (explicit) and in combination. Thin Wall Struct 41(2–3):227–244CrossRef
Zurück zum Zitat Santosa SP, Wierzbicki T, Hanssen AG, Langseth M (2000) Experimental and numerical studies of foam-filled sections. Int J Impact Eng 24(5):509–534CrossRef Santosa SP, Wierzbicki T, Hanssen AG, Langseth M (2000) Experimental and numerical studies of foam-filled sections. Int J Impact Eng 24(5):509–534CrossRef
Zurück zum Zitat Seitzberger M, Rammerstorfer FG, Gradinger R, Degischer HP, Blaimschein M, Walch C (2000) Experimental studies on the quasi-static axial crushing of steel columns filled with aluminium foam. Int J Solids Struct 37(30):4125–4147CrossRef Seitzberger M, Rammerstorfer FG, Gradinger R, Degischer HP, Blaimschein M, Walch C (2000) Experimental studies on the quasi-static axial crushing of steel columns filled with aluminium foam. Int J Solids Struct 37(30):4125–4147CrossRef
Zurück zum Zitat Shahbeyk S, Petrinic N, Vafai A (2007) Numerical modelling of dynamically loaded metal foam-filled square columns. Int J Impact Eng 34(3):573–586CrossRef Shahbeyk S, Petrinic N, Vafai A (2007) Numerical modelling of dynamically loaded metal foam-filled square columns. Int J Impact Eng 34(3):573–586CrossRef
Zurück zum Zitat Song XG, Sun GY, Li GY, Gao WZ, Li Q (2013) Crashworthiness optimization design of foam-filled tapered thin-walled structures using multiple surrogate models. Struct Multidisc Optim 47(2):221–231CrossRefMathSciNetMATH Song XG, Sun GY, Li GY, Gao WZ, Li Q (2013) Crashworthiness optimization design of foam-filled tapered thin-walled structures using multiple surrogate models. Struct Multidisc Optim 47(2):221–231CrossRefMathSciNetMATH
Zurück zum Zitat Sun GY, Li GY, Hou SJ, Zhou SW, Li W, Li Q (2010) Crashworthiness design for functionally graded foam-filled thin-walled structures. Mater Sci Eng A Struct 527(7–8):1911–1919CrossRef Sun GY, Li GY, Hou SJ, Zhou SW, Li W, Li Q (2010) Crashworthiness design for functionally graded foam-filled thin-walled structures. Mater Sci Eng A Struct 527(7–8):1911–1919CrossRef
Zurück zum Zitat Sun GY, Li GY, Zhou SW, Li HZ, Hou SJ, Li Q (2011) Crashworthiness design of vehicle by using multiobjective robust optimization. Struct Multidisc Optim 44(1):99–110CrossRef Sun GY, Li GY, Zhou SW, Li HZ, Hou SJ, Li Q (2011) Crashworthiness design of vehicle by using multiobjective robust optimization. Struct Multidisc Optim 44(1):99–110CrossRef
Zurück zum Zitat Sun GY, Song XG, Baek S, Li Q (2014) Robust optimization of foam-filled thin-walled structure based on sequential Kriging metamodel. Struct Multidisc Optim 49(6):897–913CrossRef Sun GY, Song XG, Baek S, Li Q (2014) Robust optimization of foam-filled thin-walled structure based on sequential Kriging metamodel. Struct Multidisc Optim 49(6):897–913CrossRef
Zurück zum Zitat Tang ZL, Liu ST, Zhang ZH (2013) Analysis of energy absorption characteristics of cylindrical multi-cell columns. Thin Wall Struct 62:75–84CrossRef Tang ZL, Liu ST, Zhang ZH (2013) Analysis of energy absorption characteristics of cylindrical multi-cell columns. Thin Wall Struct 62:75–84CrossRef
Zurück zum Zitat Tarigopula V, Langseth M, Hopperstad OS, Clausen AH (2006) Axial crushing of thin-walled high-strength steel sections. Int J Impact Eng 32(5):847–882CrossRef Tarigopula V, Langseth M, Hopperstad OS, Clausen AH (2006) Axial crushing of thin-walled high-strength steel sections. Int J Impact Eng 32(5):847–882CrossRef
Zurück zum Zitat Vanderplaats GN, Moses F (1973) Structural optimization by methods of feasible directions. Comput Struct 3(4):739–755CrossRef Vanderplaats GN, Moses F (1973) Structural optimization by methods of feasible directions. Comput Struct 3(4):739–755CrossRef
Zurück zum Zitat Wang GG, Shan S (2007) Review of metamodeling techniques in support of engineering design optimization. Int J Mech Des 129(4):370–380MathSciNet Wang GG, Shan S (2007) Review of metamodeling techniques in support of engineering design optimization. Int J Mech Des 129(4):370–380MathSciNet
Zurück zum Zitat Wang QC, Fan ZJ, Gui LJ (2006) A theoretical analysis for the dynamic axial crushing behaviour of aluminium foam-filled hat sections. Int J Solids Struct 43(7–8):2064–2075CrossRefMATH Wang QC, Fan ZJ, Gui LJ (2006) A theoretical analysis for the dynamic axial crushing behaviour of aluminium foam-filled hat sections. Int J Solids Struct 43(7–8):2064–2075CrossRefMATH
Zurück zum Zitat Wang QC, Fan ZJ, Gui LJ (2007) Theoretical analysis for axial crushing behaviour of aluminium foam-filled hat sections. Int J Mech Sci 49(4):515–521CrossRef Wang QC, Fan ZJ, Gui LJ (2007) Theoretical analysis for axial crushing behaviour of aluminium foam-filled hat sections. Int J Mech Sci 49(4):515–521CrossRef
Zurück zum Zitat White MD, Jones N (1999) Experimental quasi-static axial crushing of top-hat and double-hat thin-walled sections. Int J Mech Sci 41:179–208CrossRefMATH White MD, Jones N (1999) Experimental quasi-static axial crushing of top-hat and double-hat thin-walled sections. Int J Mech Sci 41:179–208CrossRefMATH
Zurück zum Zitat Wierzbicki T, Abramowicz W (1983) On the crushing mechanics of thin-walled structures. J Appl Mech 50(4):727–734CrossRefMATH Wierzbicki T, Abramowicz W (1983) On the crushing mechanics of thin-walled structures. J Appl Mech 50(4):727–734CrossRefMATH
Zurück zum Zitat Williams CKI (1998) Prediction with Gaussian processes: from linear regression to linear prediction and beyond. Learning Graph Models 89:599–621CrossRef Williams CKI (1998) Prediction with Gaussian processes: from linear regression to linear prediction and beyond. Learning Graph Models 89:599–621CrossRef
Zurück zum Zitat Xiang YJ, Wang Q, Fan ZJ, Fang HB (2006) Optimal crashworthiness design of a spot-welded thin-walled hat section. Finite Elem Anal Des 42(10):846–855CrossRef Xiang YJ, Wang Q, Fan ZJ, Fang HB (2006) Optimal crashworthiness design of a spot-welded thin-walled hat section. Finite Elem Anal Des 42(10):846–855CrossRef
Zurück zum Zitat Yin HF, Wen GL, Gan NF (2011a) Crashworthiness design for honeycomb structures under axial dynamic loading. Int J Comput Methods 8(4):863–877CrossRef Yin HF, Wen GL, Gan NF (2011a) Crashworthiness design for honeycomb structures under axial dynamic loading. Int J Comput Methods 8(4):863–877CrossRef
Zurück zum Zitat Yin HF, Wen GL, Hou SJ, Chen K (2011b) Crushing analysis and multiobjective crashworthiness optimization of honeycomb-filled single and bitubular polygonal tubes. Mater Des 32(8):4449–4460CrossRef Yin HF, Wen GL, Hou SJ, Chen K (2011b) Crushing analysis and multiobjective crashworthiness optimization of honeycomb-filled single and bitubular polygonal tubes. Mater Des 32(8):4449–4460CrossRef
Zurück zum Zitat Yin HF, Wen GL, Hou SJ, Qing QX (2013) Multiobjective crashworthiness optimization of functionally lateral graded foam-filled tubes. Mater Des 44:414–428CrossRef Yin HF, Wen GL, Hou SJ, Qing QX (2013) Multiobjective crashworthiness optimization of functionally lateral graded foam-filled tubes. Mater Des 44:414–428CrossRef
Zurück zum Zitat Yin HF, Wen GL, Wu X, Qing QX, Hou SJ (2014a) Crashworthiness design of functionally graded foam-filled multi-cell thin-walled structures. Thin Wall Struct 85:142–155CrossRef Yin HF, Wen GL, Wu X, Qing QX, Hou SJ (2014a) Crashworthiness design of functionally graded foam-filled multi-cell thin-walled structures. Thin Wall Struct 85:142–155CrossRef
Zurück zum Zitat Yin HF, Wen GL, Liu ZB, Qing QX (2014b) Crashworthiness optimization design for foam-filled multi-cell thin-walled structures. Thin Wall Struct 75:8–17CrossRef Yin HF, Wen GL, Liu ZB, Qing QX (2014b) Crashworthiness optimization design for foam-filled multi-cell thin-walled structures. Thin Wall Struct 75:8–17CrossRef
Zurück zum Zitat Zarei HR, Kroger M (2007) Crashworthiness optimization of empty and filled aluminum crash boxes. Int J Crashworth 12(3):255–264CrossRef Zarei HR, Kroger M (2007) Crashworthiness optimization of empty and filled aluminum crash boxes. Int J Crashworth 12(3):255–264CrossRef
Zurück zum Zitat Zarei HR, Kroger M (2008) Optimization of the foam-filled aluminum tubes for crush box application. Thin Wall Struct 46(2):214–221CrossRef Zarei HR, Kroger M (2008) Optimization of the foam-filled aluminum tubes for crush box application. Thin Wall Struct 46(2):214–221CrossRef
Zurück zum Zitat Zhang X, Huh H (2009) Energy absorption of longitudinally grooved square tubes under axial compression. Thin Wall Struct 47(12):1469–1477CrossRef Zhang X, Huh H (2009) Energy absorption of longitudinally grooved square tubes under axial compression. Thin Wall Struct 47(12):1469–1477CrossRef
Zurück zum Zitat Zhang X, Zhang H (2013a) Energy absorption limit of plates in thin-walled structures under compression. Int J Impact Eng 57:81–98CrossRef Zhang X, Zhang H (2013a) Energy absorption limit of plates in thin-walled structures under compression. Int J Impact Eng 57:81–98CrossRef
Zurück zum Zitat Zhang X, Zhang H (2013b) Energy absorption of multi-cell stub columns under axial compression. Thin Wall Struct 68:156–163CrossRef Zhang X, Zhang H (2013b) Energy absorption of multi-cell stub columns under axial compression. Thin Wall Struct 68:156–163CrossRef
Zurück zum Zitat Zhang X, Zhang H (2014) Axial crushing of circular multi-cell columns. Int J Impact Eng 65:110–125CrossRef Zhang X, Zhang H (2014) Axial crushing of circular multi-cell columns. Int J Impact Eng 65:110–125CrossRef
Zurück zum Zitat Zhang X, Cheng GD, Zhang H (2006) Theoretical prediction and numerical simulation of multi-cell square thin-walled structures. Thin Wall Struct 44(11):1185–1191CrossRef Zhang X, Cheng GD, Zhang H (2006) Theoretical prediction and numerical simulation of multi-cell square thin-walled structures. Thin Wall Struct 44(11):1185–1191CrossRef
Zurück zum Zitat Zhang X, Cheng GD, You Z, Zhang H (2007a) Energy absorption of axially compressed thin-walled square tubes with patterns. Thin Wall Struct 45(9):737–746CrossRef Zhang X, Cheng GD, You Z, Zhang H (2007a) Energy absorption of axially compressed thin-walled square tubes with patterns. Thin Wall Struct 45(9):737–746CrossRef
Zurück zum Zitat Zhang Y, Zhu P, Chen GL (2007b) Lightweight design of automotive front side rail based on robust optimisation. Thin Wall Struct 45(7–8):670–676CrossRef Zhang Y, Zhu P, Chen GL (2007b) Lightweight design of automotive front side rail based on robust optimisation. Thin Wall Struct 45(7–8):670–676CrossRef
Zurück zum Zitat Zhang X, Cheng GD, Zhang H (2009) Numerical investigations on a new type of energy-absorbing structure based on free inversion of tubes. Int J Mech Sci 51(1):64–76CrossRefMATH Zhang X, Cheng GD, Zhang H (2009) Numerical investigations on a new type of energy-absorbing structure based on free inversion of tubes. Int J Mech Sci 51(1):64–76CrossRefMATH
Zurück zum Zitat Zhang ZH, Liu ST, Tang ZL (2011) Comparisons of honeycomb sandwich and foam-filled cylindrical columns. Thin Wall Struct 49(9):1071–1079CrossRef Zhang ZH, Liu ST, Tang ZL (2011) Comparisons of honeycomb sandwich and foam-filled cylindrical columns. Thin Wall Struct 49(9):1071–1079CrossRef
Zurück zum Zitat Zhang X, Wen ZZ, Zhang H (2014a) Axial crushing and optimal design of square tubes with graded thickness. Thin Wall Struct 84:263–274CrossRef Zhang X, Wen ZZ, Zhang H (2014a) Axial crushing and optimal design of square tubes with graded thickness. Thin Wall Struct 84:263–274CrossRef
Zurück zum Zitat Zhang Y, Sun GY, Xu XP, Li GY, Li Q (2014b) Multiobjective crashworthiness optimization of hollow and conical tubes for multiple load cases. Thin Wall Struct 82:331–342CrossRef Zhang Y, Sun GY, Xu XP, Li GY, Li Q (2014b) Multiobjective crashworthiness optimization of hollow and conical tubes for multiple load cases. Thin Wall Struct 82:331–342CrossRef
Zurück zum Zitat Zhu P, Zhang Y, Chen GL (2009) Metamodel-based light weight design of an automotive front-body structure using robust optimization. Proc Inst Mech Eng Part D-J Automob Eng 223(D9):1133–1147CrossRef Zhu P, Zhang Y, Chen GL (2009) Metamodel-based light weight design of an automotive front-body structure using robust optimization. Proc Inst Mech Eng Part D-J Automob Eng 223(D9):1133–1147CrossRef
Metadaten
Titel
Multi-objective robust optimization of foam-filled tapered multi-cell thin-walled structures
verfasst von
Hanfeng Yin
Hongbing Fang
Youye Xiao
Guilin Wen
Qixiang Qing
Publikationsdatum
20.07.2015
Verlag
Springer Berlin Heidelberg
Erschienen in
Structural and Multidisciplinary Optimization / Ausgabe 6/2015
Print ISSN: 1615-147X
Elektronische ISSN: 1615-1488
DOI
https://doi.org/10.1007/s00158-015-1299-8

Weitere Artikel der Ausgabe 6/2015

Structural and Multidisciplinary Optimization 6/2015 Zur Ausgabe

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.