Skip to main content
Top
Published in: Structural and Multidisciplinary Optimization 2/2014

01-08-2014 | INDUSTRIAL APPLICATION

Two-stage size-layout optimization of axially compressed stiffened panels

Authors: Bo Wang, Peng Hao, Gang Li, Kuo Tian, Kaifan Du, Xiaojun Wang, Xi Zhang, Xiaohan Tang

Published in: Structural and Multidisciplinary Optimization | Issue 2/2014

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this study, a two-stage optimization framework is proposed for cylindrical or flat stiffened panels under uniform or non-uniform axial compression, which are extensively used in the aerospace industry. In the first stage, traditional sizing optimization is performed. Based on the buckling or collapse-like deformed shape evaluated for the optimized design, the panel can be divided in sub-regions each of which shows characteristic deformations along axial and circumferential directions. Layout optimization is then performed using a stiffener spacing distribution function to represent the location of each stiffener. A layout coefficient is assigned to each sub-region and the overall layout of the panel is optimized. Three test problems are solved in order to demonstrate the validity of the proposed optimization framework: remarkably, the load-carrying capacity improves by 17.4 %, 66.2 % and 102.2 % with respect to the initial design.

Dont have a licence yet? Then find out more about our products and how to get one now:

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!

Literature
go back to reference ABAQUS (2008) Standard user’s manual version 6.7. Hibbit, Karlsson and Sorensen Inc., Abaqus, Pawtucket ABAQUS (2008) Standard user’s manual version 6.7. Hibbit, Karlsson and Sorensen Inc., Abaqus, Pawtucket
go back to reference Ahmed KM (2009) Elastic buckling behaviour of a four-lobed cross section cylindrical shell with variable thickness under non-uniform axial loads. Math Probl Eng 1–17 Ahmed KM (2009) Elastic buckling behaviour of a four-lobed cross section cylindrical shell with variable thickness under non-uniform axial loads. Math Probl Eng 1–17
go back to reference Bushnell D (1981) Buckling of shells – pitfall for designers. AIAA J 19(9):1183–1226CrossRef Bushnell D (1981) Buckling of shells – pitfall for designers. AIAA J 19(9):1183–1226CrossRef
go back to reference Bushnell D (1987) PANDA2-Program for minimum weight design of stiffened, composite, locally buckled panels. Comput Struct 25(4):469–605CrossRefMATH Bushnell D (1987) PANDA2-Program for minimum weight design of stiffened, composite, locally buckled panels. Comput Struct 25(4):469–605CrossRefMATH
go back to reference Calladine CR (1983) Theory of shell structures. Cambridge University Press, Cambridge Calladine CR (1983) Theory of shell structures. Cambridge University Press, Cambridge
go back to reference Calladine CR (1995) Understanding imperfection-sensitivity in the buckling of thin-walled shells. Thin-Walled Struct 23(1–4):215–235CrossRef Calladine CR (1995) Understanding imperfection-sensitivity in the buckling of thin-walled shells. Thin-Walled Struct 23(1–4):215–235CrossRef
go back to reference Crisfield MA (1981) A fast incremental/iteration solution procedure that handles snap-through. Comput Struct 13(1–3):55–62CrossRefMATH Crisfield MA (1981) A fast incremental/iteration solution procedure that handles snap-through. Comput Struct 13(1–3):55–62CrossRefMATH
go back to reference Croll JGA, Ellinas CP (1983) Reduced stiffness axial load buckling of cylinders. Int J Solids Struct 19(5):461–477CrossRef Croll JGA, Ellinas CP (1983) Reduced stiffness axial load buckling of cylinders. Int J Solids Struct 19(5):461–477CrossRef
go back to reference Engelbrecht AP (2005) Fundamentals of computational swarm intelligence. Wiley, Chichester Engelbrecht AP (2005) Fundamentals of computational swarm intelligence. Wiley, Chichester
go back to reference Eurocode 3 (1999) Design of steel structures, part 1.6: general rules-supplementary rules for the strength and stability of shell structures. CEN, Brussels Eurocode 3 (1999) Design of steel structures, part 1.6: general rules-supplementary rules for the strength and stability of shell structures. CEN, Brussels
go back to reference Ganesh S, Ramesh S, Mira M (2013) Buckling behavior of composite laminates (with and without cutouts) subjected to nonuniform in-plane loads. Int J Struct Stab Dyn 13(8):1–20 Ganesh S, Ramesh S, Mira M (2013) Buckling behavior of composite laminates (with and without cutouts) subjected to nonuniform in-plane loads. Int J Struct Stab Dyn 13(8):1–20
go back to reference Greenberg JB, Stavsky Y (1995) Buckling of composite orthotropic cylindrical shells under non-uniform axial loads. Compos Struct 30(4):399–406CrossRef Greenberg JB, Stavsky Y (1995) Buckling of composite orthotropic cylindrical shells under non-uniform axial loads. Compos Struct 30(4):399–406CrossRef
go back to reference Hao P, Wang B, Li G (2012) Surrogate-based optimum design for stiffened shells with adaptive sampling. AIAA J 50(11):2389–2407CrossRef Hao P, Wang B, Li G (2012) Surrogate-based optimum design for stiffened shells with adaptive sampling. AIAA J 50(11):2389–2407CrossRef
go back to reference Hao P, Wang B, Li G, Tian K, Du KF, Wang XJ, Tang XH (2013) Surrogate-based optimization of stiffened shells including load-carrying capacity and imperfection sensitivity. Thin-Walled Struct 72(15):164–174CrossRef Hao P, Wang B, Li G, Tian K, Du KF, Wang XJ, Tang XH (2013) Surrogate-based optimization of stiffened shells including load-carrying capacity and imperfection sensitivity. Thin-Walled Struct 72(15):164–174CrossRef
go back to reference Huybrechts S, Meink TE (1997) Advanced grid stiffened structures for the next generation of launch vehicles. IEEE Aerospace Conf 1:263–270 Huybrechts S, Meink TE (1997) Advanced grid stiffened structures for the next generation of launch vehicles. IEEE Aerospace Conf 1:263–270
go back to reference Jaunky N, Knight NF Jr, Ambur DR (1996) Formulation of an improved smeared stiffener theory for buckling analysis of grid-stiffened composite panels. Compos Part B Eng 27(5):519–526CrossRef Jaunky N, Knight NF Jr, Ambur DR (1996) Formulation of an improved smeared stiffener theory for buckling analysis of grid-stiffened composite panels. Compos Part B Eng 27(5):519–526CrossRef
go back to reference Jaunky N, Knight NF Jr, Ambur DR (1998) Optimal design of general stiffened composite circular cylinders for global buckling with strength constraints. Compos Struct 41(3):243–252CrossRef Jaunky N, Knight NF Jr, Ambur DR (1998) Optimal design of general stiffened composite circular cylinders for global buckling with strength constraints. Compos Struct 41(3):243–252CrossRef
go back to reference Jin R, Chen W, Simpson TW (2001) Comparative studies of metamodelling techniques under multiple modelling criteria. Struct Multidisc Optim 23(1):1–13CrossRef Jin R, Chen W, Simpson TW (2001) Comparative studies of metamodelling techniques under multiple modelling criteria. Struct Multidisc Optim 23(1):1–13CrossRef
go back to reference Kidane S, Li G, Helms J, Pang SS, Wolddsenbet E (2003) Buckling load analysis of grid stiffened composite cylinders. Compos Part B Eng 34(1):1–9CrossRef Kidane S, Li G, Helms J, Pang SS, Wolddsenbet E (2003) Buckling load analysis of grid stiffened composite cylinders. Compos Part B Eng 34(1):1–9CrossRef
go back to reference Lamberti L, Venkataraman S, Haftka RT, Johnson TF (2003) Preliminary design optimization of stiffened panels using approximate analysis models. Int J Numer Meth Eng 57(10):1351– 1380CrossRefMATH Lamberti L, Venkataraman S, Haftka RT, Johnson TF (2003) Preliminary design optimization of stiffened panels using approximate analysis models. Int J Numer Meth Eng 57(10):1351– 1380CrossRefMATH
go back to reference Lanzi L, Giavotto V (2006) Post-buckling optimization of composite stiffened panels: computations and experiments. Compos Struct 73(2):208–220CrossRef Lanzi L, Giavotto V (2006) Post-buckling optimization of composite stiffened panels: computations and experiments. Compos Struct 73(2):208–220CrossRef
go back to reference Lekhnitskii SG (1968) Anisotropic plates. Science Publishers, Gordon and Breach Lekhnitskii SG (1968) Anisotropic plates. Science Publishers, Gordon and Breach
go back to reference Leriche R, Haftka RT (1993) Optimization of laminate stacking sequence for buckling load maximization by genetic algorithm. AIAA J 31(5):951–956CrossRef Leriche R, Haftka RT (1993) Optimization of laminate stacking sequence for buckling load maximization by genetic algorithm. AIAA J 31(5):951–956CrossRef
go back to reference Lindgaard E, Lund E, Rasmussen K (2010) Nonlinear buckling optimization of composite structures considering worst shape imperfections. Int J Solids Struct 47(22–23):3186–3202CrossRefMATH Lindgaard E, Lund E, Rasmussen K (2010) Nonlinear buckling optimization of composite structures considering worst shape imperfections. Int J Solids Struct 47(22–23):3186–3202CrossRefMATH
go back to reference Mack Y, Goel T, Shyy W, Haftka RT (2007) Surrogate model-based optimization framework: a case study in aerospace design. In: Evolutionary computation in dynamic and uncertain environments, vol 51. Springer Kluwer Academic Press, pp 323–342 Mack Y, Goel T, Shyy W, Haftka RT (2007) Surrogate model-based optimization framework: a case study in aerospace design. In: Evolutionary computation in dynamic and uncertain environments, vol 51. Springer Kluwer Academic Press, pp 323–342
go back to reference Mazzolani FM, Mandara A, Di Lauro G (2004) Plastic buckling of axially loaded aluminium cylinders: a new design approach. In: 4th international conference on coupled instabilities in metal structures. Rome Mazzolani FM, Mandara A, Di Lauro G (2004) Plastic buckling of axially loaded aluminium cylinders: a new design approach. In: 4th international conference on coupled instabilities in metal structures. Rome
go back to reference Nagendra S, Haftka RT, Gürdal Z, Starnes JH Jr (1994) Buckling and failure characteristics of compression-loaded stiffened composite panels with a hole. Compos Struct 28(1):1–17CrossRef Nagendra S, Haftka RT, Gürdal Z, Starnes JH Jr (1994) Buckling and failure characteristics of compression-loaded stiffened composite panels with a hole. Compos Struct 28(1):1–17CrossRef
go back to reference Noor AK, Venneri SL, Paul DB, Hopkins MA (2000) Structures technology for future aerospace systems. Comput Struct 74(5):507–519CrossRef Noor AK, Venneri SL, Paul DB, Hopkins MA (2000) Structures technology for future aerospace systems. Comput Struct 74(5):507–519CrossRef
go back to reference Ooka R, Komamura K (2009) Optimal design method for building energy systems using genetic algorithms. Build Environ 44(7):1538–1544CrossRef Ooka R, Komamura K (2009) Optimal design method for building energy systems using genetic algorithms. Build Environ 44(7):1538–1544CrossRef
go back to reference Panda S, Padhy NP (2008) Comparison of particle swarm optimization and genetic algorithm for FACTS-based controller design. Appl Soft Comput 8(4):1418–1427CrossRef Panda S, Padhy NP (2008) Comparison of particle swarm optimization and genetic algorithm for FACTS-based controller design. Appl Soft Comput 8(4):1418–1427CrossRef
go back to reference Park O, Haftka RT, Sankar BV, Starnes JH Jr, Nagendra S (2001) Analytical-experimental correlation for a stiffened composite panel loaded in axial compression. J Aircraft 38(2):379– 387CrossRef Park O, Haftka RT, Sankar BV, Starnes JH Jr, Nagendra S (2001) Analytical-experimental correlation for a stiffened composite panel loaded in axial compression. J Aircraft 38(2):379– 387CrossRef
go back to reference Park C, Kim NH, Haftka RT (2012) Estimating probability of failure of composite laminated panel with multiple potential failure modes. In: 53rd AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference. Honolulu, AIAA-2012-1592 Park C, Kim NH, Haftka RT (2012) Estimating probability of failure of composite laminated panel with multiple potential failure modes. In: 53rd AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference. Honolulu, AIAA-2012-1592
go back to reference Queipo NV, Haftka RT, Shyy W, Geol T, Vaidyanathan R, Tucker PK (2005) Surrogate-based analysis and optimization. Prog Aerosp Sci 41(1):1–28CrossRef Queipo NV, Haftka RT, Shyy W, Geol T, Vaidyanathan R, Tucker PK (2005) Surrogate-based analysis and optimization. Prog Aerosp Sci 41(1):1–28CrossRef
go back to reference Reiko T (1989) Distributed genetic algorithms. In: Proceedings of 3rd ICGA, pp 434–439 Reiko T (1989) Distributed genetic algorithms. In: Proceedings of 3rd ICGA, pp 434–439
go back to reference Sadeghifar M, Bagheri M, Jafari AA (2010) Multiobjective optimization of orthogonally stiffened cylindrical shells for minimum weight and maximum axial buckling load. Thin-Walled Struct 48(12):979–988CrossRef Sadeghifar M, Bagheri M, Jafari AA (2010) Multiobjective optimization of orthogonally stiffened cylindrical shells for minimum weight and maximum axial buckling load. Thin-Walled Struct 48(12):979–988CrossRef
go back to reference Schultz MR, Nemeth MP (2010) Buckling imperfection sensitivity of axially compressed orthotropic cylinders. In: 51st AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference. Orlando, AIAA-2010-2531 Schultz MR, Nemeth MP (2010) Buckling imperfection sensitivity of axially compressed orthotropic cylinders. In: 51st AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference. Orlando, AIAA-2010-2531
go back to reference Thompson JMT, Hunt GW (1984) Elastic instability phenomena. Wiley, Chicester Thompson JMT, Hunt GW (1984) Elastic instability phenomena. Wiley, Chicester
go back to reference Timoshenko SP, Gere JM (1961) Theory of elastic stability. McGraw-Hill Timoshenko SP, Gere JM (1961) Theory of elastic stability. McGraw-Hill
go back to reference Venkataraman S, Lamberti L, Haftka RT, Johnson TF (2003) Challenges in comparing numerical solutions for optimum weights of stiffened shells. J Spacecraft Rockets 40(2):183–192CrossRef Venkataraman S, Lamberti L, Haftka RT, Johnson TF (2003) Challenges in comparing numerical solutions for optimum weights of stiffened shells. J Spacecraft Rockets 40(2):183–192CrossRef
go back to reference Vitali R, Park O, Haftka RT, Sankar BV, Rose CA (2002) Structural optimization of a hat-stiffened panel using response surfaces. J Aircraft 39(1):158–166CrossRef Vitali R, Park O, Haftka RT, Sankar BV, Rose CA (2002) Structural optimization of a hat-stiffened panel using response surfaces. J Aircraft 39(1):158–166CrossRef
go back to reference Wang B, Hao P, Du KF, Li G (2011) Knockdown factor based on imperfection sensitivity analysis for stiffened shells. Int J Aerosp Lightweight Struct 1(2):315–333CrossRef Wang B, Hao P, Du KF, Li G (2011) Knockdown factor based on imperfection sensitivity analysis for stiffened shells. Int J Aerosp Lightweight Struct 1(2):315–333CrossRef
go back to reference Wang B, Hao P, Li G, Fang YC, Wang XJ, Zhang X (2013) Determination of realistic worst imperfection for cylindrical shells using surrogate model. Struct Multidisc Optim 48(4):777– 794CrossRef Wang B, Hao P, Li G, Fang YC, Wang XJ, Zhang X (2013) Determination of realistic worst imperfection for cylindrical shells using surrogate model. Struct Multidisc Optim 48(4):777– 794CrossRef
go back to reference Wu H, Yan Y, Yan W, Liao BH (2010) Adaptive approximation-based optimization of composite advanced grid-stiffened cylinder. Chinese J Aeronaut 23(4):423–429 Wu H, Yan Y, Yan W, Liao BH (2010) Adaptive approximation-based optimization of composite advanced grid-stiffened cylinder. Chinese J Aeronaut 23(4):423–429
Metadata
Title
Two-stage size-layout optimization of axially compressed stiffened panels
Authors
Bo Wang
Peng Hao
Gang Li
Kuo Tian
Kaifan Du
Xiaojun Wang
Xi Zhang
Xiaohan Tang
Publication date
01-08-2014
Publisher
Springer Berlin Heidelberg
Published in
Structural and Multidisciplinary Optimization / Issue 2/2014
Print ISSN: 1615-147X
Electronic ISSN: 1615-1488
DOI
https://doi.org/10.1007/s00158-014-1046-6

Other articles of this Issue 2/2014

Structural and Multidisciplinary Optimization 2/2014 Go to the issue

ACKNOWLEDGEMENT TO THE REVIEWERS

Thanks to our reviewers

Premium Partners