Skip to main content
SpringerLink
Log in

Shape optimization of thin-walled pressure vessel end closures

  • Industrial Application
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

In this paper the problem of shape optimization of thin-walled pressure vessel heads is investigated. Shape of a meridian which minimizes the functional containing a depth and capacity of a vessel closure is sought. The meridian is approximated either by the convex Bézier polynomial or by functions with free parameters. Domes consisting of both two- and one-arc are considered. The optimal solutions are obtained using the simulated annealing algorithm.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20

Similar content being viewed by others

References

  • Banichuk NV (1990) Introduction to optimization of structures. Springer, Berlin

    Book  MATH  Google Scholar 

  • Banichuk NV (2002) Optimization of shells from quasi-brittle materials loaded by constant and cyclic forces. Mech Solids 5:99–107

    Google Scholar 

  • Banichuk NV, Ragnedda F, Serra M (2003) Probabilistic guaranteed optimal design of membrane shells against quasi-brittle fracture. Mech Based Des Struct Mach 31(4):459–474

    Article  Google Scholar 

  • Banichuk NV, Barthold FJ, Serra M (2005) Optimization of axisymmetric membrane shells against brittle fracture. Meccanica 40:135–145

    Article  MATH  Google Scholar 

  • Banichuk NV, Yu IS, Makeev EV, Sinitsin AV (2006) Optimal shape design of axisymmetric shells for crack initiation and propagation under cyclic loading. Mech Based Des Struct Mach 33(2):253–269

    Article  Google Scholar 

  • Banichuk NV, Ragnedda F, Serra M (2008) Optimization of mass effectiveness of axisymmetric pressure vessels. Struct Multidiscip Optim 35(5):453–459

    Article  MathSciNet  Google Scholar 

  • Barski M, Krużelecki J (2005) Optimal design of shells against buckling by means of the simulated annealing method. Struct Multidiscip Optim 29:61–72

    Article  Google Scholar 

  • Batchelor MJ, Taylor TE (1995) Equivalent torispherical pressure vessel heads. Int J Press Vessel Pip 7(3):229–244

    Article  Google Scholar 

  • Biezeno CB (1922) Bijdrage tot de berekening van katelfronten. de Ingenieur 37

  • Błachut J (1992) Influence of meridional shaping on the collapse strength of FRP domes. Eng Optim 19:65–80

    Article  Google Scholar 

  • Blachut J (1997) Minimum weight design of internally pressurized domes subjected to plastic load failure. Thin-Walled Struct 22(2):127–146

    Article  Google Scholar 

  • Błachut J, Eschenauer HA (2001) Emerging methods for multidisciplinary optimization. CISM Course and Lectures No 425. Springer, Wien

  • Błachut J, Magnucki K (2008) Strength, stability, and optimization of pressure vessels: review of selected problems. Trans ASME Appl Mech Rev 61(6):1–33

    Google Scholar 

  • Carbonari RC, Muñoz-Rojas PA, Andrade EQ, Paulino GH, Nishimoto K, Silva ECN (2011) Design of pressure vessels using shape optimization: an integrated approach. Int J Press Vessels Pip 88:198–212

    Article  Google Scholar 

  • Csonka P (1966) Membranschalen. Verlag von W. Ernest & Sohn, Berlin

    Google Scholar 

  • Dow M, Nakamura H, Rozvany GIN (1982) Optimal Cupolas of uniform strength: spherical M-shells and axisymmetric T-shells. Ingenieur-Archiv 52:335–353

    Article  MATH  Google Scholar 

  • Elin VD, Haritonov VI (1977) Determination of optimal size of thin-walled vessels. Roboty po Mechanike Sploshnich Sredov, Tula, 107–112 (in Russian)

  • Flügge W (1967) Stresses in shells. Springer, Berlin

    Google Scholar 

  • Hoffman GA (1962a) Minimum weight proportions pressure vessel heads. Trans ASME E 29(4):662–668

    Article  Google Scholar 

  • Hoffman GA (1962b) Optimal proportions of pressure vessel heads. J Aerosp Sci 29(12):1471–1475

    Google Scholar 

  • Kirkpatrick S, Gelatt CD Jr, Vecchi MP (1983) Optimization by simulated annealing. Science 220:671–680

    Article  MathSciNet  MATH  Google Scholar 

  • Krivoshapko SN (2007) Research on general and axisymmetric ellipsoidal shells used as domes, pressure vessels, and tanks. Appl Mech Rev 60(6):336–355

    Article  Google Scholar 

  • Krużelecki J (1979) Some problems of optima design of axially-symmetrical shells in membrane state. Mech Teor Stosow 17(1):75–92 (in Polish)

    MATH  Google Scholar 

  • Krużelecki J (2004) Review of optimal structural design of shells. In: Joniak S, Magnucki K, Mielniczuk J (eds) Proceedings of the Third Conference on Thin-Walled Vessels, Karłów, Poland. Poznań University of Technology, Poznań, pp 35–72

  • Krużelecki J, Stawiarski A (2010) Optimal design of thin-walled columns for buckling under loadings controlled by displacements. Struc Multidiscip Optim 42:305–314

    Article  Google Scholar 

  • Krużelecki J, Życzkowski M (1985) Optimal structural design of shells—a survey. SM Arch 10:101–170

    MATH  Google Scholar 

  • Leit JPV, Topping BHV (1999) Parallel simulated annealing for structural optimization. Comput Struct 73:545–564

    Article  Google Scholar 

  • Lewiński J, Magnucki K (2010) Shaping of a middle surface of a dished head of a circular cylindrical pressure vessels. J Theor Appl Mech 48(2):297–307

    Google Scholar 

  • Łukasiewicz S (1979) Local loads in plates and shells. PWN - Polish Scientific Publishers, Warsaw

    Google Scholar 

  • Magnucki K (1998) Strength and optimization of thin-walled vessels. PWN, Warszawa Poznañ (in Polish)

    Google Scholar 

  • Magnucki K, Lewiński J (1998) Shape optimization of heads of cylindrical pressure vessels. In: Topping BHV (ed) Advances in computational structural mechanics Civil-Comp Ltd., Edinburgh, pp 421–425

  • Magnucki K, Lewiński J (2000) Fully stressed head of a pressure vessel. Thin-Walled Struct 38:167–178

    Article  Google Scholar 

  • Magnucki K, Lewiński J (2003) Optimal design of an ellipsoidal head of a pressure cylindrical vessel. Proc Appl Math Mech 3:517–518

    Article  Google Scholar 

  • Magnucki K, Szyc W, Lewiński J (2002) Minimization of stress concentration factor in cylindrical pressure vessels with ellipsoidal heads. Int J Press Vessel Pip 79:841–846

    Article  Google Scholar 

  • Mansfield EH (1981) An optimum surface of revolution for pressurized shells. Int J Mech Sci 23:57–62

    Article  MATH  Google Scholar 

  • Masters T (1993) Practical Neural Network Recipes in C+ +. Academic Press

  • Middleton J (1979) Optimal design of torispherical pressure vessel end closures. Eng Optim 4:129–138

    Article  Google Scholar 

  • Muc A, Gruba W (2001) Optimization of dome heads using splines conjugated with genetic algorithms. In: Magnucki K, Mielniczuk J (eds) Proceedings of the Second Conference on Thin-Walled Vessels, Karłów, Poland, Wyższa szkoła Pedagogiczna w Zielonej Górze, pp 149–156

  • Nakamura H, Dow M, Rozvany GIN (1981) Optimal spherical cupola of uniform strength: allowance for selfweight. Ingenieur-Archiv 51:159–181

    MATH  Google Scholar 

  • Prager W, Rozvany GIN (1980) Optimal spherical cupola of uniform strength. Ingenieur-Archiv 49:287–293

    Article  MATH  Google Scholar 

  • Stadler W, Krishnan V (1989) Natural structural shapes for shells of revolution in the membrane theory of shells. Struct Optim 1(1):19–27

    Article  Google Scholar 

  • Struble RA (1956) Biezeno pressure vessel heads. J Appl Mech 23:642–645

    MATH  Google Scholar 

  • Timoshenko S (1959) Theory of plates and shells. Mc-Graw Hill, New York

    Google Scholar 

  • van Laarhoven PJM, Aarts EHL (1992) Simulated annealing - theory and applications. Kluwer Academic Publishers, Dordrecht

    Google Scholar 

  • Yushan Z, Wang ZR (1996) Stress analysis of two-arc approximate ellipsoidal pressure vessel heads and parameter optimization. Int J Press Vessel Pip 67:199–202

    Article  Google Scholar 

  • Yushan Z, Wang ZR, Wei C (1996) Stress analysis of approximately ellipsoidal cold-spun tri-arc tank head and parameter optimization. Int J Press Vessel Pip 68:237–242

    Article  Google Scholar 

  • Wilczyński B (2000) Shape optimization to minimize stress concentration in shell structures. In: De Roeck G, Topping BHV (eds) Identification, control and optimisation of engineering structures. Civil-Comp Ltd., Edinburgh, pp 119–132

  • Wilczyński B (2001) Shape optimization of thick pressure vessels. In: Magnucki K, Mielniczuk J (eds) Proceedings of the Second Conference on Thin-Walled Vessels, Karłów, Poland, Wyższa szkoła Pedagogiczna w Zielonej Górze, pp 201–213

  • Życzkowski M (1992) Recent advances in optimal structural design of shells. Eur J Mech A/Solids 11(Special issue):5–24

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Applied Mechanics, Cracow University of Technology, Jana Pawła II 37, 31-864, Kraków, Poland

    Jacek Krużelecki & Rafał Proszowski

Authors
  1. Jacek Krużelecki
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rafał Proszowski
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jacek Krużelecki.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Krużelecki, J., Proszowski, R. Shape optimization of thin-walled pressure vessel end closures. Struct Multidisc Optim 46, 739–754 (2012). https://doi.org/10.1007/s00158-012-0789-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-012-0789-1

Keywords

Search

Navigation