Skip to main content
SpringerLink
Log in

Isogeometric analysis with embedded stiffened shells for the hull structural mechanical analysis

  • Original article
  • Published:
Journal of Marine Science and Technology Aims and scope Submit manuscript

Abstract

Isogeometric analysis (IGA) is a newly emerging numerical method, aiming to bridge the gap between computer-aided design systems and computer-aided engineering. IGA shows many advantages compared with the traditional finite element analysis. However, in ship building industry, IGA has not got enough attention. There have been a few works that introduce IGA to hull structural analysis. However, these approaches use only shell elements to simulate stiffened shell structures, which is a great waste of computational power. In this paper, a 4 degrees-of-freedom (DOFs) Kirchhoff–Love curved shell element and a 4-DOFs Euler–Bernoulli beam element are constructed in the IGA framework, and the weighted non-symmetric Nitsche’s method is used to couple shell patches and beam patches that embedded in the former. Using the elements and coupling methods, the modeling of stiffened shell structures is greatly simplified, and the integration of modeling and analysis is realized. A cylinder stiffened shell structure and a typical hull block structure are taken as numerical examples to verify the robustness and correctness of the methods. The commercial software ANSYS 17.0 is used to obtain reference solutions. The maximum relative error of all the displacements in the two examples is 1.81% and the maximum relative error of Von-Mises stresses is 2.66%, which is acceptable in engineering.

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

Similar content being viewed by others

References

  1. Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput Methods Appl Mech Eng 194:4135–4195. https://doi.org/10.1016/j.cma.2004.10.008

    Article  MathSciNet  MATH  Google Scholar 

  2. Yu Y-Y, Lin Y, Ji Z-S (2009) New method for ship finite element method preprocessing based on a 3D parametric technique. J Mar Sci Technol 14:398–407. https://doi.org/10.1007/s00773-009-0058-1

    Article  Google Scholar 

  3. Yu Y, Wang Y, Li K, Lin Y (2018) An isogeometric analysis approach for hull structural mechanical analysis. Proceedings of International Offshore Polar Engineering Conference, vol 2018-June, pp 421–7

  4. Wang Y, Yu Y, Lin Y (2021) Isogeometric analysis with the Reissner–Mindlin shell for hull structural mechanical analysis. Ocean Eng 231:109047. https://doi.org/10.1016/j.oceaneng.2021.109047

    Article  Google Scholar 

  5. Kiendl J, Bletzinger K-U, Linhard J, Wüchner R (2009) Isogeometric shell analysis with Kirchhoff–Love elements. Comput Methods Appl Mech Eng 198:3902–3914. https://doi.org/10.1016/j.cma.2009.08.013

    Article  MathSciNet  MATH  Google Scholar 

  6. Kiendl J, Bazilevs Y, Hsu M-C, Wüchner R, Bletzinger K-U (2010) The bending strip method for isogeometric analysis of Kirchhoff–Love shell structures comprised of multiple patches. Comput Methods Appl Mech Eng 199:2403–2416. https://doi.org/10.1016/j.cma.2010.03.029

    Article  MathSciNet  MATH  Google Scholar 

  7. Babuska I (1973) The finite element method with penalty. Math Comput 27:221. https://doi.org/10.2307/2005611

    Article  MathSciNet  MATH  Google Scholar 

  8. Breitenberger M, Apostolatos A, Philipp B, Wüchner R, Bletzinger K-U (2015) Analysis in computer aided design: nonlinear isogeometric B-Rep analysis of shell structures. Comput Methods Appl Mech Eng 284:401–457. https://doi.org/10.1016/j.cma.2014.09.033

    Article  MathSciNet  MATH  Google Scholar 

  9. Babuška I (1973) The finite element method with Lagrangian multipliers. Numer Math 20:179–192. https://doi.org/10.1007/BF01436561

    Article  MathSciNet  MATH  Google Scholar 

  10. Schuß S, Dittmann M, Wohlmuth B, Klinkel S, Hesch C (2019) Multi-patch isogeometric analysis for Kirchhoff–Love shell elements. Comput Methods Appl Mech Eng 349:91–116. https://doi.org/10.1016/j.cma.2019.02.015

    Article  MathSciNet  MATH  Google Scholar 

  11. Nitsche J (1971) Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. Abhandlungen Aus Dem Math Semin Der Univ Hambg 36:9–15. https://doi.org/10.1007/BF02995904

    Article  MATH  Google Scholar 

  12. Embar A, Dolbow J, Harari I (2010) Imposing Dirichlet boundary conditions with Nitsche’s method and spline-based finite elements. Int J Numer Methods Eng 83:877–898. https://doi.org/10.1002/nme.2863

    Article  MathSciNet  MATH  Google Scholar 

  13. Ruess M, Schillinger D, Özcan AI, Rank E (2014) Weak coupling for isogeometric analysis of non-matching and trimmed multi-patch geometries. Comput Methods Appl Mech Eng 269:46–71. https://doi.org/10.1016/j.cma.2013.10.009

    Article  MathSciNet  MATH  Google Scholar 

  14. Nguyen VP, Kerfriden P, Brino M, Bordas SPA, Bonisoli E (2014) Nitsche’s method for two and three dimensional NURBS patch coupling. Comput Mech 53:1163–1182. https://doi.org/10.1007/s00466-013-0955-3

    Article  MathSciNet  MATH  Google Scholar 

  15. Guo Y, Ruess M (2015) Nitsche’s method for a coupling of isogeometric thin shells and blended shell structures. Comput Methods Appl Mech Eng 284:881–905. https://doi.org/10.1016/j.cma.2014.11.014

    Article  MathSciNet  MATH  Google Scholar 

  16. Griebel M, Schweitzer MA (2003) A particle-partition of unity method part V: boundary conditions. Geom Anal Nonlinear Partial Differ Equ. https://doi.org/10.1007/978-3-642-55627-2_27

    Article  MATH  Google Scholar 

  17. Baumann CE, Oden JT (1999) A discontinuoushp finite element method for the Euler and Navier–Stokes equations. Int J Numer Methods Fluids 31:79–95. https://doi.org/10.1002/(SICI)1097-0363(19990915)31:1%3c79::AID-FLD956%3e3.0.CO;2-C

    Article  MATH  Google Scholar 

  18. Guo Y, Ruess M, Schillinger D (2017) A parameter-free variational coupling approach for trimmed isogeometric thin shells. Comput Mech 59:693–715. https://doi.org/10.1007/s00466-016-1368-x

    Article  MathSciNet  MATH  Google Scholar 

  19. Annavarapu C, Hautefeuille M, Dolbow JE (2012) A robust Nitsche’s formulation for interface problems. Comput Methods Appl Mech Eng 225–228:44–54. https://doi.org/10.1016/j.cma.2012.03.008

    Article  MathSciNet  MATH  Google Scholar 

  20. Jiang W, Annavarapu C, Dolbow JE, Harari I (2015) A robust Nitsche’s formulation for interface problems with spline-based finite elements. Int J Numer Methods Eng 104:676–696. https://doi.org/10.1002/nme.4766

    Article  MathSciNet  MATH  Google Scholar 

  21. Hu Q, Chouly F, Hu P, Cheng G, Bordas SPA (2018) Skew-symmetric Nitsche’s formulation in isogeometric analysis: Dirichlet and symmetry conditions, patch coupling and frictionless contact. Comput Methods Appl Mech Eng 341:188–220. https://doi.org/10.1016/j.cma.2018.05.024

    Article  MathSciNet  MATH  Google Scholar 

  22. Hirschler T, Bouclier R, Duval A, Elguedj T, Morlier J (2019) The embedded isogeometric Kirchhoff–Love shell: from design to shape optimization of non-conforming stiffened multipatch structures. Comput Methods Appl Mech Eng 349:774–797. https://doi.org/10.1016/j.cma.2019.02.042

    Article  MathSciNet  MATH  Google Scholar 

  23. Qin XC, Dong CY, Wang F, Qu XY (2017) Static and dynamic analyses of isogeometric curvilinearly stiffened plates. Appl Math Model 45:336–364. https://doi.org/10.1016/j.apm.2016.12.035

    Article  MathSciNet  MATH  Google Scholar 

  24. Piegl L, Tiller W (1997) The NURBS book. Springer, Berlin

    Book  Google Scholar 

  25. Hughes TJR, Liu WK (1981) Nonlinear finite element analysis of shells: Part I. Three-dimensional shells. Comput Methods Appl Mech Eng 26:331–362. https://doi.org/10.1016/0045-7825(81)90121-3

    Article  MATH  Google Scholar 

  26. Ferguson GH, Clark RD (1979) A variable thickness, curved beam and shell stiffening element with shear deformations. Int J Numer Methods Eng 14:581–592. https://doi.org/10.1002/nme.1620140409

    Article  MATH  Google Scholar 

  27. Moler CB, Stewart GW (1973) An algorithm for generalized matrix eigenvalue problems. SIAM J Numer Anal 10:241–256. https://doi.org/10.1137/0710024

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant no. 51409042).

Author information

Authors and Affiliations

  1. Ship CAD Engineering Center, Dalian University of Technology, Dalian, Liaoning, China

    Yao Wang, Yanyun Yu & Yan Lin

  2. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, Liaoning, China

    Yao Wang, Yanyun Yu & Yan Lin

Authors
  1. Yao Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yanyun Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yan Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yanyun Yu.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, Y., Yu, Y. & Lin, Y. Isogeometric analysis with embedded stiffened shells for the hull structural mechanical analysis. J Mar Sci Technol 27, 786–805 (2022). https://doi.org/10.1007/s00773-021-00868-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00773-021-00868-0

Keywords

Search

Navigation