Skip to main content

Isogeometric Boundary Element Method for Analysis and Design Optimization—A Survey

  • Conference paper
  • First Online:
Numerical Heat Transfer and Fluid Flow

Part of the book series: Lecture Notes in Mechanical Engineering ((LNME))

  • 1971 Accesses

Abstract

Analysis of potential problems related to fluid flow and heat transfer can be solved effectively with Boundary Element Methods (BEMs) due to the reason that the interaction takes place at boundaries. BEMs too suffer the traditional problem of approximated geometry. A recent method called Isogeometric Analysis (IGA) was proposed for exact geometric analysis. The combination of the IGA and BEM leads to Isogeometric Boundary Element Method (IGBEM), which has the feature of exact boundary analysis. It suits well for the problems where boundaries of the domains are of interest like fluid structure interaction, shape optimization, etc. This paper provides a brief review on IGBEM by clearly explaining its methodology, applications, limitations and future directions.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Hughes, T.J., Cottrell, J.A., Bazilevs, Y.: Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput. Methods Appl. Mech. Eng. 194(39–41), 4135–4195 (2005). https://doi.org/10.1016/j.cma.2004.10.008

    Article  MathSciNet  MATH  Google Scholar 

  2. Simpson, R.N., Bordas, S.P., Trevelyan, J., Rabczuk, T.: A two-dimensional isogeometric boundary element method for elastostatic analysis. Comput. Methods Appl. Mech. Eng. 209, 87–100 (2012). https://doi.org/10.1016/j.cma.2011.08.008

    Article  MathSciNet  MATH  Google Scholar 

  3. Gondegaon, S., Voruganti, H.K.: Static structural and modal analysis using Isogeometric analysis. JTAM 46(4), 36–75 (2016). https://doi.org/10.1515/jtam-2016-0020

    Article  MathSciNet  Google Scholar 

  4. Ummidivarapu, V.K., Voruganti, H.K.: Shape optimisation of two-dimensional structures using isogeometric analysis. IJESMS 9(3), 169–176 (2017). https://doi.org/10.1504/IJESMS.2017.085080

    Article  Google Scholar 

  5. Scott, M.A., Simpson, R.N., Evans, J.A., Lipton, S., Bordas, S.P., Hughes, T.J., Sederberg, T.W.: Isogeometric boundary element analysis using unstructured T-splines. Comput. Methods Appl. Mech. Eng. 254, 197–221 (2013). https://doi.org/10.1016/j.cma.2012.11.001

    Article  MathSciNet  MATH  Google Scholar 

  6. Becker, A.A.: The Boundary Element Method in Engineering: A Complete Course. McGraw-Hill, London (1992)

    Google Scholar 

  7. Banerjee, P.K., Butterfield, R.: Boundary Element Methods in Engineering Science. McGraw-Hill, New York (1981)

    MATH  Google Scholar 

  8. Gondegaon, S., Voruganti, H.K.: Spline parameterization of complex planar domains for isogeometric analysis. JTAM 47(1), 18–35 (2017). https://doi.org/10.1515/jtam-2017-0002

    Article  MathSciNet  Google Scholar 

  9. Rogers, D.F.: An Introduction to NURBS: With Historical Perspective. Academeic Press, Elsevier, Oxford (2000)

    Google Scholar 

  10. Lian, H., Kerfriden, P., Bordas, S.: Implementation of regularized isogeometric boundary element methods for gradient-based shape optimization in two-dimensional linear elasticity. Int. J. Numer. Meth. Eng 106(12), 972–1017 (2016). https://doi.org/10.1002/nme.5149

    Article  MathSciNet  MATH  Google Scholar 

  11. Telles, J.C.F.: A self-adaptive co-ordinate transformation for efficient numerical evaluation of general boundary element integrals. Int. J. Numer. Meth. Eng. 24(5), 959–973 (1987). https://doi.org/10.1002/nme.1620240509

    Article  MATH  Google Scholar 

  12. Guiggiani, M., Casalini, P.: Direct computation of Cauchy principal value integrals in advanced boundary elements. Int. J. Numer. Meth. Eng. 24(9), 1711–1720 (1987). https://doi.org/10.1002/nme.1620240908

    Article  MathSciNet  MATH  Google Scholar 

  13. Politis, C., Ginnis, A. I., Kaklis, P. D., Belibassakis, K., Feurer, C.: An isogeometric BEM for exterior potential-flow problems in the plane. In: SIAM/ACM Joint Conference on Geometric and Physical Modeling, pp. 349-354. ACM (2009). https://doi.org/10.1145/1629255.1629302

  14. Beer, G., Mallardo, V., Ruocco, E., Dnser, C.: Isogeometric boundary element analysis of steady incompressible viscous flow, Part 1: plane problems. Comput. Methods in Appl. Mech. Eng. 326, 51–69 (2017). https://doi.org/10.1016/j.cma.2017.08.005

    Article  MathSciNet  Google Scholar 

  15. Gong, Y.P., Dong, C.Y., Qin, X.C.: An isogeometric boundary element method for three dimensional potential problems. J. Comput. Appl. Math. 313, 454–468 (2017). https://doi.org/10.1016/j.cam.2016.10.003

    Article  MathSciNet  MATH  Google Scholar 

  16. Li, K., Qian, X.: Isogeometric analysis and shape optimization via boundary integral. Comput.-Aided Des. 43(11), 1427–1437 (2011). https://doi.org/10.1016/j.cad.2011.08.031

    Article  Google Scholar 

  17. Lian, H., Kerfriden, P., Bordas, S.P.A.: Shape optimization directly from CAD: an isogeometric boundary element approach using T-splines. Comput. Methods Appl. Mech. Eng. 317, 1–41 (2017). https://doi.org/10.1016/j.cma.2016.11.012

    Article  MathSciNet  Google Scholar 

  18. Kostas, K.V., Ginnis, A.I., Politis, C.G., Kaklis, P.D.: Ship-hull shape optimization with a T-spline based BEM isogeometric solver. Comput. Methods Appl. Mech. Eng. 284, 611–622 (2015). https://doi.org/10.1016/j.cma.2014.10.030

    Article  MathSciNet  MATH  Google Scholar 

  19. Gu, J., Zhang, J., Sheng, X., Li, G.: B-spline approximation in boundary face method for three-dimensional linear elasticity. Eng. Anal. Bound. Elem. 35(11), 1159–1167 (2011). https://doi.org/10.1016/j.enganabound.2011.05.013

    Article  MathSciNet  MATH  Google Scholar 

  20. Bai, Y., Dong, C.Y., Liu, Z.Y.: Effective elastic properties and stress states of doubly periodic array of inclusions with complex shapes by isogeometric boundary element method. Compos. Struct. 128, 54–69 (2015). https://doi.org/10.1016/j.compstruct.2015.03.061

    Article  Google Scholar 

  21. Beer, G., Marussig, B., Zechner, J., Dnser, C., Fries, T.P.: Isogeometric boundary element analysis with elasto-plastic inclusions. Part 1: plane problems. Comput. Methods Appl. Mech. Eng. 308, 552–570 (2016). https://doi.org/10.1016/j.cma.2016.03.035

    Article  MathSciNet  Google Scholar 

  22. Peng, X., Atroshchenko, E., Kerfriden, P., Bordas, S.P.A.: Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth. Comput. Methods Appl. Mech. Eng. 316, 151–185 (2017). https://doi.org/10.1016/j.cma.2016.05.038

    Article  MathSciNet  Google Scholar 

  23. Nguyen, B.H., Tran, H.D., Anitescu, C., Zhuang, X., Rabczuk, T.: An isogeometric symmetric Galerkin boundary element method for two-dimensional crack problems. Comput. Methods Appl. Mech. Eng. 306, 252–275 (2016). https://doi.org/10.1016/j.cma.2016.04.002

    Article  MathSciNet  Google Scholar 

  24. https://sourceforge.net/projects/igabem/

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hari K. Voruganti .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Ummidivarapu, V.K., Voruganti, H.K. (2019). Isogeometric Boundary Element Method for Analysis and Design Optimization—A Survey. In: Srinivasacharya, D., Reddy, K. (eds) Numerical Heat Transfer and Fluid Flow. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-13-1903-7_21

Download citation

  • DOI: https://doi.org/10.1007/978-981-13-1903-7_21

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-1902-0

  • Online ISBN: 978-981-13-1903-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics