Skip to main content
SpringerLink
Log in

Accurate fluid-structure interaction computations using elements without mid-side nodes

  • Original Paper
  • Published:
Computational Mechanics Aims and scope Submit manuscript

Abstract

The paper proposes a new analysis method for fluid-structure problems, which has nodal consistency at the fluid-structure interface and its calculation efficiency and accuracy are high. The incompressible viscous fluid analysis method using the P1-P1 element based on SUPG/PSPG developed by Tezduyar et al. is used for fluid analysis, while the high-accuracy analysis method based on EFMM developed by the authors is adopted for structure analysis. As the common feature of these methods, it is possible to analyze a fluid or a structure rather accurately by using the first-order triangular or tetrahedral elements. In addition, variables are exchanged exactly at the common nodes on the fluid-structure boundary without deteriorating accuracy and calculation efficiency due to the interpolation of variables between nodes. The present method is applied to a fluid-structure interaction problem by simulating the deformation of a red blood cell.

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

Similar content being viewed by others

References

  1. Zienkiewicz OC, Taylor RL (2000) The finite element method, 5th edn. Elsevier, Amsterdam

    MATH  Google Scholar 

  2. Hughes TJR (1987) The finite element method: linear static and dynamic finite element analysis. Prentice Hall, New York

    MATH  Google Scholar 

  3. Zienkiewicz OC, Taylor RL, Nithiarasu P (2005) The finite element method for fluid dynamics, 6th edn. Elsevier, Amsterdam

    Google Scholar 

  4. Brooks AN, Hughes TJR (1982) Streamline upwind/Petrov–Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier–Stokes equations. Comput Methods Appl Mech Eng 32: 199–259

    Article  MathSciNet  MATH  Google Scholar 

  5. Tezduyar TE (1992) Stabilized finite element formulations for incompressible flow computations. Adv Appl Mech 28: 1–44

    Article  MathSciNet  MATH  Google Scholar 

  6. Tezduyar TE, Mittal S, Ray SE, Shih R (1992) Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements. Comput Methods Appl Mech Eng 95: 221–242

    Article  MATH  Google Scholar 

  7. Tezduyar TE (2003) “Computation of Moving Boundaries and Interfaces and Stabilization Parameters”. Int J Numer Methods Fluids 43: 555–575

    Article  MathSciNet  MATH  Google Scholar 

  8. Tezduyar TE, Sathe S, Keedy R, Stein K (2006) Space-time finite element techniques for computation of fluid-structure interactions. Comput Methods Appl Mech Eng 195: 2002–2027

    Article  MathSciNet  MATH  Google Scholar 

  9. Tezduyar TE, Sathe S (2007) Modeling of fluid-structure interactions with the space-time finite elements: solution techniques. Int J Numer Methods Fluids 54: 855–900

    Article  MathSciNet  MATH  Google Scholar 

  10. Tezduyar TE, Sathe S, Pausewang J, Schwaab M, Christopher J, Crabtree J (2008) Interface projection techniques for fluid-structure interaction modeling with moving-mesh methods. Comput Mech 43: 39–49

    Article  MATH  Google Scholar 

  11. Tezduyar TE, Takizawa K, Moorman C, Wright S, Christopher J (2010) Multiscale sequentially-coupled arterial FSI technique. Comput Mech 46: 17–29

    Article  MathSciNet  MATH  Google Scholar 

  12. Takizawa K, Moorman C, Wright S, Christopher J, Tezduyar TE (2010) Wall shear stress calculations in space-time finite element computation of arterial fluid-structure interactions. Comput Mech 46: 31–41

    Article  MathSciNet  MATH  Google Scholar 

  13. Takizawa K, Tezduyar TE (2011) Multiscale space-time fluid-structure interaction techniques. Comput Mech. doi:10.1007/s00466-011-0571-z

  14. Yagawa G, Matsubara H (2007) Enriched free mesh method: an accuracy improvement for node-based fem, computational plasticity. Comput Methods Appl Sci 7: 207–219

    Article  Google Scholar 

  15. Yagawa G, Yamada T (1996) Free mesh method a new meshless finite element method. Comput Mech 18: 383–386

    Article  MATH  Google Scholar 

  16. Yagawa G, Yamada T (1996) Performance of Parallel computing of free mesh method. In: Proceedings of the 45th National Congress of Theroretical & Applied Mechanics

  17. Berg M, Cheong O, Kreveld M, Overmars M (2008) Computational geometry: algorithms and applications, 3rd edn. Springer, New York

    MATH  Google Scholar 

  18. Inaba M, Fujisawa T, Okuda Y, Yagawa G (2002) Local mesh generation algorithm for free mesh method. The Japan Society of Mechanical Engineers [No. 02-9] Dynamic and Design Conference

  19. Zienkiewicz OC, Taylor RL (1996) Matrix finite element method I (Recision new publication) Kagaku Gijutsu Shuppan, Inc

  20. Newmark NM (1962) A method of computation for structural dynamics, civil engineering. Trans ASCE 127: 1406–1435

    Google Scholar 

  21. Franca LP, Frey SL (1992) Stabilized finite element methods II. The incompressible Navier–Stokes equations. Comput Methods Appl Mech Eng 99: 209–233

    Article  MathSciNet  MATH  Google Scholar 

  22. Zhang S (1997) GPBi-CG generalized product-type methods based on Bi-CG for solving non-symmetriclinear systems. SIAM J Sci Stat Comput 18: 537–551

    Article  MATH  Google Scholar 

  23. Thuthu M, Fujino S (2008) Stability of GPBiCG AR method based on minimization of associate residual. ASCM 5081: 108–120

    Google Scholar 

  24. Belytschko T, Flanagan DF, Kennedy JM (1982) Finite element method with user-controlled meshes for fulid-structure interactions. Comput Methods Appl Mech Eng 33: 689–723

    Article  Google Scholar 

  25. Huetra A, Liu WK (1988) Viscous flow with large free surface motion. Comput Methods Appl Mech Eng 69: 277–324

    Article  Google Scholar 

  26. Huetra A, Liu WK (1988) Viscous flow structure interaction. J Press Vessel Technol 110: 15–21

    Google Scholar 

  27. Nitikipaiboon C, Bathe KJ (1993) An arbitrary Lagrangian-Eulerian velocity potential formulation for fluid-structure interaction. Comput Struct 47: 871–891

    Article  Google Scholar 

  28. Bathe KJ, Nitikitpaiboon C, Wang X (1995) A mixed displacement-based finite element formulation for acoustic fluid-structure interaction. Comput Struct 56: 225–237

    Article  MathSciNet  MATH  Google Scholar 

  29. Bathe KJ, Zhang H, Wang MH (1995) Finite element analysis of incompressible and compressible fluid flows with free interfaces and structural interactions. Comput Struct 56: 193–213

    Article  MATH  Google Scholar 

  30. Chakrabarti SK (2007) Fluid structure interaction and moving boundary problems. WIT Press, Southampton

    Book  MATH  Google Scholar 

  31. Mittal S, Tezduyar TE (1992) A finite element study of incompressible flows past oscillating cylinders and airfoils. Int J Numer Methods Fluids 15: 1073–1118

    Article  Google Scholar 

  32. Tezduyar TE, Behr M, Liou J (1992) A new strategy for finite element computations involving moving boundaries and interfaces – the deforming-spatial -domain/space-time procedure: I. The concept and the preliminary numerical tests. Comput Methods Appl Mech Eng 94: 339–351

    Article  MathSciNet  MATH  Google Scholar 

  33. Tezduyar TE, Behr M, Mittal S, Liou J (1992) A new strategy for finite element computations involving moving boundaries and interfaces – the deforming-spatial-domain/space-time procedure: II. Computation of free-surface flows, two-liquid flows, and flows with drifting cylinders. Comput Methods Appl Mech Eng 94: 353–371

    Article  MathSciNet  MATH  Google Scholar 

  34. Nomura T (1992) Finite element analysis of vortex-induced vibrations of bluff cylinders. J Wind Eng 52: 553

    Google Scholar 

  35. Anagnostopoulos P, Bearman PW (1967) Response characteristics of vortex-exited cylinder at low Reynolds numbers. J Fluids Struct 6: 501–502

    Google Scholar 

  36. Koopman GH (1967) The vortex wakes of vibrating cylinders at low Reynolds numbers. J Fluid Mech 28: 501–502

    Article  Google Scholar 

  37. Tanaka M, Sakamoto T, Sugawara S, Nakajima H, Katahira Y, Ohtsuki S, Kanai H (2008) Blood flow structure and dynamics, and ejection mechanism in the left ventricle. J Cardiol 52: 86–101

    Article  Google Scholar 

  38. Kanno H, Morimoto M, Fujii H, Tsujimura T, Asai H, Noguchi T, Kitamura Y, Miwa S (1995) Primary structure of marine red blood cell-type Pyruvate Kinase (PK) and molecular characterization of PK deficiency identified in the CBA strain. Blood 86: 3205–3210

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Information Sciences and Arts, Toyo University, Kawagoe, Japan

    Yasushi Nakabayashi

  2. Toyo University, Kawagoe, Japan

    Shinsuke Nagaoka & Genki Yagawa

  3. Mechanical Engineering, Sungkyunkwan University, Suwon, Republic of Korea

    Young Jin Kim

Authors
  1. Shinsuke Nagaoka
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yasushi Nakabayashi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Genki Yagawa
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Young Jin Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yasushi Nakabayashi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nagaoka, S., Nakabayashi, Y., Yagawa, G. et al. Accurate fluid-structure interaction computations using elements without mid-side nodes. Comput Mech 48, 269–276 (2011). https://doi.org/10.1007/s00466-011-0620-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00466-011-0620-7

Keywords

Search

Navigation