Skip to main content
SpringerLink
Log in

Lagrangian finite element method with nodal integration for fluid–solid interaction

  • Published:
Computational Particle Mechanics Aims and scope Submit manuscript

Abstract

This work presents a fully Lagrangian Finite Element Method (FEM) with nodal integration for the simulation of fluid–structure interaction (FSI) problems. The Particle Finite Element Method (PFEM) is used to solve the incompressible fluids and to track their evolving free surface, while the solid bodies are modeled with the standard FEM. The coupled problem is solved through a monolithic approach to ensure a strong FSI coupling. Accuracy and convergence of the proposed nodal integration method are proved against several benchmark tests, involving complex interactions between unsteady free-surface fluids and solids undergoing large displacements. A very good agreement with the numerical and experimental results of the literature is obtained. The numerical results of the nodal integration algorithm are also compared to those given by a standard Gaussian method, and their upper-bound convergent behavior is also discussed.

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
Fig. 21
Fig. 22

Similar content being viewed by others

References

  1. Belytschko T, Bindeman LP (1993) Assumed strain stabilization of eight node hexahedral element. Comput Methods Appl Mech Eng 105:225–260

    Article  MATH  Google Scholar 

  2. Belytschko T, Liu WK, Moran B, Elkhodadry KI (2014) Nonlinear finite elements for continua and structures, 2nd edn. Wiley, New York

    Google Scholar 

  3. Brezzi F (1974) On the existence, uniqueness and approximation of saddle-point problems arising from lagrange multipliers. Revue francaise d’automatique, informatique, recherche opérationnelle. Série rouge. Analyse numérique 8(R–2):129–151

  4. Cerquaglia ML, Thomas D, Boman R, Terrapon V, Ponthot JP (2019) A fully partitioned lagrangian framework for fsi problems characterized by free surfaces, large solid deformations and displacements, and strong added-mass effects. Comput Methods Appl Mech Eng 348:409–442

    Article  MathSciNet  MATH  Google Scholar 

  5. Cremonesi M, Frangi A, Perego U (2010) A lagrangian finite element approach for the analysis of fluid-structure interaction problems. Int J Numer Methods Eng 84(5):610–630

    MathSciNet  MATH  Google Scholar 

  6. Cremonesi M, Meduri S, Perego U (2019) Lagrangian–Eulerian enforcement of non-homogeneous boundary conditions in the particle finite element method. Comput Part Mech 7:1–16

    Google Scholar 

  7. Dohrmann CR, Heinstein MW, Jung J, Key SW, Witkowski WR (2000) Node-based uniform strain elements for three-node triangular and four-node tetrahedral meshes. Int J Numer Methods Eng 47(9):1549–1568

    Article  MATH  Google Scholar 

  8. Feng H, Cui XY, Li GY (2016) A stable nodal integration method with strain gradient for static and dynamic analysis of solid mechanics. Eng Anal Boundary Elem 62:78–92

    Article  MathSciNet  MATH  Google Scholar 

  9. Franci A, Cremonesi M (2017) On the effect of standard PFEM remeshing on volume conservation in free-surface fluid flow problems. Comput Part Mech 4(3):331–343

    Article  Google Scholar 

  10. Franci A, Oñate E, Carbonell JM (2015) On the effect of the bulk tangent matrix in partitioned solution schemes for nearly incompressible fluids. Int J Numer Meth Eng 102(3–4):257–277

    Article  MathSciNet  MATH  Google Scholar 

  11. Franci A, Oñate E, Carbonell JM (2016a) Unified lagrangian formulation for solid and fluid mechanics and FSI problems. Comput Methods Appl Mech Eng 298:520–547

    Article  MathSciNet  MATH  Google Scholar 

  12. Franci A, Oñate E, Carbonell JM (2016b) Velocity-based formulations for standard and quasi-incompressible hypoelastic-plastic solids. Int J Numer Meth Eng 107(11):970–990

    Article  MathSciNet  MATH  Google Scholar 

  13. Franci A, de Pouplana I, Casas G, Celigueta MA, González-Usúa J, Oñate E (2019) PFEM–DEM for particle-laden flows with free surface. Comput Part Mech 7:1–20

    Google Scholar 

  14. Franci A, Cremonesi M, Perego U, Oñate E (2020) A lagrangian nodal integration method for free-surface fluid flows. Comput Methods Appl Mech Eng 361:112816

    Article  MathSciNet  MATH  Google Scholar 

  15. Idelsohn SR, Oñate E, Del Pin F (2004) The particle finite element method: a powerful tool to solve incompressible flows with free-surfaces and breaking waves. Int J Numer Meth Eng 61(7):964–989

    Article  MathSciNet  MATH  Google Scholar 

  16. Idelsohn SR, Oñate E, Del Pin F, Calvo N (2006) Fluid-structure interaction using the particle finite element method. Comput Methods Appl Mech Eng 195(17–18):2100–2113

    Article  MathSciNet  MATH  Google Scholar 

  17. Idelsohn SR, Marti J, Limache A, Oñate E (2008) Unified lagrangian formulation for elastic solids and incompressible fluids: applications to fluid-structure interaction problems via the PFEM. Comput Methods Appl Mech Eng 197(19–20):1762–1776

    Article  MathSciNet  MATH  Google Scholar 

  18. Li E, Zhang Z, Chang CC, Liu GR, Li Q (2015) Numerical homogenization for incompressible materials using selective smoothed finite element methods. Compos Struct 123:216–232

    Article  Google Scholar 

  19. Liu GR, Zhang GY (2008) Upper bound solution to elasticity problems: a unique property of linearly conforming point interpolation method (LC-PIM). Int J Numer Methods Eng 74:1128–1161

    Article  MathSciNet  MATH  Google Scholar 

  20. Liu GR, Nguyen TT, Dai KY, Lam KY (2006) Theoretical aspects of the smoothed finite element method (SFEM). Int J Nume Methods Eng 71(8):902–930

    Article  MathSciNet  MATH  Google Scholar 

  21. Liu GR, Nguyen TT, Nguyen-Xuan H, Lam KY (2009) A node-based smoothed finite element method (NS-FEM) for upper bound solutions to solid mechanics problems. Comput Struct 87:14–26

    Article  Google Scholar 

  22. Lobovský L, Botia-Vera E, Castellana F, Mas-Soler J, Souto-Iglesias A (2014) Experimental investigation of dynamic pressure loads during dam break. J Fluids Struct 48:407–434

    Article  Google Scholar 

  23. Meduri S, Cremonesi M, Perego U (2019) An efficient runtime mesh smoothing technique for 3d explicit lagrangian free-surface fluid flow simulations. Int J Numer Meth Eng 117(4):430–452

    Article  MathSciNet  Google Scholar 

  24. Meduri S, Cremonesi M, Perego U, Bettinotti O, Kurkchubasche A, Oancea VM (2018) A partitioned fully explicit lagrangian finite element method for highly nonlinear fluid-structure interaction problems. Int J Numer Meth Eng 113:43–64

    Article  MathSciNet  Google Scholar 

  25. Monforte L, Navas P, Carbonell JM, Arroyo M, Gens A (2019) Low-order stabilized finite element for the full biot formulation in soil mechanics at finite strain. Int J Numer Anal Meth Geomech 43(7):1488–1515

    Article  Google Scholar 

  26. Nguyen-Thoi T, Liu GR, Lam KY, Zhang GY (2009) A face-based smoothed finite element method (FS-FEM) for 3d linear and geometrically non-linear solid mechanics problems using 4-node tetrahedral elements. Int J Numer Methods Eng 78(3):324–353

    Article  MathSciNet  MATH  Google Scholar 

  27. Oñate E, Idelsohn SR, Del Pin F, Aubry R (2004) The particle finite element method. An overview. Int J Comput Methods 1:267–307

    Article  MATH  Google Scholar 

  28. Oñate E, Franci A, Carbonell JM (2014) Lagrangian formulation for finite element analysis of quasi-incompressible fluids with reduced mass losses. Int J Numer Meth Fluids 74(10):699–731

    Article  MathSciNet  Google Scholar 

  29. Ryzhakov P, Oñate E, Idelsohn SR (2012) Improving mass conservation in simulation of incompressible flows. Int J Numer Methods Eng 90:1435–1451

    Article  MathSciNet  MATH  Google Scholar 

  30. Salazar F, San-Mauro J, Celigueta MA, Oñate E (2019) Shockwaves in spillways with the particle finite element method. Comput Part Mech 7:1–13

    Google Scholar 

  31. Sun P, Ming F, Zhang A (2015) Numerical simulation of interactions between free surface and rigid body using a robust SPH method. Ocean Eng 98:32–49

    Article  Google Scholar 

  32. Walhorn E, Kolke A, Hubner B, Dinkler D (2005) Fluid-structure coupling within a monolithic model involving free surface flows. Comput Struct Methods Appl Mech Eng 83(25–26):2100–2111

    Google Scholar 

  33. Yettou EM, Desrochers A, Champoux Y (2006) Experimental study on the water impact of a symmetrical wedge. Fluid Dyn Res 38(1):47–66

    Article  MATH  Google Scholar 

  34. Yuan WH, Wang B, Zhang W, Jiang Q, Feng XT (2019) Development of an explicit smoothed particle finite element method for geotechnical applications. Comput Geotech 106:42–51

    Article  Google Scholar 

  35. Zhang ZQ, Liu GR, Khoo BC (2012) Immersed smoothed finite element method for two dimensional fluid-structure interaction problems. Int J Numer Methods Eng 90:1292–1320

    Article  MathSciNet  MATH  Google Scholar 

  36. Zhang W, Yuan WH, Dai B (2018) Smoothed particle finite-element method for large-deformation problems in geomechanics. Int J Geomech 18(4):04018010

    Article  Google Scholar 

  37. Zhang X, Oñate E, Torres SAG, Bleyer J, Krabbenhoft K (2019a) A unified lagrangian formulation for solid and fluid dynamics and its possibility for modelling submarine landslides and their consequences. Comput Methods Appl Mech Eng 343:314–338

    Article  MathSciNet  MATH  Google Scholar 

  38. Zhang ZL, Long T, Chang JZ, Liu MB (2019b) A smoothed particle element method (SPEM) for modeling fluid-structure interaction problems with large fluid deformations. Comput Methods Appl Mech Eng 356:261–293

    Article  MathSciNet  MATH  Google Scholar 

  39. Zheng W, Liu GR (2018) Smoothed finite element methods (S-FEM): an overview and recent developments. Arch Comput Methods Eng 25:397–435

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The Spanish Ministry of Economy and Competitiveness (Ministerio de Economia y Competitividad, MINECO) through the project PRECISE (BIA2017- 83805-R) is gratefully acknowledged by the author for the economic support.

Author information

Authors and Affiliations

  1. International Center for Numerical Methods in Engineering (CIMNE), Universitat Politecnica de Catalunya, Carrer Gran Capitan, UPC Campus Nord, Barcelona, Spain

    Alessandro Franci

Authors
  1. Alessandro Franci
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alessandro Franci.

Ethics declarations

Conflict of interest

The author declares that he has no conflict of interest.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Franci, A. Lagrangian finite element method with nodal integration for fluid–solid interaction. Comp. Part. Mech. 8, 389–405 (2021). https://doi.org/10.1007/s40571-020-00338-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40571-020-00338-1

Keywords

Search

Navigation