0
Research Papers: Fluid-Structure Interaction

Finite Difference-Based Cellular Automaton Technique for Structural and Fluid–Structure Interaction Applications

[+] Author and Article Information
Y. W. Kwon

Department of Mechanical and
Aerospace Engineering,
Naval Postgraduate School,
Monterey, CA 93943
e-mail: ywkwon@nps.edu

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received November 15, 2016; final manuscript received December 9, 2016; published online March 10, 2017. Special. Editor: Jong Chull Jo.

J. Pressure Vessel Technol 139(4), 041301 (Mar 10, 2017) (9 pages) Paper No: PVT-16-1215; doi: 10.1115/1.4035464 History: Received November 15, 2016; Revised December 09, 2016

A new cellular automaton technique was developed based on the finite difference scheme to analyze structures such as beams and plates as well as the acoustic wave equation. The technique uses rules for a cell, and the rules are applied to all the cells repeatedly. The technique is very easy to write a computer code and computationally efficient. Like the standard cellular automaton, many different boundary conditions can be applied easily to the new technique. The technique was applied to both structural and fluid–structure interaction problems. The fluid domain was modeled as either the acoustic medium without flow using the newly developed cellular automaton rules or the fluid flow medium using the lattice Boltzmann technique. Multiple example problems were presented to demonstrate the new technique. Those included dynamic analyses of beams and plates, acoustic wave problems, and coupled fluid–structure interaction problems.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Zienkiewicz, O. C. , and Taylor, R. L. , 1991, The Finite Element Method, 4th ed., McGraw-Hill, London, UK.
Bathe, K.-J. , 1996, Finite Element Procedures, Prentice Hall, Upper Saddle River, NJ.
Hughes, T. J. R. , 2000, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, Englewood Cliffs, NJ.
Akin, J. E. , 1986, Finite Element Analysis for Undergraduate, Academic Press, London, UK.
Kwon, Y. W. , and Bang, H.-C. , 2000, The Finite Element Method Using Matlab, 2nd ed., CRC Press, Boca Raton, FL.
Atluri, S. N. , 2002, The Meshless Local Petrov–Galerkin (MLPG) Method, Tech Science Press, Duluth, GA.
Atluri, S. N. , and Zhu, T. , 2000, “ The Meshless Local Petrov–Galerkin (MLPG) Approach for Solving Problems in Elasto-Statics,” Comput. Mech., 25(2), pp. 169–179. [CrossRef]
Beissel, S. , and Belytschko, T. , 1996, “ Nodal Integration of the Element-Free Galerkin Method,” Comput. Methods Appl. Mech. Eng., 139(1–4), pp. 49–74. [CrossRef]
Belytschko, T. , Gu, L. , and Lu, Y. Y. , 1994, “ Fracture and Crack Growth by Element-Free Galerkin Methods,” Model. Simul. Mater. Sci. Eng., 2(3A), pp. 519–534. [CrossRef]
Belytschko, T. , Guo, Y. , Liu, W. K. , and Xiao, S. P. , 2000, “ A Unified Stability Analysis of Meshfree Particle Methods,” Int. J. Numer. Methods Eng., 48(9), pp. 1359–1400. [CrossRef]
Moukalled, F. , Mangani, L. , and Darwish, M. , 2015, The Finite Volume Method in Computational Fluid Dynamics: An Advanced Introduction With Open FOAM and Matlab, Springer, Heidelberg, Germany.
Patankar, S. V. , 1980, Numerical Heat Transfer and Fluid Flow, Taylor & Francis, New York.
Chen, H. , 1993, “ Discrete Boltzmann Systems and Fluid Flows,” Comp. Phys., 7(6), pp. 632–637. [CrossRef]
Chen, S. , and Doolen, G. D. , 1998, “ Lattice Boltzmann Method for Fluid Flow,” Annu. Rev. Fluid Mech., 30(1), pp. 329–364. [CrossRef]
Guo, Z. , and Zhao, T. S. , 2002, “ Lattice Boltzmann Model for Incompressible Flows Through Porous Media,” Phys. Rev. E, 66(3), p. 036304. [CrossRef]
Tang, G. H. , Tao, W. Q. , and He, Y. L. , 2005, “ Gas Slippage Effect on Microscale Porous Flow Using the Lattice Boltzmann Method,” Phys. Rev. E, 72(5), p. 056301. [CrossRef]
Nourgaliev, R. , Dinh, T. , Theofanous, T. , and Joseph, D. , 2003, “ The Lattice Boltzmann Equation Method: Theoretical Interpretation, Numerics and Implications,” Int. J. Multiphase Flow, 29(1), pp. 117–169. [CrossRef]
D'Humières, D. , 1992, “ Generalized Lattice–Boltzmann Equations,” Rarefied Gas Dynamics-Theory and Simulations; Proceedings of the 18th International Symposium on Rarefied Gas Dynamics, University of British Columbia, Vancouver, Canada, pp. 450–458.
Lallemand, P. , and Luo, L.-S. , 2000, “ Theory of the Lattice Boltzmann Method: Dispersion, Dissipation, Isotropy, Galilean Invariance, and Stability,” Phys. Rev. E, 61(6), pp. 6546–6562. [CrossRef]
Kwon, Y. W. , and Jo, J. C. , 2009, “ Development of Weighted Residual Based Lattice Boltzmann Techniques for Fluid–Structure Interaction Application,” ASME J. Pressure Vessel Technol., 131(3), p. 031304. [CrossRef]
Blair, S. R. , and Kwon, Y. W. , 2015, “ Modeling of Fluid–Structure Interaction Using Lattice Boltzmann and Finite Element Methods,” ASME J. Pressure Vessel Technol., 137(2), p. 021302. [CrossRef]
Wolfram, S. , 1986, “ Cellular Automaton Fluids 1: Basic Theory,” J. Stat. Phys., 45(3), pp. 471–526. [CrossRef]
Frisch, U. , Hasslacher, B. , and Pomeau, Y. , 1986, “ Lattice-Gas Automata for the Navier–Stokes Equation,” Phys. Rev. Lett., 56(14), pp. 1505–1508. [CrossRef] [PubMed]
Doolen, G. , ed., 1990, Lattice Gas Method for Partial Differential Equations, Addison-Wesley, Ann Arbor, MI.
Perdang, J. , and Lejeune, A. , ed., 1993, Cellular Automata: Prospect in Astrophysical Applications, World Scientific, Singapore.
Wolfram, S. , 1994, Cellular Automata and Complexity: Collected Papers, Addison-Wesley, Reading, MA.
Wolfram, S. , ed., 1986, Theory and Application of Cellular Automata, Addison-Wesley, Reading, MA.
Preston, K., Jr. , and Duff, M. J. B. , 1985, Modern Cellular Automata: Theory and Applications, Plenum, New York.
Wolfram, S. , 1983, “ Statistical Mechanics of Cellular Automata,” Rev. Mod. Phys., 55(3), pp. 601–644. [CrossRef]
Chopard, B. , and Droz, M. , 1998, Cellular Automata Modeling of Physical Systems, Cambridge University Press, Cambridge, UK.
Chopard, B. , 1990, “ A Cellular Automata Model of Large-Scale Moving Objects,” J. Phys. A: Math. Gen., 23(10), p. 1671. [CrossRef]
Chopard, B. , Luthi, P. , and Marconi, S. , 1998, “ A Lattice Boltzmann Model for Wave and Fracture Phenomena,” Condens. Mater., Paper No. 9812220.
Kwon, Y. W. , and Hosoglu, S. , 2008, “ Application of Lattice Boltzmann Method, Finite Element Method, and Cellular Automata and Their Coupling to Wave Propagation Problems,” Comput. Struct., 86(7–8), pp. 663–670. [CrossRef]
Craugh, L. E. , and Kwon, Y. W. , 2013, “ Coupled Finite Element and Cellular Automata Methods for Analysis of Composite Structures With Fluid–Structure Interaction,” Compos. Struct., 102, pp. 124–137. [CrossRef]
Kwon, Y. W. , 2016, Multiphysics and Multiscale Modeling: Techniques and Applications, CRC Press, Boca Raton, FL.

Figures

Grahic Jump Location
Fig. 1

Checkerboard pattern for application of old CA rules for acoustic wave equation

Grahic Jump Location
Fig. 2

Two-dimensional lattice structure called D2Q9

Grahic Jump Location
Fig. 12

Plot of the center displacement of beam with reflected boundaries of different acoustic domain sizes H in Fig. 10

Grahic Jump Location
Fig. 13

Plot of acoustic pressure at 0.125 m below the beam center with reflected boundaries of different acoustic domain sizes H in Fig. 8

Grahic Jump Location
Fig. 14

Sketch of lid-driven cavity flow

Grahic Jump Location
Fig. 15

Comparison of velocity distribution across the width of the channel

Grahic Jump Location
Fig. 16

Comparison of the center displacement of the beam inside the lid-driven cavity flow model

Grahic Jump Location
Fig. 11

Comparison of the center displacement of beam between FDCA and FEM

Grahic Jump Location
Fig. 10

Interaction of beam and acoustic domain

Grahic Jump Location
Fig. 9

Contour plots of initial pressure and propagating pressures after 80 time steps: (a) initial pressure distribution and (b) pressure distribution after 41 time steps

Grahic Jump Location
Fig. 8

One-dimensional wave propagation and interaction with different boundaries: (a) initial wave profile, (b) rigid wall boundary, (c) free boundary, and (d) nonreflective boundary

Grahic Jump Location
Fig. 7

Vibration of a clamped plate subjected to a uniform load

Grahic Jump Location
Fig. 6

Vibration of a simply supported plate subjected to a uniform load

Grahic Jump Location
Fig. 5

Vibration of a clamped beam subjected to a uniform load

Grahic Jump Location
Fig. 4

Vibration of a simply supported beam subjected to a uniform load

Grahic Jump Location
Fig. 3

Convergence plot for simply supported beam with uniform pressure

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In