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.

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Fig. 1

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

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Fig. 2

Two-dimensional lattice structure called D2Q9

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Fig. 3

Convergence plot for simply supported beam with uniform pressure

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Fig. 4

Vibration of a simply supported beam subjected to a uniform load

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Fig. 5

Vibration of a clamped beam subjected to a uniform load

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Fig. 6

Vibration of a simply supported plate subjected to a uniform load

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Fig. 7

Vibration of a clamped plate subjected to a uniform load

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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

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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

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Fig. 10

Interaction of beam and acoustic domain

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Fig. 11

Comparison of the center displacement of beam between FDCA and FEM

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Fig. 12

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

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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

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Fig. 14

Sketch of lid-driven cavity flow

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Fig. 15

Comparison of velocity distribution across the width of the channel

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Fig. 16

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




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