Displacement based finite elements for acoustic fluid–structure interaction
Main Article Content
Keywords
Acoustic, Finite element, Fluid–structure interaction.
Abstract
This paper compares two finite elements formulations used for solving fluid structure interaction problems in acoustics. In this case the displacement is used as variable for representing the behavior of the acoustic fluid. Finite element codes are writing for each formulation and typical fluid structure interaction problems are solved. The results obtained with each formulation are compared and advantages and disadvantages are obtained.
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References
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[27] K. J. Bathe and W. Hahn. On transient analysis of fluid–structure systems. Computers and Structures, ISSN 0045–7949, 10, 383–391 (1978).
[28] M. A. Hamdi, et al. A displacement method for the analysis of vibrations of coupled fluid–structure systems. International Journal for Numerical Methods in Engineering, ISSN 0029–5981, 13(1), 139–150 (1978).
[29] G. Larsson and P. Svenkvist. Experiences using the ADINA fluid element for large displacement analysis. Proceedings of the ADINA Conference, ISSN 0045– 7949, 383–406 (1979).
[30] T. B. Belytschko and U. Schumann. Fluid–structure interactions in light wa- ter reactor systems. Nuclear engineering Design, ISSN 0029–5493, 60, 173–195 (1980).
[31] T. B. Belytschko. Fluid–structure interaction. Computer & Structures, ISSN 0045–7949, 12, 459–469 (1980).
[32] T. B. Belytschko and R. Mullen. Two dimensional fluid structure impact computations with regularization. Computer Methods in Applied Mechanics and Engineering, ISSN 0045–7825, 27, 139–154 (1981).
[33] T. B. Belytschko and D. P. Flanagan. A uniform strain hexahedron and quadrilateral with orthogonal hourglass control . International Journal for Numerical Methods in Engineering, ISSN 0029–5981, 17(5), 676–706 (1981).
[34] O. C. Zienkiewicz and R. E. Newton. Coupled vibrations of a structure submerged in a compressible fluid. Symposium on Finite Element Techniques. Stuttgart, 1969.
[35] Craggs. The transient response of a coupled plateacoustic system using plate and acoustic finite elements. Journal of Sound and Vibration, ISSN 0022–460X, 15, 509–528 (1971).
[36] Henri Morand and Roger Ohayon. Substructure variational analysis of coupled fluid structure systems. Finite elment results. International Journal for Numerical Methods in Engineering, ISSN 0029–5981, 14(5), 741–755 (1979).
[37] G. C. Everstine. A symmetric potential formulation for fluid–structure interaction. Journal of Sound and Vibration, ISSN 0022–460X, 79(1), 157–160 (1981).
[38] L. G. Olson and K. J. Bathe. Analysis of fluid–structure interactions. A direct symmetric coupled formulation based on the fluid velocity potencial. Computers & Structures, ISSN 0045–7949, 21, 21–32 (1985).
[39] C. A. Felippa and R. Ohayon. Mixed variational formulation of finite element analysis of acoustoelastic/slosh fluid–structure interaction. Journal of Fluids and Structures, ISSN 0889–9746, 4, 35–57 (1990).
[40] K. J. Bathe, C. Nitikitpaiboon and X. Wang. A mixed displacement–based finite element formulation for acoustic fluid–structure interaction. Computers & Structures, ISSN 0045–7949, 56(2), 225–237 (1995).
[41] Xiaodong Wang and Klaus–J¨urgen Bathe. Displacement/pressure based finite element formulations for acoustic fluid–structure interaction problems. International Journal for Numerical Methods in Engineering, ISSN 0029–5981, 40(11), 2001–2017 (1997).
[42] S. Dey, D. K. Datta, J. J. Shirron and M. S. Shepard. p–Version FEM for structural acoustics with a posteriori error estimation. Computer Methods in Applied Mechanics and Engineering, ISSN 0045–7825, 195, 1946–1957 (2006).
[43] W. Cristoph Muller. Simplified analysis of linear fluid–structure interaction. International Journal for Numerical Methods in Engineering, ISSN 0029–5981,17(1), 113–121 (1981).
[44] M. Petyt and S. P. Lim. Finite element analysis of the noise inside a mechanically excited cylinder . International Journal for Numerical Methods in Engineering, ISSN 0029–5981, 13(1), 109–122 (1978).
[45] L. G. Olson and K. J. Bathe. A study of displacement–based fluid finite elements for calculating frequencies of fluid and fluid–structure systems. Nuclear Engineering and Design, ISSN 0029–5493, 76, 137–151 (1983).
[46] Alfredo Bermúdez and Rodolfo Rodríguez. Finite Element Computation of the Vibration Modes of a Fluid–Soil System. Computer Methods in Applied Mechanics and Engineering, ISSN 0045–7825, 119(4), 355–370 (1994).
[47] Harn C. Chen and Robert L. Taylor. Vibration analysis of fluid–solid systems using a finite element displacement formulation. International Journal for Numerical Methods in Engineering, ISSN 0029–05981, 29(4), 683–698 (1990).
[48] Y. S. Kim and C. B. Yung. A spurious free four–node displacement–based fluid element for fluid–structure interaction analysis. Engineering Structures, ISSN 0141–0296, 19(8), 665–678. (1997).
[49] R. L. Taylor et al. The patch test–a condition for assessing FEM convergence. International Journal for Numerical Methods in Engineering, ISSN 0029–5981, 22(1), 39–62 (1986).
[50] Klaus-Jurgen Bathe. Finite Element Procedures in Engineering Analysis, ISBN 9780133173055. New Jersey: Prentice Hall. 1982.
[51] J. Donea, S. Giuliani and J. P. Halleux. An arbitrary Lagrangian–Eulerian finite element method for transient dynamic fluid–structure interactions. Computer Methods in Applied Mechanics and Engineering, ISSN 0045–7825, 33, 689–723 (1982).
[2] L. H. Chen and D. G. Schweikert. Sound radiation from an arbitrary body. The Journal of the Acoustical Society of America, ISSN 0001–4966, 35(10), 1626–1632 (1963).
[3] Harry A. Schenck. Improved integral formulation for acoustic radiation problems. The Journal of the Acoustical Society of America, ISSN 0001–4966, 44(1), 41–58 (1968).
[4] J. J. Engblom and R. B. Nelson. Consistent formulation of sound radiation from arbitrary structure. Journal of Applied Mechanics, ISSN 0021–8936, 42, 295–300 (1975).
[5] Ian C. Mathews. Numerical technique for three dimensional steady–state fluid– structure interaction. The Journal of the Acoustical Society of America, ISSN 0001–4966, 79(5), 1317–1325 (1986).
[6] Gordon C. Everstine and Francis M. Henderson. Coupled finite element/boundary element approach for fluid structure interaction. The Journal of the Acoustical Society of America, ISSN 0001–4966, 87(5), 1938–1947 (1990).
[7] Gordon C. Everstine and Raymond S. Cheng. The coupling of finite elements and boundary elements for scattering from fluid–filled structures. In Computer Technology: Advances and Applications. American Society of Mechanical Engineers, New York, PVP–234, 43–47 (1992).
[8] L. Gaul andW.Wenzel. A coupled symmetric BE–FE for acoustics fluid-structure interaction. Engineering Analysis with boundary elements, ISSN 0955–7997, 26(7), 629–636 (2002).
[9] D. Fritze, S. Marburg and H. S. Hardtke. FEM-BEM coupling and structural acoustic sensitivity analysis for shell geometries. Computers & Structures, ISSN 0045–7949, 83, 143–154 (2005).
[10] Peter Bettess. Infinite elements. International Journal for Numerical Methods in Engineering, ISSN 0029–5981, 11(1), 53–64 (1977).
[11] Peter Bettess. More on infinite elements. International Journal for Numerical Methods in Engineering, ISSN 0029–5981, 15(11), 1613–1626 (1980).
[12] O. C. Zienkiewicz, C. Emson and P. Bettess. A novel boundarv infinite element . International Journal for Numerical Methods in Engineering, ISSN 0029–5981, 19(3), 393–404 (1983).
[13] O. C. Zienkiewicz, K. Bando, P. Bettess and T. C Chiam. Mapped infinite elements for exterior wave problems. International Journal for Numerical Methods in Engineering, ISSN 0029–5981, 21(7), 1229–1251 (1985).
[14] E. T. Moyer, Jr. Performance of mapped infinite elements for exterior wave scattering applications. Communications in Applied Numerical Methods, ISSN 0748–8025, 8(1), 27–39 (1992).
[15] Peter Bettes. Infinite elements, ISBN 0–9518806–0–8. Sunderland. UK: Penshaw Press, 264 (1992).
[16] John T. Hunt, Max R. Knittel and Don Barach. Finite element approach to acoustic radiation from elastic structures. The Journal of the Acoustical Society of America, ISSN 0001–4966, 55(2), 269–280 (1974).
[17] John T. Hunt, Max R. Knittel, Charles S. Nichols and Don Barach. Finite-element approach to acoustic scattering from elastic structures. The Journal of the Acoustical Society of America, ISSN 0001–4966, 57(2), 287–299 (1975).
[18] J. B. Keller and D. Givoli. Exact non-reflecting boundary conditions. Journal of Computational Physics, ISSN 0021–9991, 82(1), 172–192 (1989).
[19] MDC. Magalhaes and NS. Ferguson. Acoustic–structural interaction analysis using the component mode synthesis method. Applied Acoustics, ISSN 0003–682X, 64(11), 1049–1067 (2003).
[20] G. M. L. Gladwell and G. Zimmerman. On energy and complementary energy formulations of acoustic and structural vibration problems. Journal of Sound and Vibration, ISSN 0022–460X, 3(3), 233–241 (1966).
[21] G. M. Gladwell. A variational formulation of damped acousto-structural vibra- tion problems. Journal of Sound and Vibration, ISSN 0022–460X, 4(2), 172–186 (1966).
[22] Anil K. Chopra, E. L. Wilson and I. Farhoomand. Earthquake analysis of reservoir–dam systems. Proceedings of the 4th World Conference on Earthquake Engineering, Santiago, Chile, 1969.
[23] E. L. Wilson. Chap. 10 of Finite Elements in Geomechanics. Ed.: Gudehus John Wiley and Sons, New York, 1977, paper at the International Symposium of NumericalMethods in Soil Mechanics and Rock Mechanics, Karlsruhe, September 1975.
[24] D. Shantaram, D. R. J. Owen and O. C. Zienkiewicz. Dinamic transient behaviour of two and three–dimensional structures including plasticity, large deformation effects, and fluid interaction. Earthquake Engineering & Structural Dynamics, ISSN 0098–8847, 4(6), 561–578 (1976).
[25] T. B. Belytschko and J. M. Kennedy. A fluid–structure finite element method for the analysis of reactor safety problems. Nuclear engineering Design, ISSN 0029–5493, 38, 71–81 (1976).
[26] T. B. Belytschko and J. M. Kennedy. Computer models for subassembly simulation. Nuclear engineering Design, ISSN 0029–5493, 49, 17–38 (1978).
[27] K. J. Bathe and W. Hahn. On transient analysis of fluid–structure systems. Computers and Structures, ISSN 0045–7949, 10, 383–391 (1978).
[28] M. A. Hamdi, et al. A displacement method for the analysis of vibrations of coupled fluid–structure systems. International Journal for Numerical Methods in Engineering, ISSN 0029–5981, 13(1), 139–150 (1978).
[29] G. Larsson and P. Svenkvist. Experiences using the ADINA fluid element for large displacement analysis. Proceedings of the ADINA Conference, ISSN 0045– 7949, 383–406 (1979).
[30] T. B. Belytschko and U. Schumann. Fluid–structure interactions in light wa- ter reactor systems. Nuclear engineering Design, ISSN 0029–5493, 60, 173–195 (1980).
[31] T. B. Belytschko. Fluid–structure interaction. Computer & Structures, ISSN 0045–7949, 12, 459–469 (1980).
[32] T. B. Belytschko and R. Mullen. Two dimensional fluid structure impact computations with regularization. Computer Methods in Applied Mechanics and Engineering, ISSN 0045–7825, 27, 139–154 (1981).
[33] T. B. Belytschko and D. P. Flanagan. A uniform strain hexahedron and quadrilateral with orthogonal hourglass control . International Journal for Numerical Methods in Engineering, ISSN 0029–5981, 17(5), 676–706 (1981).
[34] O. C. Zienkiewicz and R. E. Newton. Coupled vibrations of a structure submerged in a compressible fluid. Symposium on Finite Element Techniques. Stuttgart, 1969.
[35] Craggs. The transient response of a coupled plateacoustic system using plate and acoustic finite elements. Journal of Sound and Vibration, ISSN 0022–460X, 15, 509–528 (1971).
[36] Henri Morand and Roger Ohayon. Substructure variational analysis of coupled fluid structure systems. Finite elment results. International Journal for Numerical Methods in Engineering, ISSN 0029–5981, 14(5), 741–755 (1979).
[37] G. C. Everstine. A symmetric potential formulation for fluid–structure interaction. Journal of Sound and Vibration, ISSN 0022–460X, 79(1), 157–160 (1981).
[38] L. G. Olson and K. J. Bathe. Analysis of fluid–structure interactions. A direct symmetric coupled formulation based on the fluid velocity potencial. Computers & Structures, ISSN 0045–7949, 21, 21–32 (1985).
[39] C. A. Felippa and R. Ohayon. Mixed variational formulation of finite element analysis of acoustoelastic/slosh fluid–structure interaction. Journal of Fluids and Structures, ISSN 0889–9746, 4, 35–57 (1990).
[40] K. J. Bathe, C. Nitikitpaiboon and X. Wang. A mixed displacement–based finite element formulation for acoustic fluid–structure interaction. Computers & Structures, ISSN 0045–7949, 56(2), 225–237 (1995).
[41] Xiaodong Wang and Klaus–J¨urgen Bathe. Displacement/pressure based finite element formulations for acoustic fluid–structure interaction problems. International Journal for Numerical Methods in Engineering, ISSN 0029–5981, 40(11), 2001–2017 (1997).
[42] S. Dey, D. K. Datta, J. J. Shirron and M. S. Shepard. p–Version FEM for structural acoustics with a posteriori error estimation. Computer Methods in Applied Mechanics and Engineering, ISSN 0045–7825, 195, 1946–1957 (2006).
[43] W. Cristoph Muller. Simplified analysis of linear fluid–structure interaction. International Journal for Numerical Methods in Engineering, ISSN 0029–5981,17(1), 113–121 (1981).
[44] M. Petyt and S. P. Lim. Finite element analysis of the noise inside a mechanically excited cylinder . International Journal for Numerical Methods in Engineering, ISSN 0029–5981, 13(1), 109–122 (1978).
[45] L. G. Olson and K. J. Bathe. A study of displacement–based fluid finite elements for calculating frequencies of fluid and fluid–structure systems. Nuclear Engineering and Design, ISSN 0029–5493, 76, 137–151 (1983).
[46] Alfredo Bermúdez and Rodolfo Rodríguez. Finite Element Computation of the Vibration Modes of a Fluid–Soil System. Computer Methods in Applied Mechanics and Engineering, ISSN 0045–7825, 119(4), 355–370 (1994).
[47] Harn C. Chen and Robert L. Taylor. Vibration analysis of fluid–solid systems using a finite element displacement formulation. International Journal for Numerical Methods in Engineering, ISSN 0029–05981, 29(4), 683–698 (1990).
[48] Y. S. Kim and C. B. Yung. A spurious free four–node displacement–based fluid element for fluid–structure interaction analysis. Engineering Structures, ISSN 0141–0296, 19(8), 665–678. (1997).
[49] R. L. Taylor et al. The patch test–a condition for assessing FEM convergence. International Journal for Numerical Methods in Engineering, ISSN 0029–5981, 22(1), 39–62 (1986).
[50] Klaus-Jurgen Bathe. Finite Element Procedures in Engineering Analysis, ISBN 9780133173055. New Jersey: Prentice Hall. 1982.
[51] J. Donea, S. Giuliani and J. P. Halleux. An arbitrary Lagrangian–Eulerian finite element method for transient dynamic fluid–structure interactions. Computer Methods in Applied Mechanics and Engineering, ISSN 0045–7825, 33, 689–723 (1982).