Archives of Acoustics, 42, 1, pp. 37–48, 2017
10.1515/aoa-2017-0005

2D Structural Acoustic Analysis Using the FEM/FMBEM with Different Coupled Element Types

Leilei CHEN
Xinyang Normal University
China

Wenchang ZHAO
University of Science and Technology of China CAS Key Laboratory of Mechanical Behavior and Design of Materials
China

Cheng LIU
University of Science and Technology of China CAS Key Laboratory of Mechanical Behavior and Design of Materials
China

Haibo CHEN
University of Science and Technology of China CAS Key Laboratory of Mechanical Behavior and Design of Materials
China

A FEM-BEM coupling approach is used for acoustic fluid-structure interaction analysis. The FEM is used to model the structure and the BEM is used to model the exterior acoustic domain. The aim of this work is to improve the computational efficiency and accuracy of the conventional FEM-BEM coupling approach. The fast multipole method (FMM) is applied to accelerating the matrix-vector products in BEM. The Burton-Miller formulation is used to overcome the fictitious eigen-frequency problem when using a single Helmholtz boundary integral equation for exterior acoustic problems. The continuous higher order boundary elements and discontinuous higher order boundary elements for 2D problem are developed in this work to achieve higher accuracy in the coupling analysis. The performance for coupled element types is compared via a simple example with analytical solution, and the optimal element type is obtained. Numerical examples are presented to show the relative errors of different coupled element types.
Keywords: boundary element method; finite element method; discontinuous boundary elements; acoustic fluid-structure interaction; fast multipole method
Full Text: PDF

References

Burton A.J., Miller G.F. (1971), The application of integral equation methods to the numerical solution of some exterior boundary-value problems, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 323, 1553, 201–210.

Chen L.L., Chen H.B. (2015), Structural-acoustic design sensitivity analysis based on direct differentiation method with different element types, CMES: Computer Modeling in Engineering & Sciences, 107, 3, 249–276.

Chen L.L., Chen H.B., Zheng C.J. (2013a), FEM/wideband FMBEM coupling for fluid-structure interaction problem and 2D acoustic design sensitivity analysis, Comput. Model. Eng. Sci., 94, 6, 459–483.

Chen Z.S., Hofstetter G., Mang H.A. (1998), A Galerkin-type BE-FE formulation for elasto-acoustic coupling, Computer Methods in Applied Mechanics and Engineering, 152, 1–2, 147–155.

Chen L., Zheng C., Chen H. (2013b), A wideband FMBEM for 2D acoustic design sensitivity analysis based on direct differentiation method, Computational Mechanics, 52, 3, 631–648.

Chen L., Zheng C., Chen H. (2014), FEM/wideband FMBEM coupling for structural-acoustic design sensitivity analysis, Computer Methods in Applied Mechanics and Engineering, 276, 1–19.

Coifman R., Rokhlin V., Wandzura S. (1993), The fast multipole method for the wave equation: a pedestrian prescription, Antennas and Propagation Magazine, IEEE, 35, 3, 7–12.

Everstine G.C., Henderson F.M. (1990), Coupled finite element/boundary element approach for fluidstructure interaction, The Journal of the Acoustical Society of America, 87, 5, 1938–1947.

Fritze D., Marburg S., Hardtke H.-J. (2005), FEM-BEM-coupling and structural-acoustic sensitivity analysis for shell geometries, Computers & Structures, Advances in Analysis of Fluid Structure Interaction, 83, 2–3, 143–154.

He Z.C., Liu G.R., Zhong Z.H., Zhang G.Y., Cheng A.G. (2011), A coupled ES-FEM/BEM method for fluid-structure interaction problems, Engineering Analysis with Boundary Elements, 35, 1, 140–147.

Li S., Huang Q. (2011), A new fast multipole boundary element method for two dimensional acoustic problems, Computer Methods in Applied Mechanics and Engineering, 200, 1333–1340.

Marburg S., Schneider S. (2003), Influence of element types on numeric error for acoustic boundary elements, Journal of Computational Acoustics, 11, 03, 363–386.

Márquez A., Meddahi S., Selgas V. (2004), A new BEM-FEM coupling strategy for two-dimensional fluidsolid interaction problems, Journal of Computational Physics, 199, 1, 205–220.

Peters H., Marburg S., Kessissoglou N. (2012), Structural-acoustic coupling on non-conforming meshes with quadratic shape functions, International Journal for Numerical Methods in Engineering, 91, 1, 27–38.

Rajakumar C., Ali A. (1996), Boundary elementfinite element coupled eigenanalysis of fluid-structure systems, International Journal for Numerical Methods in Engineering, 39, 10, 1625–1634.

Schneider S. (2008), FE/FMBE coupling to model fluid-structure interaction, International Journal for Numerical Methods in Engineering, 76, 13, 2137–2156.

Tadeu A., Antonio J. (2000), Use of constant, linear and quadratic boundary elements in 3D wave diffraction analysis, Engineering Analysis with Boundary Elements, 24, 2, 131–144.

Yu C., Yu H., Chen Y. (2012), Fast multipole boundary element method for 2-D Helmholtz equation problems and its error analysis, Journal of Information & Computational Science, 9, 18, 5571–5578.

Wu H., Jiang W., Liu Y.J. (2011), Diagonal form fast multipole boundary element method for 2D acoustic problems based on Burton-Miller boundary integral equation formulation and its applications, Applied Mathematics and Mechanics, 32, 8, 981–996.

Zhang X., Zhang X. (2002), Coupling FEM and discontinuous BEM for elastostatics and fluid-structure interaction, Engineering Analysis with Boundary Elements, 26, 8, 719–725.




DOI: 10.1515/aoa-2017-0005

Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN)