**42**, 1, pp. 49–59, 2017

**10.1515/aoa-2017-0006**

### A Coupled Smoothed Finite Element-Boundary Element Method for Structural-Acoustic Analysis of Shell

by coupling the SFEM for the structure and the BEM for the fluid. The solutions of SFEM are often found to be much more accurate than those of the FEM model. Based on its attractive features, it was decided in the present work to extend SFEM further for use in structural-acoustic analysis by coupling it with BEM, the present SFEM/BEM is implemented to predict the vehicle structure-acoustic frequency response analysis, and two numerical experiments results show that the present method can provide more accurate results compared with the standard FEM/BEM using the same mesh. It indicates that the present SFEM/BEM can be widely applied to solving many engineering noise, vibration and harshness (NVH) problems with more accurate solutions.

**Keywords**: Smoothed finite element method (SFEM); FEM; BEM; structural-acoustic analysis

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#### References

Bathe K.J., Dvorkin E.N. (1985), A four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation, International Journal for Numerical Methods in Engineering, 21, 367–383.

Bathe K.J., Nitikitpaiboon C., Wang X. (1995), A mixed displacement-based finite element formulation for acoustic fluid-structure interaction, Computers & Structures, 56, 2–3, 225–237.

Chen P.T., Ju S.H., Cha K.C. (2000), A symmetric formulation of coupled BEM/FEM in solving responses of submerged elastic structures for large degree of freedoms, Journal of Sound and Vibration, 233, 407–422.

Choi P. (1997), Application of a directly coupled boundary element and finite element model to the dynamics of coupled acoustic silencers, PhD dissertation, North Carolina State University.

Coyette J.P. (1999), The use of finite-element and boundary-element models for predicting the vibro-acoustic behaviour of layered structures, Advances in Engineering Software, 30, 133–139.

Davidsson P. (2004), Structure-acoustic analysis: finite element modeling and reduction methods, PhD dissertation, Lund University.

Everstine G.C. (1981), A symmetric potential formulation for fluid–structure interaction, Journal of Sound and Vibration, 79, 1, 157–160.

Everstine G.C. (1997), Finite element formulations of structural acoustics problems, Computers & Structures, 65, 3, 307–321.

Everstine G.C., Henderson F.M. (1990), Coupled finite element/boundary element approach for fluid structure interaction, The Journal of the Acoustical Society of America, 87, 5, 1938–1945.

Fredrik H. (2001), Structure-acoustic analysis using BEM/FEM: Implementation in MATLAB, Master Dissertation, Lund University.

Hamdi M.A., Ousset Y., Verchery G. (1978), A displacement method for the analysis of vibrations of coupled fluid & structure systems, International Journal for Numerical Methods in Engineering, 13, 139–150.

He Z.C., Li G.Y. et al. (2013), An improved eigen-frequencies prediction for three-dimensional problems using face-based smoothed finite element method (FSFEM), Acta Mechanica Solida Sinica, 26, 2, 140–150.

He Z.C., Liu G.R. et al. (2011), A coupled ESFEM/BEM method for fluid-structure interaction problems, Engineering Analysis with Boundary Elements, 35, 140–147.

Jeans R.A., Mathews I.C. (1990), Solution of fluidstructure interaction problems using a coupled finite element and variational boundary element technique, The Journal of the Acoustical Society of America, 88, 2459–2466.

Jeans R.A., Mathews I.C. (1993), A unique coupled boundary element/finite element method for the elasto-acoustic analysis of fliud-filled thin shell, The Journal of the Acoustical Society of America, 94, 3473–3479.

Kopuz S. (1996), Integrated FEM/BEM approach to the dynamic and acoustic analysis of plate structures, Engineering Analysis with Boundary Elements, 17, 269–277.

Li W., Chai Y.B. et al. (2014), Analysis of coupled structural-acoustic problems based on the smoothed finite element method (S-FEM), Engineering Analysis with Boundary Elements, 40, 84–91.

Liu G.R., Dai K.Y., Nguyen T.T. (2007a), A smoothed finite element method for mechanics problems, Computational Mechanics, 39, 859–877.

Liu G.R., Nguyen T.T., Dai K.Y., Lam K.Y. (2007b), Theoretical aspects of the smoothed finite element method (SFEM), International Journal for Numerical Methods in Engineering, 71, 902–930.

Morand H., Ohayon R. (1979), Substructure variational analysis of the vibrations of coupled fluid structure systems-finite-element results, International Journal for Numerical Methods in Engineering, 14, 5, 741– 755.

Nehete D.V., Modak S.V., Gupta K. (2015), Structural FE model updating of cavity systems incorporating vibro-acoustic coupling, Mechanical Systems and Signal Processing, 50–51, 362–379.

Tonga Z., Zhang Y., Zhang Z., Hua H. (2007), Dynamic behavior and sound transmission analysis of a fluid-structure coupled system using the directBEM/FEM, Journal of Sound and Vibration, 299, 645–655.

Wang G., Cui X.Y., Liang Z.M., Li G.Y. (2015), A coupled smoothed finite element method (S-FEM) for structural-acoustic analysis of shells, Engineering Analysis with Boundary Elements, 61, 207–217.

DOI: 10.1515/aoa-2017-0006

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