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Structural and Multidisciplinary Optimization

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27-12-2017 | RESEARCH PAPER

Minimization of sound radiation in fully coupled structural-acoustic systems using FEM-BEM based topology optimization

Authors: Wenchang Zhao, Changjun Zheng, Cheng Liu, Haibo Chen

Published in: Structural and Multidisciplinary Optimization | Issue 1/2018

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Abstract

A topology optimization approach is proposed for the optimal design of bi-material distribution on underwater shell structures. The coupled finite element method (FEM) / boundary element method (BEM) scheme is used for the system response analysis, where the strong interaction between the structural and the acoustic domain is considered. 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 design variables are the artificial densities of design material elements in a bi-material model constructed by the solid isotropic material with penalization (SIMP) method, and the minimization of sound power level (SWL) is chosen to be the design objective. In this study, the adjoint operator method is employed to calculate the sensitivity of the objective function with respect to the design variables. Based on the sensitivity information, the gradient-based optimization solver is finally applied for updating the design variables during the optimization process. Numerical tests are provided to illustrate the correctness of the sensitivity analysis approach and the validity of the proposed optimization procedure. Results show that the heavy fluid feedback has a big impact on the final design, and thus it is necessary to conduct a strong coupling scheme between the fluid and structures. In addition, the optimal design is strongly frequency dependent, and performing an optimization in a frequency band is generally needed.

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Allaire G, Jouve F, Toader AM (2004) Structural optimization using sensitivity analysis and a level-set method. J Comput Phys 194(1):363–393MathSciNetMATHCrossRef

Bendsøe MP (1989) Optimal shape design as a material distribution problem. Structural optimization 1 (4):193–202CrossRef

Bendsøe MP, Sigmund O (1999) Material interpolation schemes in topology optimization. Arch Appl Mech 69(9):635–654MATH

Brunner D, Junge M, Gaul L (2009) A comparison of FE–BE coupling schemes for large-scale problems with fluid–structure interaction. Int J Numer Methods Eng 77(5):664–688MathSciNetMATHCrossRef

Burton AJ, Miller GF (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, Phys Eng Sci 323 (1553):201–210MathSciNetMATHCrossRef

Chen L, Zheng C, Chen H (2014) FEM/Wideband FMBEM coupling for structural–acoustic design sensitivity analysis. Comput Methods Appl Mech Eng 276:1–19MathSciNetCrossRef

Chen L, Chen H, Zheng C, Marburg S (2016) Structural-acoustic sensitivity analysis of radiated sound power using a finite element/ discontinuous fast multipole boundary element scheme. Int J Numer Methods Fluids 82(12):858–878. fld.4244MathSciNetCrossRef

Chen L, Marburg S, Chen H, Zhang H, Gao H (1750) (2017) An adjoint operator approach for sensitivity analysis of radiated sound power in fully coupled structural-acoustic systems. J Comput Acoust 25(01):003

Chen Z, Hofstetter G, Mang H (1998) A Galerkin-type BE-FE formulation for elasto-acoustic coupling. Comput Methods Appl Mech Eng 152(1):147–155MATHCrossRef

Denli H, Sun J (2008) Structural–acoustic optimization of sandwich cylindrical shells for minimum interior sound transmission. J Sound Vib 316(1-5):32–49CrossRef

Du J, Olhoff N (2007) Minimization of sound radiation from vibrating bi-material structures using topology optimization. Struct Multidiscip Optim 33(4):305–321CrossRef

Du J, Olhoff N (2010) Topological design of vibrating structures with respect to optimum sound pressure characteristics in a surrounding acoustic medium. Struct Multidiscip Optim 42(1):43–54MathSciNetMATHCrossRef

Du J, Sun C (2017) Reliability-based vibro-acoustic microstructural topology optimization. Struct Multidiscip Optim 55(4):1195–1215MathSciNetCrossRef

Du J, Yang R (2015) Vibro-acoustic design of plate using bi-material microstructural topology optimization. J Mech Sci Technol 29(4):1413–1419CrossRef

Du J, Song X, Dong L (2011) Design of material distribution of acoustic structure using topology optimization. Chinese Journal of Theoretical & Applied Mechanics 43(2):306–315

Everstine GC, Henderson FM (1990) Coupled finite element/boundary element approach for fluid-structure interaction. J Acoust Soc Am 87(5):1938–1947CrossRef

Fritze D, Marburg S, Hardtke HJ (2005) FEM-BEM-Coupling and structural-acoustic sensitivity analysis for shell geometries. Comput Struct 83(2-3):143–154CrossRef

Guiggiani M, Krishnasamy G, Rudolphi TJ, Rizzo F (1992) A general algorithm for the numerical solution of hypersingular boundary integral equations. J Appl Mech 59:604MathSciNetMATHCrossRef

Haftka RT, Adelman HM (1989) Recent developments in structural sensitivity analysis. Structural Optimization 1(3):137–151CrossRef

Huang X, Xie YM (2008) Bi-directional evolutionary topology optimization of continuum structures with one or multiple materials. Comput Mech 43(3):393MathSciNetMATHCrossRef

JOG C (2002) Topology design of structures subjected to periodic loading. J Sound Vib 253(3):687–709CrossRef

Kang Z, Zhang X, Jiang S, Cheng G (2012) On topology optimization of damping layer in shell structures under harmonic excitations. Struct Multidiscip Optim 46(1):51–67MathSciNetMATHCrossRef

Koo K, Pluymers B, Desmet W, Wang S (2011) Vibro-acoustic design sensitivity analysis using the wave-based method. J Sound Vib 330(17):4340–4351CrossRef

Lamancusa J (1993) Numerical optimization techniques for structural-acoustic design of rectangular panels. Comput Struct 48(4):661–675MATHCrossRef

Liu C, Chen L, Zhao W, Chen H (2017) Shape optimization of sound barrier using an isogeometric fast multipole boundary element method in two dimensions. Engineering Analysis with Boundary Elements 85:142–157MathSciNetCrossRef

Liu H, Zhang W, Gao T (2015) A comparative study of dynamic analysis methods for structural topology optimization under harmonic force excitations. Struct Multidiscip Optim 51(6):1321–1333MathSciNetCrossRef

Ma ZD, Kikuchi N, Cheng HC (1995) Topological design for vibrating structures. Comput Methods Appl Mech Eng 121(1):259–280MathSciNetMATHCrossRef

Marburg S (2002) Developments in structural-acoustic optimization for passive noise control. Arch Comput Meth Eng 9(4):291–370MATHCrossRef

Márquez A, Meddahi S, Selgas V (2004) A new BEM-FEM coupling strategy for two-dimensional fluid-solid interaction problems. J Comput Phys 199(1):205–220MathSciNetMATHCrossRef

Matsumoto T, Zheng C, Harada S, Takahashi T (2010) Explicit evaluation of hypersingular boundary integral equation for 3-D helmholtz equation discretized with constant triangular element. J Comput Sci Technol 4 (3):194–206CrossRef

Merz S, Kessissoglou N, Kinns R, Marburg S (2010) Minimisation of the sound power radiated by a submarine through optimisation of its resonance changer. J Sound Vib 329(8):980–993CrossRef

Niu B, Olhoff N, Lund E, Cheng G (2010) Discrete material optimization of vibrating laminated composite plates for minimum sound radiation. Int J Solids Struct 47(16):2097–2114MATHCrossRef

Olhoff N, Du J (2009) On topological design optimization of structures against vibration and noise emission. In: Sandberg G, Ohayon R (eds) Computational aspects of structural acoustics and vibration. Springer Vienna, Vienna, pp 217–276

Olhoff N, Du J (2014) Topological design for minimum dynamic compliance of structures under forced vibration. In: Rozvany GIN, Lewiński T (eds) Topology optimization in structural and continuum mechanics. Springer Vienna, Vienna, pp 325– 339

Pedersen N (2000) Maximization of eigenvalues using topology optimization. Struct Multidiscip Optim 20 (1):2–11CrossRef

Peters H, Marburg S, Kessissoglou N (2012) Structural-acoustic coupling on non-conforming meshes with quadratic shape functions. Int J Numer Methods Eng 91(1):27–38MathSciNetMATHCrossRef

Rong J, Wen L, Xiao J (2014) Efficiency improvement of the polar coordinate transformation for evaluating BEM singular integrals on curved elements. Engineering Analysis with Boundary Elements 38:83–93MathSciNetMATHCrossRef

Rong JH, Tang ZL, Xie YM, Li FY (2013) Topological optimization design of structures under random excitations using SQP method. Eng Struct 56(6):2098–2106CrossRef

Schneider S (2008) FE/FMBE Coupling to model fluid–structure interaction. Int J Numer Methods Eng 76 (13):2137–2156MathSciNetMATHCrossRef

Shang L, Zhao G (2016) Optimality criteria-based topology optimization of a bi-material model for acoustic-structural coupled systems. Eng Optim 48(6):1060–1079MathSciNetCrossRef

Sigmund O (1997) On the design of compliant mechanisms using topology optimization. Mech Struct Mach 25(4):493–524CrossRef

Sigmund O (2007) Morphology-based black and white filters for topology optimization. Struct Multidiscip Optim 33(4):401–424MathSciNetCrossRef

Svanberg K (1987) The method of moving asymptotes–a new method for structural optimization. Int J Numer Methods Eng 24(2):359–373MathSciNetMATHCrossRef

Takezawa A, Daifuku M, Nakano Y, Nakagawa K, Yamamoto T, Kitamura M (2016) Topology optimization of damping material for reducing resonance response based on complex dynamic compliance. J Sound Vib 365:230–243CrossRef

Wang MY, Wang X, Guo D (2003) A level set method for structural topology optimization. Comput Methods Appl Mech Eng 192(1-2):227–246MathSciNetMATHCrossRef

Xie Y, Steven G (1993) A simple evolutionary procedure for structural optimization. Comput Struct 49 (5):885–896CrossRef

Xu S, Cai Y, Cheng G (2010) Volume preserving nonlinear density filter based on heaviside functions. Struct Multidiscip Optim 41(4):495–505MathSciNetMATHCrossRef

Xu Z, Huang Q, Zhao Z (2011) Topology optimization of composite material plate with respect to sound radiation. Engineering Analysis with Boundary Elements 35(1):61–67MathSciNetMATHCrossRef

Yang R, Du J (2013) Microstructural topology optimization with respect to sound power radiation. Struct Multidiscip Optim 47(2):191–206MATHCrossRef

Zhang Q, Zhang W, Zhu J, Gao T (2012) Layout optimization of multi-component structures under static loads and random excitations. Eng Struct 43(Supplement C):120–128

Zhang X, Kang Z (2013) Topology optimization of damping layers for minimizing sound radiation of shell structures. J Sound Vib 332(10):2500–2519CrossRef

Zhao W, Chen L, Zheng C, Liu C, Chen H (2017) Design of absorbing material distribution for sound barrier using topology optimization. Struct Multidiscip Optim 56(2):315–329MathSciNetCrossRef

Zheng C, Matsumoto T, Takahashi T, Chen H (2012) A wideband fast multipole boundary element method for three dimensional acoustic shape sensitivity analysis based on direct differentiation method. Engineering Analysis with Boundary Elements 36(3):361–371MathSciNetMATHCrossRef

Zheng C, Zhang C, Bi C, Gao H, Du L, Chen H (2017) Coupled FE–BE method for eigenvalue analysis of elastic structures submerged in an infinite fluid domain. Int J Numer Methods Eng 110(2):163–185MathSciNetMATHCrossRef

Zheng CJ, Chen HB, Gao HF, Du L (2015) Is the Burton-Miller formulation really free of fictitious eigenfrequencies?. Engineering Analysis with Boundary Elements 59:43–51MathSciNetCrossRef

Zheng H, Cai C, Pau G, Liu G (2005) Minimizing vibration response of cylindrical shells through layout optimization of passive constrained layer damping treatments. J Sound Vib 279(3):739–756CrossRef

Zhu JH, He F, Liu T, Zhang WH, Liu Q, Yang C (2017) Structural topology optimization under harmonic base acceleration excitations. Structural and Multidisciplinary Optimization. https://doi.org/10.1007/s00158-017-1795-0

Title: Minimization of sound radiation in fully coupled structural-acoustic systems using FEM-BEM based topology optimization
Authors: Wenchang Zhao
Changjun Zheng
Cheng Liu
Haibo Chen
Publication date: 27-12-2017
Publisher: Springer Berlin Heidelberg
Published in: Structural and Multidisciplinary Optimization / Issue 1/2018
Print ISSN: 1615-147X
Electronic ISSN: 1615-1488
DOI: https://doi.org/10.1007/s00158-017-1881-3

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