×

Combined shape and topology optimization for sound barrier by using the isogeometric boundary element method. (English) Zbl 1464.76091

Summary: This study presents a combined shape and topology optimization method for designing sound barriers by using the isogeometric boundary element method. The objective function of combined optimization is defined as the sound pressure in reference plane. The sensitivity analysis for the combined optimization is conducted by using either the direct differentiation method or the adjoint variable method. For a shape design, the design variables are the positions of control points in isogeometric analysis, which can control the barrier shape flexibly. In the topology update, the artificial density of an integral element is selected as the design variable to find the optimal distribution of sound absorbing material (SAM) on the barrier surface. In the combined optimization process, the shape and SAM distribution of the sound barrier can be changed in each iteration process to improve the noise reduction. Four different iteration schemes for combined optimization are compared to find an effective one. Numerical tests are provided to demonstrate the validity and efficiency of the proposed methods.

MSC:

76M15 Boundary element methods applied to problems in fluid mechanics
65N38 Boundary element methods for boundary value problems involving PDEs
65D07 Numerical computation using splines
76Q05 Hydro- and aero-acoustics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] De Lacerda, L. A.; Wrobel, L. C.; Power, H.; Mansur, W. J., A novel boundary integral formulation for three-dimensional analysis of thin acoustic barriers over an impedance plane, J Acoust Soc Am, 104, 2, 671-678 (1998)
[2] Ishizuka, T.; Fujiwara, K., Performance of noise barriers with various edge shapes and acoustical conditions, Appl Acoust, 65, 2, 125-141 (2004)
[3] Monazzam, M. R.; Lam, Y. W., Performance of profiled single noise barriers covered with quadratic residue diffusers, Appl Acoust, 66, 6, 709-730 (2005)
[4] Baulac, M.; Defrance, J.; Jean, P., Optimization of multiple edge barriers with genetic algorithms coupled with a Nelder-Mead local search, J Sound Vib, 300, 1-2, 71-87 (2007)
[5] Baulac, M.; Defrance, J.; Jean, P., Optimisation with genetic algorithm of the acoustic performance of t-shaped noise barriers with a reactive top surface, Appl Acoust, 69, 4, 332-342 (2008)
[6] Toledo, R.; Aznárez, J.; Maeso, O.; Greiner, D., Optimization of thin noise barrier designs using evolutionary algorithms and a dual BEM formulation, J Sound Vib, 334, 219-238 (2015)
[7] Toledo, R.; Aznárez, J.; Greiner, D.; Maeso, O., Shape design optimization of road acoustic barriers featuring top-edge devices by using genetic algorithms and boundary elements, Eng Anal Bound Elem, 63, 49-60 (2016) · Zbl 1403.74241
[8] Kim, K. H.; Yoon, G. H., Optimal rigid and porous material distributions for noise barrier by acoustic topology optimization, J Sound Vib, 339, 123-142 (2015)
[9] Zhao, W.; Chen, L.; Zheng, C.; Liu, C.; Chen, H., Design of absorbing material distribution for sound barrier using topology optimization, Struct Multidiscip Optim, 56, 2, 315-329 (2017)
[10] Liu, C.; Chen, L.; Zhao, W.; Chen, H., Shape optimization of sound barrier using an isogeometric fast multipole boundary element method in two dimensions, Eng Anal Bound Elem, 85, 142-157 (2017) · Zbl 1403.76092
[11] Svanberg, K., The method of moving asymptotes a new method for structural optimization, Int J Numer Methods Eng, 24, 2, 359-373 (1987) · Zbl 0602.73091
[12] Shaaban, A. M.; Anitescu, C.; Rabczuk, T., Shape optimization by conventional and extended isogeometric boundary element method with PSO for two-dimensional helmholtz acoustic problems, Eng Anal Bound Elem, 113, 156-169 (2020) · Zbl 1464.76188
[13] Chen, L.; Liu, C.; Zhao, W.; Liu, L., An isogeometric approach of two dimensional acoustic design sensitivity analysis and topology optimization analysis for absorbing material distribution, Comput Methods Appl Mech Eng, 336, 507-532 (2018) · Zbl 1440.74286
[14] Burger, M.; Hackl, B.; Ring, W., Incorporating topological derivatives into level set methods, J Comput Phys, 194, 1, 344-362 (2004) · Zbl 1044.65053
[15] Zhuang, C. G.; Xiong, Z. H.; Ding, H., A level set method for topology optimization of heat conduction problem under multiple load cases, Comput Methods Appl Mech Eng, 196, 4/6, 1074-1084 (2007) · Zbl 1120.80312
[16] Matsumoto, T.; Yamada, T.; Takahashi, T.; Zheng, C. J.; Harada, S., Acoustic design shape and topology sensitivity formulations based on adjoint method and BEM, Comput Model Eng Sci, 78, 2, 77-94 (2011) · Zbl 1356.76303
[17] Christiansen, A. N.; Nobeljorgensen, M.; Aage, N.; Sigmund, O.; Baerentzen, J. A., Topology optimization using an explicit interface representation, Struct Multidiscip Optim, 49, 3, 387-399 (2014)
[18] Christiansen, A. N.; Bærentzen, J. A.; Nobel-Jørgensen, M.; Aage, N.; Sigmund, O., Combined shape and topology optimization of 3D structures, Comput Graph, 46, 25-35 (2015)
[19] Lian, H.; Christiansen, A. N.; Tortorelli, D. A.; Sigmund, O.; Aage, N., Combined shape and topology optimization for minimization of maximal von mises stress, Struct Multidiscip Optim, 55, 5, 1541-1557 (2017)
[20] Dunning, P. D.; Kim, H. A., A new hole insertion method for level set based structural topology optimization, Int J Numer Methods Eng, 93, 1, 118-134 (2013) · Zbl 1352.74236
[21] Lin, W.; Newman, J. C.; Anderson, W. K.; Zhang, X., Topology and shape optimization of broadband acoustic metamaterials and phononic crystals, Acoust Sci Technol, 38, 5, 254-260 (2017)
[22] Wadbro, E.; Udawalpola, R.; Berggren, M., Shape and topology optimization of an acoustic horn-lens combination, J Comput Appl Math, 234, 6, 1781-1787 (2010) · Zbl 1256.74020
[23] Gu, J.; Zhang, J.; Li, G., Isogeometric analysis in bie for 3-D potential problem, Eng Anal Bound Elem, 36, 5, 858-865 (2012) · Zbl 1352.65585
[24] Gong, Y.; Dong, C.; Qin, X., An isogeometric boundary element method for three dimensional potential problems, J Comput Appl Math, 313, 454-468 (2017) · Zbl 1353.65129
[25] Sun, F.; Dong, C.; Wu, Y.; Gong, Y., Fast direct isogeometric boundary element method for 3D potential problems based on HODLR matrix, Appl Math Comput, 359, 17-33 (2019) · Zbl 1429.65290
[26] Simpson, R. N.; Bordas, S. P.; Trevelyan, J.; Rabczuk, T., A two-dimensional isogeometric boundary element method for elastostatic analysis, Comput Methods Appl Mech Eng, 209, 87-100 (2012) · Zbl 1243.74193
[27] Bai, Y.; Dong, C.; Liu, Z., Effective elastic properties and stress states of doubly periodic array of inclusions with complex shapes by isogeometric boundary element method, Compos Struct, 128, 54-69 (2015)
[28] Simpson, R. N.; Scott, M. A.; Taus, M.; Thomas, D. C.; Lian, H., Acoustic isogeometric boundary element analysis, Comput Methods Appl Mech Eng, 269, 265-290 (2014) · Zbl 1296.65175
[29] Sun, Y.; Trevelyan, J.; Hattori, G.; Lu, C., Discontinuous isogeometric boundary element (IGABEM) formulations in 3D automotive acoustics, Eng Anal Bound Elem, 105, 303-311 (2019) · Zbl 1464.65246
[30] Chen, L.; Marburg, S.; Zhao, W.; Liu, C.; Chen, H., Implementation of isogeometric fast multipole boundary element methods for 2D half-space acoustic scattering problems with absorbing boundary condition, J Theoret Comput Acoust, 27, 02, 1850024 (2019)
[31] Chen, L.; Zhao, W.; Liu, C.; Chen, H.; Marburg, S., Isogeometric fast multipole boundary element method based on burton-miller formulation for 3D acoustic problems, Arch Acoust, 44, 3, 475-492 (2019)
[32] Venås, J. V.; Kvamsdal, T., Isogeometric boundary element method for acoustic scattering by a submarine, Comput Methods Appl Mech Eng, 359, 112670 (2020) · Zbl 1441.76112
[33] Chen, L.; Zhang, Y.; Lian, H.; Atroshchenko, E.; Ding, C.; Bordas, S., Seamless integration of computer-aided geometric modeling and acoustic simulation: isogeometric boundary element methods based on catmull-clark subdivision surfaces, Adv Eng Software, 149, 1-15 (2020)
[34] Chen, L.; Lian, H.; Liu, Z.; Chen, H.; Atroshchenko, E.; Bordas, S., Structural shape optimization of three dimensional acoustic problems with isogeometric boundary element methods, Comput Methods Appl Mech Eng, 355, 926-951 (2019) · Zbl 1441.74290
[35] Chen, L.; Lu, C.; Lian, H.; Liu, Z.; Zhao, W.; Li, S., Acoustic topology optimization of sound absorbing materials directly from subdivision surfaces with isogeometric boundary element methods, Comput Methods Appl Mech Eng, 362, 112806 (2020) · Zbl 1439.74263
[36] Zheng, C.; Matsumoto, T.; Takahashi, T.; Chen, H., Explicit evaluation of hypersingular boundary integral equations for acoustic sensitivity analysis based on direct differentiation method, Eng Anal Bound Elem, 35, 11, 1225-1235 (2011) · Zbl 1259.76035
[37] Zheng, C.; Matsumoto, T.; Takahashi, T.; Chen, H., A wideband fast multipole boundary element method for three dimensional acoustic shape sensitivity analysis based on direct differentiation method, Eng Anal Bound Elem, 36, 3, 361-371 (2012) · Zbl 1245.74097
[38] Chen, L.; Zheng, C.; Chen, H., A wideband fmbem for 2D acoustic design sensitivity analysis based on direct differentiation method, Comput Mech, 52, 3, 631-648 (2013) · Zbl 1282.74101
[39] Lian, H.; Kerfriden, P.; Bordas, S., Shape optimization directly from CAD: an isogeometric boundary element approach using t-splines, Comput Methods Appl Mech Eng, 317, 1-41 (2017) · Zbl 1439.74486
[40] Bendsøe, M. P., Optimal shape design as a material distribution problem, Struct Optim, 1, 4, 193-202 (1989)
[41] Bendsøe, M. P.; Sigmund, O., Material interpolation schemes in topology optimization, Arch Appl Mech, 69, 9-10, 635-654 (1999) · Zbl 0957.74037
[42] Du, J.; Olhoff, N., Minimization of sound radiation from vibrating bi-material structures using topology optimization, Struct Multidiscip Optim, 33, 4-5, 305-321 (2007)
[43] Zuo, W.; Saitou, K., Multi-material topology optimization using ordered SIMP interpolation, Struct Multidiscip Optim, 55, 2, 477-491 (2017)
[44] Zhao, W.; Chen, L.; Chen, H.; Marburg, S., Topology optimization of exterior acoustic structure interaction systems using the coupled FEM BEM method, Int J Numer Methods Eng, 119, 5, 404-431 (2019) · Zbl 1425.74384
[45] Kim, D. H.; Lee, S. B.; Kwank, B. M.; Kim, H. G.; Lowther, D. A., Smooth boundary topology optimization for electrostatic problems through the combination of shape and topological design sensitivities, IEEE Trans Magn, 44, 6, 1002-1005 (2008)
[46] Seybert, A. F.; Soenarko, B., Radiation and scattering of acoustic waves from bodies of arbitrary shape in a three-dimensional half space, J Vib Acoust, 110, 1, 112-117 (1988)
[47] Zheng, C. J.; Chen, H. B.; Gao, H. F.; Du, L., Is the burton-miller formulation really free of fictitious eigenfrequencies?, Eng Anal Bound Elem, 59, 43-51 (2015) · Zbl 1403.76129
[48] Zheng, C. J.; Bi, C. X.; Zhang, C.; Zhang, Y. B.; Chen, H. B., Fictitious eigenfrequencies in the bem for interior acoustic problems, Eng Anal Bound Elem, 104, 170-182 (2019) · Zbl 1464.76120
[49] Burton A., Miller G.. 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 and physical sciences1971; 323(1553):201-210.. 10.1098/rspa.1971.0097 · Zbl 0235.65080
[50] Hughes, T. J.; Cottrell, J. A.; Bazilevs, Y., Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Comput Methods Appl Mech Eng, 194, 39-41, 4135-4195 (2005) · Zbl 1151.74419
[51] Takahashi, T.; Yamamoto, T.; Shimba, Y.; Isakari, H.; Matsumoto, T., A framework of shape optimisation based on the isogeometric boundary element method toward designing thin-silicon photovoltaic devices, Eng Comput, 35, 2, 423-449 (2019)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.