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Acoustic topology optimization of sound absorbing materials directly from subdivision surfaces with isogeometric boundary element methods. (English) Zbl 1439.74263
Summary: This paper presents an acoustic topology optimization approach using isogeometric boundary element methods based on subdivision surfaces to optimize the distribution of sound adsorption materials adhering to structural surfaces. The geometries are constructed from triangular control meshes through Loop subdivision scheme, and the associated Box-spline functions that generate limit smooth subdivision surfaces are employed to discretize the acoustic boundary integral equations. The effect of sound-absorbing materials on the acoustic response is characterized by acoustic impedance boundary conditions. The optimization problem is formulated in the framework of Solid Isotropic Material with Penalization methods and the sound absorption coefficients on elements are selected as design variables. The potential of the proposed topology optimization approach for engineering prototyping is illustrated by numerical examples.

MSC:
74P15 Topological methods for optimization problems in solid mechanics
65N38 Boundary element methods for boundary value problems involving PDEs
74M15 Contact in solid mechanics
Software:
ISOGAT
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[1] Marburg, S., Developments in structural-acoustic optimization for passive noise control, Arch. Comput. Methods Eng., 27, 291-370 (2002) · Zbl 1099.74538
[2] Bendsøe, M. P.; Sigmund, O., Topology Optimization: Theory, Methods and Applications (2003), Springer · Zbl 1059.74001
[3] Dühring, M. B.; Jensen, J. S.; Sigmund, O., Acoustic design by topology optimization, J. Sound Vib., 317, 3-5, 557-575 (2008)
[4] Du, J.; Olhoff, N., Minimization of sound radiation from vibrating bi-material structures using topology optimization, Struct. Multidiscip. Optim., 33, 305-321 (2007)
[5] Yoon, G. H.; Jensen, J. S.; Sigmund, O., Topology optimization of acoustic-structure interaction problems using a mixed finite element formulation, Internat. J. Numer. Methods Engrg., 70, 1049-1075 (2007) · Zbl 1194.74277
[6] Kang, Z.; Zhang, X.; Jiang, S.; Cheng, G., On topology optimization of damping layer in shell structures under harmonic excitations, Struct. Multidiscip. Optim., 46, 51-67 (2012) · Zbl 1274.74348
[7] Zhu, J.; He, F.; Liu, T.; Zhang, W.; Liu, Q.; Yang, C., Structural topology optimization under harmonic base acceleration excitations, Struct. Multidiscip. Optim., 57, 1061-1078 (2018)
[8] Zhao, W.; Chen, L.; Chen, H.; Marburg, S., Topology optimization of exterior acoustic-structure interaction systems using the coupled FEM-BEM method, Internat. J. Numer. Methods Engrg., 119, 1-28 (2019)
[9] Chen, L.; Zheng, C.; Chen, H.; Marburg, S., Structural-acoustic sensitivity analysis of radiated sound power using a finite element/ discontinuous fast multipole boundary element scheme, Internat. J. Numer. Methods Fluids, 82, 858-878 (2016)
[10] Hughes, T. J.R.; Cottrell, J. A.; Bazilevs, Y., Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Comput. Methods Appl. Mech. Engrg., 194, 39-41, 4135-4195 (2005) · Zbl 1151.74419
[11] Seo, H. K.; Yudeok, J. A.; Youn, S., Isogeometric topology optimization using trimmed spline surfaces, Comput. Methods Appl. Mech. Engrg., 199, 49-52, 3270-3296 (2010) · Zbl 1225.74068
[12] Dedè, L.; Borden, M. J.; Hughes, T. J.R., Isogeometric analysis for topology optimization with a phase field model, Arch. Comput. Methods Eng., 19, 3, 427-465 (2012) · Zbl 1354.74224
[13] Qian, X., Topology optimization in B-spline space, Comput. Methods Appl. Mech. Engrg., 265, 15-35 (2013) · Zbl 1286.74078
[14] Atroshchenko, E.; Tomar, S.; Xu, G.; Bordas, S. P.A., Weakening the tight coupling between geometry and simulation in isogeometric analysis: From sub-and super-geometric analysis to geometry-independent field approximation (GIFT), Internat. J. Numer. Methods Engrg., 114, 10, 1131-1159 (2018)
[15] Simpson, R. N.; Bordas, S. P.A.; Trevelyan, J.; Rabczuk, T., A two-dimensional isogeometric boundary element method for elastostatic analysis, Comput. Methods Appl. Mech. Engrg., 209, 87-100 (2012) · Zbl 1243.74193
[16] Simpson, R. N.; Bordas, S. P.A.; Lian, H.; Trevelyan, J., An isogeometric boundary element method for elastostatic analysis: 2D implementation aspects, Comput. Struct., 118, 2-12 (2013)
[17] Scott, M. A.; Simpson, R. N.; Evans, J. A.; Lipton, S.; Bordas, S. P.A.; Hughes, T. J.R.; Sederberg, T. W., Isogeometric boundary element analysis using unstructured T-splines, Comput. Methods Appl. Mech. Engrg., 254, 197-221 (2013) · Zbl 1297.74156
[18] Peng, X.; Atroshchenko, E.; Kerfriden, P.; Bordas, S. P.A., Linear elastic fracture simulation directly from CAD: 2D NURBS-based implementation and role of tip enrichment, Int. J. Fract., 204, 55-78 (2017)
[19] Xu, G.; Mourrain, B.; Duvigneau, R.; Galligo, A., Parameterization of computational domain in isogeometric analysis: methods and comparison, Comput. Methods Appl. Mech. Engrg., 200, 23-24, 2021-2031 (2011) · Zbl 1228.65232
[20] Xu, G.; Mourrain, B.; Duvigneau, R.; Galligo, A., Analysis-suitable volume parameterization of multi-block computational domain in isogeometric applications, Comput. Aided Des., 45, 2, 395-404 (2013)
[21] Xu, G.; Li, M.; Mourrain, B.; Rabczuk, T.; Xu, J.; Bordas, S. P.A., Constructing iga-suitable planar parameterization from complex cad boundary by domain partition and global/local optimization, Comput. Methods Appl. Mech. Engrg., 328, 175-200 (2018)
[22] Li, K.; Qian, X., Isogeometric analysis and shape optimization via boundary integral, Comput. Aided Des., 43, 11, 1427-1437 (2011)
[23] Kostas, K.; Ginnis, A.; Politis, C.; Kaklis, P., Ship-hull shape optimization with a T-spline based BEM-isogeometric solver, Comput. Methods Appl. Mech. Engrg., 284, 611-622 (2015) · Zbl 1425.65201
[24] Lian, H.; Kerfriden, P.; Bordas, S. P.A., Implementation of regularized isogeometric boundary element methods for gradient-based shape optimization in two-dimensional linear elasticity, Internat. J. Numer. Methods Engrg., 106, 12, 972-1017 (2016) · Zbl 1352.74467
[25] Lian, H.; Kerfriden, P.; Bordas, S. P.A., Shape optimization directly from cad: an isogeometric boundary element approach using T-splines, Comput. Methods Appl. Mech. Engrg., 317, 1-41 (2017)
[26] Li, S.; Trevelyan, J.; Wu, Z.; Lian, H.; Wang, D.; Zhang, W., An adaptive SVD-Krylov reduced order model for surrogate based structural shape optimization through isogeometric boundary element method, Comput. Methods Appl. Mech. Engrg., 349, 312-338 (2019)
[27] Simpson, R. N.; Scott, M. A.; Taus, M.; Thomas, D. C.; Lian, H., Acoustic isogeometric boundary element analysis, Comput. Methods Appl. Mech. Engrg., 269, 265-290 (2014) · Zbl 1296.65175
[28] Chen, L.; Liu, L.; Zhao, W.; Liu, C., An isogeometric approach of two dimensional acoustic design sensitivity analysis and topology optimization analysis for absorbing material distribution, Comput. Methods Appl. Mech. Engrg., 336, 507-532 (2018)
[29] Simpson, R. N.; Liu, Z., Acceleration of isogeometric boundary element analysis through a black-box fast multipole method, Eng. Anal. Bound. Elem., 66, 168-182 (2016) · Zbl 1403.65228
[30] Peng, X.; Atroshchenko, E.; Kerfriden, P.; Bordas, S. P.A., Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth, Comput. Methods Appl. Mech. Engrg., 316, 151-185 (2017)
[31] Schillinger, D.; Evans, J. A.; Reali, A.; Scott, M. A.; Hughes, T. J.R., Isogeometric collocation: Cost comparison with galerkin methods and extension to adaptive hierarchical NURBS discretizations, Comput. Methods Appl. Mech. Engrg., 267, 170-232 (2013) · Zbl 1286.65174
[32] 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
[33] Coox, L.; Greco, F.; Atak, O.; Vandepitte, D.; Desmet, W., A robust patch coupling method for NURBS-based isogeometric analysis of non-conforming multipatch surfaces, Comput. Methods Appl. Mech. Engrg., 316, 235-260 (2017)
[34] Vuong, A.; Giannelli, C.; Juttler, B.; Simeon, B., A hierarchical approach to adaptive local refinement in isogeometric analysis, Comput. Methods Appl. Mech. Engrg., 200, 49, 3554-3567 (2011) · Zbl 1239.65013
[35] Nguyen, V. P.; Kerfriden, P.; Brino, M.; Bordas, S. P.A.; Bonisoli, E., Nitsche’s method for two and three dimensional NURBS patch coupling, Comput. Mech., 53, 6, 1163-1182 (2014) · Zbl 1398.74379
[36] Nguyen, V. P.; Kerfriden, P.; Bordas, S. P.A., Two-and three-dimensional isogeometric cohesive elements for composite delamination analysis, Composites B, 60, 193-212 (2014)
[37] Hu, Q.; Chouly, F.; Hu, P.; Cheng, G.; Bordas, S. P.A., Skew-symmetric nitsche’s formulation in isogeometric analysis: Dirichlet and symmetry conditions, patch coupling and frictionless contact, Comput. Methods Appl. Mech. Engrg., 341, 188-220 (2018)
[38] Sederberg, T. W.; Zheng, J.; Bakenov, A.; Nasri, A., T-splines and T-NURCCs, ACM Trans. Graph., 22, 3, 477-484 (2003)
[39] Bazilevs, Y.; Calo, V. M.; Cottrell, J.; Evans, J. A.; Hughes, T. J.R.; Lipton, S.; Scott, M. A.; Sederberg, T. W., Isogeometric analysis using T-splines, Comput. Methods Appl. Mech. Engrg., 199, 5, 229-263 (2010) · Zbl 1227.74123
[40] Li, X.; Chen, F.; Kang, H.; Deng, J., A survey on the local refinable splines, Sci. China Math., 59, 4, 617-644 (2016) · Zbl 1338.65034
[41] Li, X.; Deng, J.; Chen, F., Surface modeling with polynomial splines over hierarchical T-meshes, Vis. Comput., 23, 12, 1027-1033 (2007)
[42] Deng, J.; Chen, F.; Li, X.; Hu, C.; Tong, W.; Yang, Z.; Feng, Y., Polynomial splines over hierarchical T-meshes, Graph. Models, 70, 4, 76-86 (2008)
[43] Li, X.; Deng, J.; Chen, F., Polynomial splines over general T-meshes, Vis. Comput., 26, 4, 277-286 (2010)
[44] Nguyenthanh, N.; Nguyenxuan, H.; Bordas, S. P.A.; Rabczuk, T., Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids, Comput. Methods Appl. Mech. Engrg., 200, 21, 1892-1908 (2011) · Zbl 1228.74091
[45] Nguyenthanh, N.; Kiendl, J.; Nguyenxuan, H.; Wuchner, R.; Bletzinger, K. U.; Bazilevs, Y.; Rabczuk, T., Rotation free isogeometric thin shell analysis using PHT-splines, Comput. Methods Appl. Mech. Engrg., 200, 47, 3410-3424 (2011) · Zbl 1230.74230
[46] Anitescu, C.; Hossain, N.; Rabczuk, T., Recovery-based error estimation and adaptivity using high-order splines over hierarchical T-meshes, Comput. Methods Appl. Mech. Engrg., 328, 638-662 (2018)
[47] Forsey, D. R.; Bartels, R. H., Hierarchical B-spline refinement, ACM Siggraph Comput. Graph., 22, 4, 205-212 (1988)
[48] Hofreither, C.; Jüttler, B.; Kiss, G.; Zulehner, W., Multigrid methods for isogeometric analysis with THB-splines, Comput. Methods Appl. Mech. Engrg., 308, 96-112 (2016)
[49] Dokken, T.; Lyche, T.; Pettersen, K. F., Polynomial splines over locally refined box-partitions, Comput. Aided Geom. Design, 30, 3, 331-356 (2013) · Zbl 1264.41011
[50] Johannessen, K. A.; Kvamsdal, T.; Dokken, T., Isogeometric analysis using LR B-splines, Comput. Methods Appl. Mech. Engrg., 269, 471-514 (2014) · Zbl 1296.65021
[51] Cirak, F.; Long, Q., Subdivision shells with exact boundary control and non-manifold geometry, Internat. J. Numer. Methods Engrg., 88, 9, 897-923 (2011) · Zbl 1242.74102
[52] Catmull, E. E.; Clark, J. H., Recursively generated B-spline surfaces on arbitrary topological meshes, Comput. Aided Des., 10, 350-355 (1978)
[53] Doo, D.; Sabin, M. A., Behaviour of recursive division surfaces near extraordinary points, Comput. Aided Des., 10, 6, 356-360 (1978)
[54] Loop, C., Smooth Subdivision Surfaces Based on Triangles (1987), Department of Mathematics, University of Utah, (Master’s thesis)
[55] Huang, Z.; Deng, J.; Wang, G., A bound on the approximation of a Catmull-Clark subdivision surface by its limit mesh, Comput. Aided Geom. Design, 25, 457-569 (2008) · Zbl 1172.65329
[56] Toshniwal, D.; Speleers, H.; Hughes, T. J.R., Smooth cubic spline spaces on unstructured quadrilateral meshes with particular emphasis on extraordinary points: Geometric design and isogeometric analysis considerations, Comput. Methods Appl. Mech. Engrg., 327, 411-458 (2017)
[57] Wu, M.; Mourrain, B.; Galligo, A.; Nkonga, B., Hermite type spline spaces over rectangular meshes with arbitrary topology, Commun. Comput. Phys., 21, 835-866 (2017)
[58] Lee, C., Automatic metric 3D surface mesh generation using subdivision surface geometrical model. Part 2: Mesh generation algorithm and examples, Int. J. Numer. Methods Eng., 56 (2003), 1615-1646 · Zbl 1025.65060
[59] Pan, Q.; Xu, G.; Zhang, Y., A unified method for hybrid subdivision surface design using geometric partial differential equations, Comput. Aided Des., 46, 110-119 (2014)
[60] Wei, X.; Zhang, Y.; Hughes, T. J.R.; Scott, M. A., Truncated hierarchical Catmull-Clark subdivision with local refinement, Comput. Methods Appl. Mech. Engrg., 291, 1-20 (2015) · Zbl 1425.65028
[61] Pan, Q.; Xu, G.; Xu, G.; Zhang, Y., Isogeometric analysis based on extended Catmull-Clark subdivision, Comput. Math. Appl., 71, 105-119 (2016)
[62] Cirak, F.; Ortiz, M.; Schröder, P., Subdivision surfaces: a new paradigm for thin-shell finite-element analysis, Internat. J. Numer. Methods Engrg., 47, 12, 2039-2072 (2000) · Zbl 0983.74063
[63] Cirak, F.; Scott, M. J.; Antonsson, E. K.; Ortiz, M.; Schröder, P., Integrated modeling, finite-element analysis, and engineering design for thin-shell structures using subdivision, Comput. Aided Des., 34, 2, 137-148 (2002)
[64] Liu, Z.; Majeed, M.; Cirak, F.; Simpson, R. N., Isogeometric FEM-BEM coupled structural-acoustic analysis of shells using subdivision surfaces, Internat. J. Numer. Methods Engrg., 113, 9, 1507-1530 (2018)
[65] Bandara, K.; Cirak, F.; Steinbach, O.; Zapletal, J., Boundary element based multiresolution shape optimisation in electrostatics, J. Comput. Phys., 297, 584-598 (2015) · Zbl 1349.78081
[66] Li, J.; Dault, D.; Liu, B.; Tong, Y.; Shanker, B., Subdivision based isogeometric analysis technique for electric field integral equations for simply connected structures, J. Comput. Phys., 319, 145-162 (2016) · Zbl 1349.78115
[67] Bandara, K.; Cirak, F., Isogeometric shape optimisation of shell structures using multiresolution subdivision surfaces, J. Phys. Conf. Ser., 734, 3, Article 032142 pp. (2016)
[68] Bandara, K.; Rüberg, T.; Cirak, F., Shape optimisation with multiresolution subdivision surfaces and immersed finite elements, Comput. Methods Appl. Mech. Engrg., 300, 510-539 (2016) · Zbl 1425.74385
[69] Burton, A.; Miller, G., The application of integral equation methods to the numerical solution of some exterior boundary-value problems, Proc. R. Soc. A, 323, 1553, 201-210 (1971) · Zbl 0235.65080
[70] Troian, R.; Gillot, F.; Besset, S., Adjoint sensitivity related to geometric parameters for mid-high frequency range vibroacoustics, Struct. Multidiscip. Optim., 52, 4, 803-811 (2015)
[71] Denli, H.; Sun, J., Structural-acoustic optimization of sandwich cylindrical shells for minimum interior sound transmission, J. Sound Vib., 316, 1, 32-49 (2008)
[72] Koo, K.; Pluymers, B.; Desmet, W.; Wang, S., Vibro-acoustic design sensitivity analysis using the wave-based method, J. Sound Vib., 330, 17, 4340-4351 (2011)
[73] Chen, L.; Marburg, S.; Chen, H.; Zhang, H.; Gao, H., An adjoint operator approach for sensitivity analysis of radiated sound power in fully coupled structural-acoustic systems, J. Comput. Acoust., 25, 01, Article 1750003 pp. (2017)
[74] 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
[75] Chen, L.; Lian, H.; Liu, Z.; Chen, H.; Atroshchenko, E.; Bordas, S. P.A., Structural shape optimization of three dimensional acoustic problems with isogeometric boundary element methods, Comput. Methods Appl. Mech. Engrg., 355, 926-951 (2019)
[76] Stam, J., Exact evaluation of catmull-clark subdivision surfaces at arbitrary parameter values, (Siggraph, Vol. 98 (1998), Citeseer), 395-404
[77] Schillinger, D.; Evans, J. A.; Reali, A.; Scott, M. A.; Hughes, T. J.R., Isogeometric collocation: Cost comparison with Galerkin methods and extension to adaptive hierarchical NURBS discretizations, Comput. Methods Appl. Mech. Engrg., 267, 170-232 (2013) · Zbl 1286.65174
[78] Zhao, W.; Zheng, C.; Liu, C.; Chen, H., Minimization of sound radiation in fully coupled structural-acoustic systems using FEM-BEM based topology optimization, Struct. Multidiscip. Optim., 58, 1, 115-128 (2017)
[79] Christiansen, A. N.; Nobel-Jørgensen, M.; Aage, N.; Sigmund, O.; Bærentzen, J. A., Topology optimization using an explicit interface representation, Struct. Multidiscip. Optim., 49, 3, 387-399 (2014)
[80] 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)
[81] Zhou, M.; Lian, H.; Sigmund, O.; Aage, N., Shape morphing and topology optimization of fluid channels by explicit boundary tracking, Internat. J. Numer. Methods Fluids, 88, 6, 296-313 (2018)
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