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Topological design for vibrating structures. (English) Zbl 0849.73045
Summary: The topological optimization technique using micro-scale voids with the homogenization method (for stress analysis of perforated structures) has been applied to solve stiffness maximization problem. Here, the homogenization design technique is extended to design problems concerning vibrating structures. An extended optimization algorithm is also derived to maximize a set of eigenvalues as well as to identify the topology design for specified eigenvalues to characterize forced vibrations of a structure.

MSC:
74P99 Optimization problems in solid mechanics
74H45 Vibrations in dynamical problems in solid mechanics
74E05 Inhomogeneity in solid mechanics
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[1] Kirsch, U., Optimum topologies of structures, Appl. mech. rev., 42, 223-239, (1989)
[2] Maxwell, G., On reciprocal figures, frames, and diagrams of forces, (), 175-177
[3] Michell, A.G.M., The limits of economy in frame structures, Philo. mag. sect., 6, 8, 589-597, (1904) · JFM 35.0828.01
[4] Hemp, W.S., Optimum structures, () · Zbl 0608.73086
[5] Prager, W.; Rozvany, G.I.N., Optimal layout of grillages, J. struct. mech., 5, 1-18, (1977)
[6] Rozvany, G.I.N., Optimality criteria for grids, shells and arches, (), 112-151 · Zbl 0371.73018
[7] Rozvany, G.I.N.; Wang, C.M., Extensions of Prager’s layout theory, (), 103-110
[8] Zhou, M.; Rozvany, G.I.N., The COC algorithm, part II: topology, geometrical and generalized shape and optimization, Comput. methods appl. mech. engrg., 89, 309-336, (1991)
[9] Olhoff, N.; Rozvany, G.I.N., Optimal grillage layout for given natural frequency, J. struct. mech. ASCE, 108, 971-974, (1982)
[10] Rozvany, G.I.N., Layout theory for grid-type structures, (), 251-272
[11] Cheng, K.T.; Olhoff, N., An investigation concerning optimal design of solid elastic plates, Int. J. solids structures, 17, 305-323, (1981) · Zbl 0457.73079
[12] Kohn, R.V.; Strang, G.; Kohn, R.V.; Strang, G.; Kohn, R.V.; Strang, G., Optimal design and relaxation of variational problem, Comm. pure. appl. math., Comm. pure. appl. math., Comm. pure. appl. math., 39, 353-377, (1986) · Zbl 0694.49004
[13] Bendsøe, M.P.; Kikuchi, N., Generating optimal topologies in structural design using a homogenization method, Comput. methods appl. mech. engrg., 71, 197-224, (1988) · Zbl 0671.73065
[14] Bendsøe, M.P., Optimal shape design as a material distribution problem, Struct. optimization, 1, 193-202, (1989)
[15] Suzuki, K.; Kikuchi, N., A homogenization method for shape and topology optimization, Comput. methods appl. mech. engrg., 93, 291-318, (1991) · Zbl 0850.73195
[16] Olhoff, N.; Bendsøe, M.P.; Rasmussen, J., On CAD-integrated structural topology and design optimization, Comput. methods appl. mech. engrg., 89, 259-279, (1991)
[17] Bendsøe, M.P.; Diaz, A.; Kikuchi, N., Topology and generalized layout optimization of elastic structures, (), 159-205
[18] Soto, C.; Diaz, A., On the modeling of ribbed plates for shape optimization, ()
[19] K. Suzuki and N. Kikuchi, Generalized layout optimization of three-dimensional shell structures, D.A. Komkov V., eds., Geometric Aspects of Industrial Design, SIAM, Philadelphia, 62-88. · Zbl 0825.73469
[20] Kikuchi, N.; Suzuki, K.; Fukushima, J., Layout optimization using the homogenization method: generalized layout design of three-dimensional shells for car bodies, (), 110-126
[21] Suzuki, K.; Kikuchi, N., Shape and topology optimization of three-dimensional solid structures, ()
[22] Diaz, A.; Kikuchi, N., Solutions to shape and topology eigenvalue optimization problems using a homogenization method. preprint, Internat. J. numer. methods engrg., 35, 1487-1502, (1992) · Zbl 0767.73046
[23] Ma, Z.-D.; Cheng, H.-C.; Kikuchi, N.; Hagiwara, I., Topology and shape optimization technique for structural dynamic problems, recent advances in structural problems, Pvp-248/ne-10, 133-143, (1992)
[24] Ma, Z.-D.; Kikuchi, N.; Hagiwara, I., Structural topology and shape optimization for a frequency response problem, Computational mech., 13, 3, 157-174, (1993) · Zbl 0790.73052
[25] Cheng, H.-C.; Kikuchi, N.; Ma, Z.-D., An improved approach for determining the optimal orientation of the orthotropic material, Struct. optimization, 8, (1994), in press
[26] Ma, Z.-D.; Hagiwara, I., Improved mode-superposition technique for modal frequency response analysis of coupled acoustic-structural systems, Aiaa j., 29, 10, 1720-1726, (1991) · Zbl 0738.73043
[27] Ma, Z.-D.; Hagiwara, I., Sensitivity analysis methods for coupled acoustic-structural systems, part 1: modal sensitivities, Aiaa j., 29, 11, 1787-1795, (1991) · Zbl 0738.76065
[28] Ma, Z.-D.; Hagiwara, I., Sensitivity calculation methods for modal frequency response analysis of coupled acousticstructural systems, JSME internat. J., 35, 14-21, (1992), Series III
[29] Li, Xing-Si, An aggregate function method for nonlinear programming, Science in China, 34, 12, 1467-1473, (1991), (series A) · Zbl 0752.90069
[30] Berke, L.; Venkayya, V.B., Review of optimality criteria approaches to structural optimization, (), 23-34 · Zbl 0305.73051
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