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Solutions to shape and topology eigenvalue optimization problems using a homogenization method. (English) Zbl 0767.73046
Summary: A solution strategy to find the shape and topology of structures that maximize a natural frequency is peresented. The methodology is based on a homogenization method and the representation of the shape of the structure as a material property. The problem is formulated as a reinforcement problem in which a given structure is reinforced using a prescribed amount of material. Plane elasticity problems are considered. Examples are presented for illustration.

MSC:
74P99 Optimization problems in solid mechanics
74E05 Inhomogeneity in solid mechanics
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[1] Bendsøe, Comp. Methods Appl. Mech. Eng. 71 pp 197– (1988)
[2] Suzuki, Comp. Methods Appl. Mech. Eng. 93 pp 291– (1991)
[3] Bendsøe, Struct. Optimization 1 pp 193– (1989)
[4] Díaz, ASME J. Mech. Des.
[5] Díaz, Struct. Optimization 4 pp 17– (1992)
[6] ’Shape optimization and CAD’, Third Air Force/NASA Symposium on Recent Advances in Multidisciplinary Analysis and Optimization, San Francisco, 1990.
[7] ’Composite materials and structural optimization’, Workshop on Smart/Intelligent Materials and Systems, Honolulu, 1990.
[8] Some Methods in the Mathematical Analysis of Systems and their Control, Gordon and Breach, New York, 1981.
[9] Dems, Int. J. Solids Struct. 19 pp 677– (1983)
[10] and , Elements of Structural Optimization, Kluwer, Dordrecht, The Netherlands, 1990. · Zbl 0702.73047 · doi:10.1007/978-94-015-7862-2
[11] Pedersen, Struct. Optimization 1 pp 101– (1989)
[12] Papalambros, J. Eng. Des. 1 pp 73– (1990)
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