Abstract
The perimeter method for variable-topology shape optimization enforces an upper-bound constraint on the perimeter of the solid part of the structure. The perimeter constraint ensures a well-posed design problem and allows the designer to control the number of holes in the optimal design and to establish their characteristic length scale. Thus single-step procedures for topology design and detailed shape design are possible.
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References
Allaire, G.; Kohn, R. V. 1993: Topology design and optimal shape design using homogenization. In: Bendsøe, M. P.; Mota Soares, C. A. (eds.) Topology design of structures, 207–218. Dordrecht: Kluwer
Ambrosio, L.; Buttazzo, G. 1993: An Optimal Design Problem with Perimeter Penalization. Calc. Var. 1, 55–69
Bends0e, M. P.; Kikuchi, N. 1988: Generating optimal topologies in structural design using a homogenization method. Comp. Meth. Appl Mech. Engng. 71, 197–224
Eschenauer, H.A.; Kobelev, V.; Schumacher, A. 1994: Bubble Method of Topology and Shape Optimization of Structures. Struct. Optim. 8, 42–51
Evans, L. C.; Gariepy, R. F. 1992: Measure theory and fine properties of functions, Boca Ratan: CRC Press
Haber, R. B.; Jog, C. S.; Bendsøe, M. P. 1994: Variable-topology shape optimization with a control on perimeter. In: Gilmore, B. J.; Hoeltzel, D. A.; Dutta, D.; Eschenauer, H. A. (eds.) Advances in Design Automation, ASME DE-Vol. 69–2, 261–272
Jog, C. S.; Haber, R. B.; Bendsøe, M. P. 1994: Topology design with optimized, self-adaptive materials. Int. J. Num. Methods Engng. 37, 1323–1350
Rodrigues, H. C.; Fernandes, P. 1994: A material based model for topology optimization of thermoelastic structures. Int. J. Num. Methods Engng. 37 (to appear)
Rozvany, G.I.N.; Bendsøe, M.P.; Kirsch, U. (1994): Layout Optimization of Structures. Appl. Mech. Rev. 48, 41–118
Sigmund, O. 1995:Design of Material Structures using Topology Optimization. DCAMM Special Report no. S69, Techn. Univ. of Denmark, 1995
Suzuki, K.; Kikuchi, N. 1991: Shape and topology optimization for generalized layout problems using the homogenization method. Comp. Meth. Appl. Mechs. Engng. 93, 291–318
Wheedon, R. L.; Zygmund, A. 1977: Measure and integral: an introduction to real analysis, Monographs in Pure and Applied Math. 43, New York: Marcel Dekker
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© 1996 Kluwer Academic Publishers
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Haber, R.B., Bendøse, M.P., Jog, C.S. (1996). Perimeter Constrained Topology Optimization of Continuum Structures. In: Bestle, D., Schiehlen, W. (eds) IUTAM Symposium on Optimization of Mechanical Systems. Solid Mechanics and its Applications, vol 43. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0153-7_15
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DOI: https://doi.org/10.1007/978-94-009-0153-7_15
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6555-9
Online ISBN: 978-94-009-0153-7
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