Abstract
A scheme for layout optimization in structures with multiple finite-sized heterogeneities is presented. Multiresolution analysis is used to compute reduced operators (stiffness matrices) representing the elastic behavior of material distributions with heterogeneities of sizes that are comparable to the size of the structure. Two approaches for computing the reduced operators are presented: one based on a multiresolution analysis of displacements and the other based on a multiresolution analysis of a function representing the material distribution. Numerical examples using the mean compliance as the objective function are presented to illustrate the method.
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Bendsøe, M.P; Diaz, A.R; Kikuchi, N. 1993: Topology and generalized layout optimization of elastic structures. In: Bendsøe, M.P.; Mota Soares, C.A. (eds.) Topology Design of Structures, pp. 159–206. Dordrecht: Kluwer Academic Publishers
Bendsøe, M.P.; Sigmund, O. 2003: Topology Optimization – Theory, Methods and Applications. Berlin, Heidelberg: Springer-Verlag
Bensoussan, A.; Lions, L.-J.; Papanicolaou, G. 1978: Asymptotic Analysis of Periodic Structures. Amsterdam: North-Holland
Brewster, M.; Beylkin, G. 1995: A multi-resolution strategy for numerical homogenization. Appl. Comput. Harmonic Anal. 2, 327–349
Chellappa, S.; Diaz, A.R. 2002: Model reduction in structural analysis using a multi-resolution analysis. In: Proc. 2002 ASME Design Engineering Technical Conf. (held in Montreal), on CD-ROM
DeRose Jr., G.C.A.; Diaz, A.R. 1999: Single scale wavelet approximations in layout optimization. Struct. Optim. 18(1), 1–11
Diaz, A.R. 1999: A wavelet-Galerkin scheme for analysis of large-scale problems on simple domains. Int. J. Numer. Methods Eng. 44, 1599–1616
Diaz, A.R.; Benard, A. 2003: Designing materials with prescribed elastic properties using polygonal cells. Int. J. Numer. Methods Eng. 57(3), 301–314
Diaz, A.R.; Chellappa, S. 2002: A multi-resolution reduction scheme for topology optimization. In: Mang, H.A.; Rammerstorfer, G.F.; Eberhardsteiner, J. (eds.) Proc. 5th World Congress on Computational Mechanics, WCCM V, on CD-ROM
Dorobantu, M.; Engquist, B. 1998: Wavelet-based numerical homogenization. SIAM J. Numer. Anal. 35, 549–559
Gilbert, A.C. 1998: A comparison of multi-resolution and classical one-dimensional homogenization schemes. Appl. Comput. Harmonic Anal. 5, 1–35
Haber, R.B.; Jog, C.S.; Bendsøe, M.P. 1996: A new approach to variable-topology shape design using constraint on perimeter. Struct. Optim. 11, 1–12
Olhoff, N.; Bendsøe, M.P.; Rasmussen, J. 1992: On CAD-integrated structural topology and design optimization. Comput. Methods Appl. Mech. Eng. 89, 259–279
Pecullan, S.; Gibiansky, L.V.; Torquato, S. 1999: Scale Effects on the elastic behavior of periodic and hierarchical two-dimensional composites. J. Mech. Phys. Solids 47(7), 1509–1542
Resnikoff, H.L.; Wells, R.O. 1999: Wavelet Analysis: The Scalable Structure of Information. New York: Springer-Verlag
Schattschneider, D. 1997: Escher’s combinatorial patterns. Electron. J. Combinatorics 4(R17)
Soto, C.A.; Yang, R.J. 1999: Optimum layout of embossed ribs to maximize natural frequencies in plates. Des. Optim.: Int. J. Prod. Proc. Improvement 1(1), 44–54
Svanberg, K. 1987: The method of moving asymptotes – a new method for structural optimization. Int. J. Numer. Methods Eng. 24, 359–373
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Chellappa , S., Diaz , A. & Bendsøe , M. Layout optimization of structures with finite-sized features using multiresolution analysis. Struct Multidisc Optim 26, 77–91 (2004). https://doi.org/10.1007/s00158-003-0306-7
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DOI: https://doi.org/10.1007/s00158-003-0306-7