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Erschienen in:
Microtruss Composites Kapitel lesen Erstes Kapitel lesen

2019 | OriginalPaper | Buchkapitel

6. Topological Optimization with Interfaces

verfasst von : N. Vermaak, G. Michailidis, A. Faure, G. Parry, R. Estevez, F. Jouve, G. Allaire, Y. Bréchet

Erschienen in: Architectured Materials in Nature and Engineering

Verlag: Springer International Publishing

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Abstract

Design of architectured materials and structures, whether in nature or in engineering, often relies on forms of optimization. In nature, controlling architecture or spatial heterogeneity is usually adaptive and incremental. Naturally occuring architectured materials exploit heterogeneity with typically graded interfaces, smoothly transitioning across properties and scales in the pursuit of performance and longevity. This chapter explores an engineering tool, topology optimization, that is at the frontier of designing architectured materials and structures. Topology optimization offers a mathematical framework to determine the most efficient material layout for prescribed constraints and loading conditions. In engineering, topology optimization is identifying designs with interfaces, materials, manufacturing methods, and functionalities unavailable to the natural world. The particular focus is on the variety of roles that interfaces may play in advancing architectured materials and structures with topology optimization.

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Vorheriges Kapitel Design Methods for Architectured Materials
Nächstes Kapitel Friction Stir Processing for Architectured Materials
Fußnoten
1
Plasma and other states of matter that occur under extreme conditions are not considered.
 
Literatur
1.
M. Ashby, Designing architectured materials. Scr. Mater. 68(1), 4–7 (2013)CrossRef
2.
M. Ashby, Y. Brechet, Designing hybrid materials. Acta Mater. 51(19), 5801–5821 (2003)CrossRef
3.
S. Torquato, Optimal design of heterogeneous materials. Ann. Rev. Mater. Res. 40, 101–129 (2010)CrossRef
4.
M. Bendsoe, O. Sigmund, in Topology Optimization: Theory, Methods and Applications (Springer, 2004)
5.
D. Wolf, J. Jaszczak, in Materials Interfaces: Atomic-level Structure and Properties (1992)
6.
G. Allaire, Conception optimale de structures, vol. 58, in Mathématiques & Applications (Springer-Verlag, Berlin, 2007)
7.
P. Christensen, A. Klarbring, in An Introduction to Structural Optimization, vol. 153. (Springer, 2009)
8.
J.D. Deaton, R.V. Grandhi, A survey of structural and multidisciplinary continuum topology optimization: post 2000. Struct. Multi. Optim. 49(1), 1–38 (2014)CrossRef
9.
G. Allaire, E. Bonnetier, G. Francfort, F. Jouve, Shape optimization by the homogenization method. Numer. Math. 76(1), 27–68 (1997)CrossRef
10.
M. Bendsøe, N. Kikuchi, Generating optimal topologies in structural design using a homogenization method. Comput. Methods Appl. Mech. Eng. 71(2), 197–224 (1988)CrossRef
11.
L. Gibiansky and A. Cherkaev, Design of composite plates of extremal rigidity, in Topics in the Mathematical Modelling of Composite Materials (Springer, 1997), pp. 95–137
12.
R. Kohn, G. Strang, Optimal design and relaxation of variational problems, I. Commun. Pure Appl. Math. 39(1), 113–137 (1986a)CrossRef
13.
R. Kohn, G. Strang, Optimal design and relaxation of variational problems, II. Commun. Pure Appl. Math. 39(2), 139–182 (1986b)CrossRef
14.
R. Kohn, G. Strang, Optimal design and relaxation of variational problems, III. Commun. Pure Appl. Math. 39(3), 353–377 (1986c)CrossRef
15.
F. Murat, L. Tartar, Calcul des variations et homogénéisation. Les méthodes de lhomogénéisation: théorie et applications en physique 57, 319–369 (1985)
16.
S. Osher, J. Sethian, Fronts propagating with curvature-dependent speed: algorithms based on hamilton-jacobi formulations. J. Comput. Phys. 79(1), 12–49 (1988)CrossRef
17.
J. Sethian, A. Wiegmann, Structural boundary design via level set and immersed interface methods. J. Comput. Phys. 163(2), 489–528 (2000)CrossRef
18.
G. Allaire, F. Jouve, A.-M. Toader, Structural optimization using sensitivity analysis and a level-set method. J. Comput. Phys. 194(1), 363–393 (2004)CrossRef
19.
M. Wang, X. Wang, D. Guo, A level set method for structural topology optimization. Comput. Methods Appl. Mech. Eng. 192(1), 227–246 (2003)CrossRef
20.
A. Christiansen, M. Nobel-Jørgensen, N. Aage, O. Sigmund, J. Bærentzen, Topology optimization using an explicit interface representation, in Structural and Multidisciplinary Optimization (2013), pp. 1–13
21.
L. Blank, M. Farshbaf-Shaker, H. Garcke, C. Rupprecht, V. Styles, Multi-material phase field approach to structural topology optimization, in Trends in PDE Constrained Optimization (Springer, 2014), pp. 231–246
22.
S. Zhou, M. Wang, Multimaterial structural topology optimization with a generalized cahn-hilliard model of multiphase transition. Struct. Multi. Optim. 33(2), 89–111 (2007)CrossRef
23.
O. Querin, G. Steven, Y. Xie, Evolutionary structural optimisation (eso) using a bidirectional algorithm. Eng. Comput. 15(8), 1031–1048 (1998)CrossRef
24.
A. Baumgartner, L. Harzheim, C. Mattheck, Sko (soft kill option): the biological way to find an optimum structure topology. Int. J. Fatigue 14(6), 387–393 (1992)CrossRef
25.
C. Mattheck, Design and growth rules for biological structures and their application to engineering. Fatigue Fract. Eng. Mater. Struct. 13(5), 535–550 (1990)CrossRef
26.
O. Sigmund, On the usefulness of non-gradient approaches in topology optimization. Struct. Multi. Optim. 43(5), 589–596 (2011)CrossRef
27.
J. Guest, Topology optimization with multiple phase projection. Comput. Methods Appl. Mech. Eng. 199(1), 123–135 (2009)CrossRef
28.
A. Clausen, N. Aage, O. Sigmund, Topology optimization of coated structures and material interface problems. Comput. Methods Appl. Mech. Eng. 290, 524–541 (2015)CrossRef
29.
30.
F. Murat, J. Simon, Etude de problèmes d’optimal design. Optim. Tech. Model. Optim. Serv. Man Part 2, 54–62 (1976)CrossRef
31.
J. Simon, F. Murat, in Sur le contrôle par un domaine géométrique. Publication 76015 du Laboratoire d’Analyse Numérique de l’Université Paris VI, (76015):222 pages (1976)
32.
B. Merriman, J.K. Bence, S.J. Osher, Motion of multiple junctions: a level set approach. J. Comput. Phys. 112(2), 334–363 (1994)CrossRef
33.
M. Wang, X. Wang, Color level sets: a multi-phase method for structural topology optimization with multiple materials. Comput. Methods Appl. Mech. Eng. 193(6), 469–496 (2004)CrossRef
34.
35.
O. Pironneau, Optimal Shape Design for Elliptic Systems, Springer Series in Computational Physics. (Springer-Verlag, New York, 1984)
36.
J. Sokołowski and J.-P. Zolésio. Introduction to Shape Optimization, vol. 16, Springer Series in Computational Mathematics. (Springer-Verlag, Berlin, 1992). Shape sensitivity analysis
37.
S. Osher, R. Fedkiw, Level set methods and dynamic implicit surfaces, in Applied Mathematical Sciences,vol. 153 (Springer-Verlag, New York, 2003)
38.
J. Sethian, Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science (Cambridge University Press, Cambridge, 1999)
39.
G. Allaire, C. Dapogny, P. Frey, A mesh evolution algorithm based on the level set method for geometry and topology optimization. Struct. Multi. Optim. 48(4), 711–715 (2013)CrossRef
40.
Q. Xia, T. Shi, S. Liu, M. Wang, A level set solution to the stress-based structural shape and topology optimization. Comput. Struct. 9091, 55–64 (2012)CrossRef
41.
L. Ambrosio, G. Buttazzo, An optimal design problem with perimeter penalization. Calc. Var. Partial. Differ. Equ. 1(1), 55–69 (1993)CrossRef
42.
43.
G. Allaire, F. Jouve, G. Michailidis, Thickness control in structural optimization via a level set method. Struct. Multi. Optim. 53(6), 1349–1382 (2016)CrossRef
44.
F. Feppon, Design and Optimization for Wear of Bi-material Composite Surfaces. Master’s thesis, Ecole Polytechnique, Promotion X2012, 2015
45.
46.
N. Vermaak, G. Michailidis, G. Parry, R. Estevez, G. Allaire, Y. Bréchet, Material interface effects on the topology optimizationof multi-phase structures using a level set method. Struct. Multi. Optim. 50(4), 623–644 (2014)CrossRef
47.
O. Sigmund, Tailoring materials with prescribed elastic properties. Mech. Mater. 20(4), 351–368 (1995)CrossRef
48.
49.
A. Clausen, N. Aage, O. Sigmund, Exploiting additive manufacturing infill in topology optimization for improved buckling load. Engineering 2(2), 250–257 (2016)CrossRef
50.
P. Zhang, J. Liu, A. To, Role of anisotropic properties on topology optimization of additive manufactured load bearing structures. Scripta Mater. 135, 148–152 (2016)CrossRef
Metadaten
Titel
Topological Optimization with Interfaces
verfasst von
N. Vermaak
G. Michailidis
A. Faure
G. Parry
R. Estevez
F. Jouve
G. Allaire
Y. Bréchet
Copyright-Jahr
2019
Buch
Architectured Materials in Nature and Engineering

Print ISBN: 978-3-030-11941-6

Electronic ISBN: 978-3-030-11942-3

Copyright-Jahr: 2019

DOI
https://doi.org/10.1007/978-3-030-11942-3_6

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