TY - JOUR
T1 - Optimization of structural topology in the high-porosity regime
AU - Bourdin, Blaise
AU - Kohn, Robert V.
N1 - Funding Information:
This work was partially supported by ARO under Grant DAAD19-00-1-0384, and by NSF under Grant DMS-0313744. We are grateful to the anonymous referee for his helpful comments, questions, and corrections.
PY - 2008/3
Y1 - 2008/3
N2 - We propose a new approach to topology optimization, based on the use of "single-scale laminates" as structural components. The method is well-founded, because in the high porosity limit these structures achieve maximal stiffness and minimal weight. The method is useful, because the Hooke's law of a single-scale laminate has a simple, explicit formula which scales linearly with weight. And it is interesting, because the selection of relatively simple, manufacturable designs can be addressed using linear or quadratic programming. Our contributions are two-fold: (a) we establish the foundation of this approach, by defining single-scale laminates and giving self-contained proofs of their optimality in the high-porosity limit; and (b) we explore two numerical applications-minimizing weight with a constraint on the Hooke's law, and imposing continuity on a spatially varying microstructure.
AB - We propose a new approach to topology optimization, based on the use of "single-scale laminates" as structural components. The method is well-founded, because in the high porosity limit these structures achieve maximal stiffness and minimal weight. The method is useful, because the Hooke's law of a single-scale laminate has a simple, explicit formula which scales linearly with weight. And it is interesting, because the selection of relatively simple, manufacturable designs can be addressed using linear or quadratic programming. Our contributions are two-fold: (a) we establish the foundation of this approach, by defining single-scale laminates and giving self-contained proofs of their optimality in the high-porosity limit; and (b) we explore two numerical applications-minimizing weight with a constraint on the Hooke's law, and imposing continuity on a spatially varying microstructure.
KW - Effective properties
KW - Extremal microstructures
KW - High-porosity limit
KW - Homogenization
KW - Optimal design
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U2 - 10.1016/j.jmps.2007.06.002
DO - 10.1016/j.jmps.2007.06.002
M3 - Article
AN - SCOPUS:39049146499
SN - 0022-5096
VL - 56
SP - 1043
EP - 1064
JO - Journal of the Mechanics and Physics of Solids
JF - Journal of the Mechanics and Physics of Solids
IS - 3
ER -