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A geometric projection method for designing three‐dimensional open lattices with inverse homogenization
Author(s) -
Watts Seth,
Tortorelli Daniel A.
Publication year - 2017
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5569
Subject(s) - homogenization (climate) , topology optimization , isotropy , topology (electrical circuits) , inverse , mathematics , void (composites) , mathematical analysis , mathematical optimization , geometry , finite element method , materials science , structural engineering , physics , biodiversity , ecology , quantum mechanics , combinatorics , composite material , biology , engineering
Summary Topology optimization is a methodology for assigning material or void to each point in a design domain in a way that extremizes some objective function, such as the compliance of a structure under given loads, subject to various imposed constraints, such as an upper bound on the mass of the structure. Geometry projection is a means to parameterize the topology optimization problem, by describing the design in a way that is independent of the mesh used for analysis of the design's performance; it results in many fewer design parameters, necessarily resolves the ill‐posed nature of the topology optimization problem, and provides sharp descriptions of the material interfaces. We extend previous geometric projection work to 3 dimensions and design unit cells for lattice materials using inverse homogenization. We perform a sensitivity analysis of the geometric projection and show it has smooth derivatives, making it suitable for use with gradient‐based optimization algorithms. The technique is demonstrated by designing unit cells comprised of a single constituent material plus void space to obtain light, stiff materials with cubic and isotropic material symmetry. We also design a single‐constituent isotropic material with negative Poisson's ratio and a light, stiff material comprised of 2 constituent solids plus void space.