TY - JOUR
T1 - A geometric projection method for designing three-dimensional open lattices with inverse homogenization
AU - Watts, Seth
AU - Tortorelli, Daniel A.
N1 - Funding Information:
This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 (LLNL-JRNL-701297). The authors gratefully acknowledge funding from LDRD-SI numbers 14-SI-005 and 17-SI-005.
PY - 2017/12/14
Y1 - 2017/12/14
N2 - 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.
AB - 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.
KW - elasticity
KW - finite element methods
KW - topology design
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U2 - 10.1002/nme.5569
DO - 10.1002/nme.5569
M3 - Article
AN - SCOPUS:85026299240
VL - 112
SP - 1564
EP - 1588
JO - International Journal for Numerical Methods in Engineering
JF - International Journal for Numerical Methods in Engineering
SN - 0029-5981
IS - 11
ER -