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Title: A geometric projection method for designing three-dimensional open lattices with inverse homogenization

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. Here, we also design a single-constituent isotropic material with negative Poisson's ratio and a light, stiff material comprised of 2 constituent solidsmore » plus void space.« less
ORCiD logo [1] ;  [2]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Univ. of Illinois at Urbana-Champaign, Urbana, IL (United States)
Publication Date:
Report Number(s):
Journal ID: ISSN 0029-5981
Grant/Contract Number:
AC52-07NA27344; 14-SI-005 and 17-SI-005
Accepted Manuscript
Journal Name:
International Journal for Numerical Methods in Engineering
Additional Journal Information:
Journal Volume: 112; Journal Issue: 11; Journal ID: ISSN 0029-5981
Research Org:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org:
Country of Publication:
United States
42 ENGINEERING; 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; elasticity; finite element methods; topology design
OSTI Identifier:
Alternate Identifier(s):
OSTI ID: 1400835