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

Abstract

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 solidsmore » plus void space.« less

Authors:
ORCiD logo [1];  [2]
+ Show Author Affiliations
  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:
Research Org.:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1410062
Alternate Identifier(s):
OSTI ID: 1400835
Report Number(s):
LLNL-JRNL-701297
Journal ID: ISSN 0029-5981
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
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
Publisher:
Wiley
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; elasticity; finite element methods; topology design

Citation Formats

Watts, Seth, and Tortorelli, Daniel A. A geometric projection method for designing three-dimensional open lattices with inverse homogenization. United States: N. p., 2017. Web. doi:10.1002/nme.5569.
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Watts, Seth, & Tortorelli, Daniel A. A geometric projection method for designing three-dimensional open lattices with inverse homogenization. United States. https://doi.org/10.1002/nme.5569
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Watts, Seth, and Tortorelli, Daniel A. Thu . "A geometric projection method for designing three-dimensional open lattices with inverse homogenization". United States. https://doi.org/10.1002/nme.5569. https://www.osti.gov/servlets/purl/1410062.
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@article{osti_1410062,
title = {A geometric projection method for designing three-dimensional open lattices with inverse homogenization},
author = {Watts, Seth and Tortorelli, Daniel A.},
abstractNote = {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.},
doi = {10.1002/nme.5569},
journal = {International Journal for Numerical Methods in Engineering},
number = 11,
volume = 112,
place = {United States},
year = {Thu Apr 13 00:00:00 EDT 2017},
month = {Thu Apr 13 00:00:00 EDT 2017}
}
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https://doi.org/10.1002/nme.5569
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