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Title: Simultaneous material, shape and topology optimization

Abstract

Using three design fields we develop an optimization environment that can simultaneously optimize material, shape and topology. We use the implicit representation of the boundaries with level-set functions that define the shape and topology. Differentiable R-functions allow us to combine these shapes and topology descriptions with Boolean operations. Additionally, we incorporate design dependent-stiffness materials with another design field. Notably, this framework accommodates design dependent loads, has the ability to introduce holes, and ensures the satisfaction of optimality criteria. It builds upon the fictitious domain, ersatz material, material interpolation and level-set methods. Additionally, it also borrows from parameterized density-based topology optimization methods. Since analytical sensitivities can be computed, we use efficient nonlinear programming algorithms to update the design instead of the Hamilton–Jacobi’s scheme of level-set methods. We illustrate the features of our framework by designing a cantilever beam with octet truss microlattice, a dam with design-dependent loads, and a composite clevis plate.

Authors:
ORCiD logo [1]; ORCiD logo [1];  [1];  [1];  [2];  [2]; ORCiD logo [1];  [1];  [1]
+ Show Author Affiliations
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Design and Optimization
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Design and Optimization; Univ. of Illinois at Urbana-Champaign, IL (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1735801
Alternate Identifier(s):
OSTI ID: 1809463
Report Number(s):
LLNL-JRNL-750458
Journal ID: ISSN 0045-7825; 935328
Grant/Contract Number:  
AC52-07NA27344; LLNL-JRNL-701297
Resource Type:
Accepted Manuscript
Journal Name:
Computer Methods in Applied Mechanics and Engineering
Additional Journal Information:
Journal Volume: 371; Journal Issue: no. 1; Journal ID: ISSN 0045-7825
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING

Citation Formats

Fernandez, Felipe, Barker, Andrew T., Kudo, Jun, Lewicki, James P., Swartz, Kenneth, Tortorelli, Daniel A., Watts, Seth, White, Daniel A., and Wong, Jonathan. Simultaneous material, shape and topology optimization. United States: N. p., 2020. Web. doi:10.1016/j.cma.2020.113321.
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Fernandez, Felipe, Barker, Andrew T., Kudo, Jun, Lewicki, James P., Swartz, Kenneth, Tortorelli, Daniel A., Watts, Seth, White, Daniel A., & Wong, Jonathan. Simultaneous material, shape and topology optimization. United States. https://doi.org/10.1016/j.cma.2020.113321
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Fernandez, Felipe, Barker, Andrew T., Kudo, Jun, Lewicki, James P., Swartz, Kenneth, Tortorelli, Daniel A., Watts, Seth, White, Daniel A., and Wong, Jonathan. Tue . "Simultaneous material, shape and topology optimization". United States. https://doi.org/10.1016/j.cma.2020.113321. https://www.osti.gov/servlets/purl/1735801.
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@article{osti_1735801,
title = {Simultaneous material, shape and topology optimization},
author = {Fernandez, Felipe and Barker, Andrew T. and Kudo, Jun and Lewicki, James P. and Swartz, Kenneth and Tortorelli, Daniel A. and Watts, Seth and White, Daniel A. and Wong, Jonathan},
abstractNote = {Using three design fields we develop an optimization environment that can simultaneously optimize material, shape and topology. We use the implicit representation of the boundaries with level-set functions that define the shape and topology. Differentiable R-functions allow us to combine these shapes and topology descriptions with Boolean operations. Additionally, we incorporate design dependent-stiffness materials with another design field. Notably, this framework accommodates design dependent loads, has the ability to introduce holes, and ensures the satisfaction of optimality criteria. It builds upon the fictitious domain, ersatz material, material interpolation and level-set methods. Additionally, it also borrows from parameterized density-based topology optimization methods. Since analytical sensitivities can be computed, we use efficient nonlinear programming algorithms to update the design instead of the Hamilton–Jacobi’s scheme of level-set methods. We illustrate the features of our framework by designing a cantilever beam with octet truss microlattice, a dam with design-dependent loads, and a composite clevis plate.},
doi = {10.1016/j.cma.2020.113321},
journal = {Computer Methods in Applied Mechanics and Engineering},
number = no. 1,
volume = 371,
place = {United States},
year = {Tue Aug 18 00:00:00 EDT 2020},
month = {Tue Aug 18 00:00:00 EDT 2020}
}
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