Multiscale eigenfrequency optimization of multimaterial lattice structures based on the asymptotic homogenization method
Fan, Zhirui LU ; Yan, Jun ; Wallin, Mathias LU ; Ristinmaa, Matti LU
; Niu, Bin
and Zhao, Guozhong
(2020)
In Structural and Multidisciplinary Optimization
61(3).
p.983-998
- Abstract
Ultralight lattice structures exhibit excellent mechanical performance and have been used widely. In structural design, the fundamental frequency is highly important. Therefore, a multiscale topology optimization method was utilized to optimize the fundamental frequency of multimaterial lattice structures in this study. Two types of optimization problems were studied, namely, maximizing the natural fundamental frequency with mass constraints and minimizing compliance with frequency constraints. The Heaviside-penalty-based discrete material optimization method was adopted for the optimal selection of candidate materials. The asymptotic homogenization method was used to evaluate the equivalent macroscale properties according to the... (More)
Ultralight lattice structures exhibit excellent mechanical performance and have been used widely. In structural design, the fundamental frequency is highly important. Therefore, a multiscale topology optimization method was utilized to optimize the fundamental frequency of multimaterial lattice structures in this study. Two types of optimization problems were studied, namely, maximizing the natural fundamental frequency with mass constraints and minimizing compliance with frequency constraints. The Heaviside-penalty-based discrete material optimization method was adopted for the optimal selection of candidate materials. The asymptotic homogenization method was used to evaluate the equivalent macroscale properties according to the microstructure of the lattice material. To enable gradient optimization, sensitivities were outlined in detail. A density filter with a volume-preserving Heaviside projection was used to eliminate the risk of a checkerboard pattern and reduce the number of gray elements. A polynomial penalization scheme was employed to eliminate localized spurious eigenmodes in the low-density region. Finally, several numerical examples were performed to validate the proposed method. These numerical examples resulted in novel microstructural configurations with remarkably improved vibration resistance.
(Less)
- author
- Fan, Zhirui
LU
; Yan, Jun
; Wallin, Mathias
LU
; Ristinmaa, Matti
LU
; Niu, Bin
and Zhao, Guozhong
- organization
- publishing date
- 2020-03
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Asymptotic homogenization, Fundamental frequency, Lattice structure, Multimaterial optimization, Multiscale topology optimization
- in
- Structural and Multidisciplinary Optimization
- volume
- 61
- issue
- 3
- pages
- 16 pages
- publisher
- Springer
- external identifiers
-
- scopus:85075347237
- ISSN
- 1615-147X
- DOI
- 10.1007/s00158-019-02399-0
- language
- English
- LU publication?
- yes
- id
- 68a560b8-db6d-4ad0-b798-defea62c6d45
- date added to LUP
- 2019-12-10 13:23:56
- date last changed
- 2022-04-18 19:17:43
@article{68a560b8-db6d-4ad0-b798-defea62c6d45,
abstract = {{<p>Ultralight lattice structures exhibit excellent mechanical performance and have been used widely. In structural design, the fundamental frequency is highly important. Therefore, a multiscale topology optimization method was utilized to optimize the fundamental frequency of multimaterial lattice structures in this study. Two types of optimization problems were studied, namely, maximizing the natural fundamental frequency with mass constraints and minimizing compliance with frequency constraints. The Heaviside-penalty-based discrete material optimization method was adopted for the optimal selection of candidate materials. The asymptotic homogenization method was used to evaluate the equivalent macroscale properties according to the microstructure of the lattice material. To enable gradient optimization, sensitivities were outlined in detail. A density filter with a volume-preserving Heaviside projection was used to eliminate the risk of a checkerboard pattern and reduce the number of gray elements. A polynomial penalization scheme was employed to eliminate localized spurious eigenmodes in the low-density region. Finally, several numerical examples were performed to validate the proposed method. These numerical examples resulted in novel microstructural configurations with remarkably improved vibration resistance.</p>}},
author = {{Fan, Zhirui and Yan, Jun and Wallin, Mathias and Ristinmaa, Matti and Niu, Bin and Zhao, Guozhong}},
issn = {{1615-147X}},
keywords = {{Asymptotic homogenization; Fundamental frequency; Lattice structure; Multimaterial optimization; Multiscale topology optimization}},
language = {{eng}},
number = {{3}},
pages = {{983--998}},
publisher = {{Springer}},
series = {{Structural and Multidisciplinary Optimization}},
title = {{Multiscale eigenfrequency optimization of multimaterial lattice structures based on the asymptotic homogenization method}},
url = {{http://dx.doi.org/10.1007/s00158-019-02399-0}},
doi = {{10.1007/s00158-019-02399-0}},
volume = {{61}},
year = {{2020}},
}