Login
Register
Reset Password
Publish & Distribute
Publishing Solutions
Distribution Solutions
Subjects
Architecture and Design
Arts
Business and Economics
Chemistry
Classical and Ancient Near Eastern Studies
Computer Sciences
Cultural Studies
Engineering
General Interest
Geosciences
History
Industrial Chemistry
Jewish Studies
Law
Library and Information Science, Book Studies
Life Sciences
Linguistics and Semiotics
Literary Studies
Materials Sciences
Mathematics
Medicine
Music
Pharmacy
Philosophy
Physics
Social Sciences
Sports and Recreation
Theology and Religion
Publications
Journals
Books
Proceedings
Publishers
Blog
Contact
Search
EUR
USD
GBP
English
English
Deutsch
Polski
Español
Français
Italiano
Cart
Home
Journals
Applied Mathematics and Nonlinear Sciences
Volume 2 (2017): Issue 2 (July 2017)
Open Access
Structural optimization under overhang constraints imposed by additive manufacturing processes: an overview of some recent results
Grégoire Allaire
Grégoire Allaire
,
Charles Dapogny
Charles Dapogny
,
Rafael Estevez
Rafael Estevez
,
Alexis Faure
Alexis Faure
and
Georgios Michailidis
Georgios Michailidis
| Sep 19, 2017
Applied Mathematics and Nonlinear Sciences
Volume 2 (2017): Issue 2 (July 2017)
About this article
Previous Article
Next Article
Abstract
Article
Figures & Tables
References
Authors
Articles in this Issue
Preview
PDF
Cite
Share
Published Online:
Sep 19, 2017
Page range:
385 - 402
Received:
Apr 06, 2017
Accepted:
Sep 19, 2017
DOI:
https://doi.org/10.21042/AMNS.2017.2.00031
Keywords
Shape optimization
,
additive manufacturing
,
level set method
,
shape derivative
© 2017 Grégoire Allaire, Charles Dapogny, Rafael Estevez, Alexis Faure and Georgios Michailidis, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.
Fig. 1
Sketch of the slicing procedure, at the beginning of all additive manufacturing processes.
Fig. 2
Setting of the two-dimensional MBB beam example.
Fig. 3
(Top) initial and (bottom) optimized shapes for Problem (8) in the two-dimensional MBB Beam test-case of Section 3.2.
Fig. 4
Optimized shapes resulting from Problem (9) in the two-dimensional MBB Beam example, using (top) φ ≡ φa and the threshold angle ν = 45°, and (bottom) φ ≡ φp and the pattern functions ψi defined in (10).
Fig. 5
Intermediate shape Ωh at the height h during the construction of the final structure Ω: the red zone is the lower boundary Γ0and the blue zone is the upper boundaryΓhu. $\Gamma^u_h.$
Fig. 6
Relative errors of the 0th- and 1st-order approximations of (top) Psw(Ω0) and (bottom) its derivative 𝒟Ω0.
Fig. 7
Optimized shapes for the two-dimensional MBB Beam example of Section 5.3: (a) optimized shape Ω*for Problem (8) (i.e. without additive manufacturing constraints), and optimized shapes for Problem (29) using parameters (b)αc = 0:50, (c) αc = 0:30, and (d) αc = 0:10.
Fig. 8
Optimized shapes for the two-dimensional MBB Beam example of Section 5.4, solving Problem (29) with the upper-weight manufacturing compliancePsw(Ω) and parameters (a)αc = 0:30, (b) αc = 0:10, (c) αc = 0:05, and (d) αc = 0:03.
Fig. 9
Setting of the three-dimensional bridge test-case.
Fig. 10
Optimized designs for the three-dimensional bridge example of Section 5.5, (left) without manufacturing constraints, (right) solving Problem (30) withαc = 0:7.
Fig. 11
(Left) Different views of the optimized shape for the three-dimensional bridge example of Section 5.5, solving Problem (30) withαc = 0:1; (right) another view on the three-dimensional bridges for Problem (30) with (top) no manufacturing constraint, (middle)αc = 0:7 and (bottom) ac = 0:1.