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Applied Mathematics and Nonlinear Sciences
Volume 2 (2017): Numero 2 (July 2017)
Accesso libero
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
e
Georgios Michailidis
Georgios Michailidis
| 19 set 2017
Applied Mathematics and Nonlinear Sciences
Volume 2 (2017): Numero 2 (July 2017)
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CONDIVIDI
Pubblicato online:
19 set 2017
Pagine:
385 - 402
Ricevuto:
06 apr 2017
Accettato:
19 set 2017
DOI:
https://doi.org/10.21042/AMNS.2017.2.00031
Parole chiave
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.