Details
| Original language | English |
|---|---|
| Pages (from-to) | 560-575 |
| Number of pages | 16 |
| Journal | International Journal of Production Research |
| Volume | 59 |
| Issue number | 2 |
| Early online date | 6 Dec 2019 |
| Publication status | Published - 2021 |
Abstract
The paper studies a layout problem of variable number of ellipses with variable sizes placed into an arbitrary disconnected polygonal domain with maximum packing factor. The ellipses can be continuously translated and rotated. Restrictions on the dimensions of the ellipses are taken into account. Tools for the mathematical modelling of placement constraints (distance constraints between ellipses and containment of ellipses into a polygonal domain) using the phi-function technique are introduced. The tools make it possible to formulate the layout problem in the form of MIP model that is equivalent to a sequence of nonlinear programming subproblems. We develop a new solution algorithm that involves the feasible starting point algorithm and optimisation procedure to search for efficient locally optimal solutions of the layout problem. This algorithm can be used in the design of parts for «support-free» additive manufacturing, taking into account the conditions for its static/ dynamic strength. Results of the algorithm implementation for a topologically optimised flat part with the analysis of a stress state are provided.
Keywords
- additive manufacturing, ellipses, layout, mathematical model, nonlinear optimisation, phi-function technique
ASJC Scopus subject areas
- Business, Management and Accounting(all)
- Strategy and Management
- Decision Sciences(all)
- Management Science and Operations Research
- Engineering(all)
- Industrial and Manufacturing Engineering
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In: International Journal of Production Research, Vol. 59, No. 2, 2021, p. 560-575.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Optimal layout of ellipses and its application for additive manufacturing
AU - Romanova, Tatiana
AU - Stoyan, Yuri
AU - Pankratov, Alexandr
AU - Litvinchev, Igor
AU - Avramov, Konstantin
AU - Chernobryvko, Marina
AU - Yanchevskyi, Igor
AU - Mozgova, Iryna
AU - Bennell, Julia
N1 - Funding Information: The work of Litvinchev I. was partially supported by CONACYT (Mexico) through the grants #167019 and #293403.
PY - 2021
Y1 - 2021
N2 - The paper studies a layout problem of variable number of ellipses with variable sizes placed into an arbitrary disconnected polygonal domain with maximum packing factor. The ellipses can be continuously translated and rotated. Restrictions on the dimensions of the ellipses are taken into account. Tools for the mathematical modelling of placement constraints (distance constraints between ellipses and containment of ellipses into a polygonal domain) using the phi-function technique are introduced. The tools make it possible to formulate the layout problem in the form of MIP model that is equivalent to a sequence of nonlinear programming subproblems. We develop a new solution algorithm that involves the feasible starting point algorithm and optimisation procedure to search for efficient locally optimal solutions of the layout problem. This algorithm can be used in the design of parts for «support-free» additive manufacturing, taking into account the conditions for its static/ dynamic strength. Results of the algorithm implementation for a topologically optimised flat part with the analysis of a stress state are provided.
AB - The paper studies a layout problem of variable number of ellipses with variable sizes placed into an arbitrary disconnected polygonal domain with maximum packing factor. The ellipses can be continuously translated and rotated. Restrictions on the dimensions of the ellipses are taken into account. Tools for the mathematical modelling of placement constraints (distance constraints between ellipses and containment of ellipses into a polygonal domain) using the phi-function technique are introduced. The tools make it possible to formulate the layout problem in the form of MIP model that is equivalent to a sequence of nonlinear programming subproblems. We develop a new solution algorithm that involves the feasible starting point algorithm and optimisation procedure to search for efficient locally optimal solutions of the layout problem. This algorithm can be used in the design of parts for «support-free» additive manufacturing, taking into account the conditions for its static/ dynamic strength. Results of the algorithm implementation for a topologically optimised flat part with the analysis of a stress state are provided.
KW - additive manufacturing
KW - ellipses
KW - layout
KW - mathematical model
KW - nonlinear optimisation
KW - phi-function technique
UR - http://www.scopus.com/inward/record.url?scp=85076412166&partnerID=8YFLogxK
U2 - 10.1080/00207543.2019.1697836
DO - 10.1080/00207543.2019.1697836
M3 - Article
AN - SCOPUS:85076412166
VL - 59
SP - 560
EP - 575
JO - International Journal of Production Research
JF - International Journal of Production Research
SN - 0020-7543
IS - 2
ER -