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Optimal layout of ellipses and its application for additive manufacturing

Author

Listed:
  • Tatiana Romanova
  • Yuri Stoyan
  • Alexandr Pankratov
  • Igor Litvinchev
  • Konstantin Avramov
  • Marina Chernobryvko
  • Igor Yanchevskyi
  • Irina Mozgova
  • Julia Bennell

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.

Suggested Citation

  • Tatiana Romanova & Yuri Stoyan & Alexandr Pankratov & Igor Litvinchev & Konstantin Avramov & Marina Chernobryvko & Igor Yanchevskyi & Irina Mozgova & Julia Bennell, 2021. "Optimal layout of ellipses and its application for additive manufacturing," International Journal of Production Research, Taylor & Francis Journals, vol. 59(2), pages 560-575, January.
    • Handle: RePEc:taf:tprsxx:v:59:y:2021:i:2:p:560-575
    DOI: 10.1080/00207543.2019.1697836
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    Cited by:

    1. Marić, Josip & Opazo-Basáez, Marco & Vlačić, Božidar & Dabić, Marina, 2023. "Innovation management of three-dimensional printing (3DP) technology: Disclosing insights from existing literature and determining future research streams," Technological Forecasting and Social Change, Elsevier, vol. 193(C).

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