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Packing Soft Convex Polygons in an Optimized Convex Container

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Abstract

Packing soft convex polygonal objects in an optimized convex container is considered. The shape of the soft object can be changed in certain limits, but the object remains convex and maintains its area unchanged under all shape transformations. Non-overlapping, containment, as well as convexity and area conservation constraints are presented. A nonlinear programming model is formulated to find the optimal container for fixed values of elasticity parameters. An inverse problem is considered to find the minimal value of the elasticity parameter resulting in the same optimal container. Numerical experiments for packing soft triangles and pentagons in optimized circular and square containers are provided.

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Acknowledgements

Tetyana Romanova would like to thank the British Academy (grant #100072) for the overall support.

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Authors and Affiliations

  1. Nuevo Leon State University (UANL), Monterrey, Av. Universidad S/N, Col. Ciudad Universitaria, 66455, San Nicolas de los Garza, Nuevo Leon, Mexico

    Igor Litvinchev, Luis Infante, Alberto Martinez-Noa & Luis Gutierrez

  2. Leeds University Business School, University of Leeds, Leeds, West Yorkshire, LS2 9JT, UK

    Tetyana Romanova

  3. Department of Mathematical Modeling and Optimal Design, Institute for Mechanical Engineering Problems of the National Academy of Sciences of Ukraine, 2/10, Pozharsky Str., Kharkiv, 61046, Ukraine

    Tetyana Romanova

Authors
  1. Igor Litvinchev
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  2. Luis Infante
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  3. Tetyana Romanova
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  4. Alberto Martinez-Noa
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  5. Luis Gutierrez
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Contributions

Conceptualization, I.L. and T.R.; methodology, I.L., L.I., and T.R.; software, L.I., A.M. and L.G.; investigation, I.L., L.I. and T.R.; writing (original draft preparation), I.L., L.I., T.R., A.M., L.G.; numerical experiments and visualization, L.I., A.M., L.G. All authors reviewed the manuscript.

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Correspondence to Igor Litvinchev.

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Litvinchev, I., Infante, L., Romanova, T. et al. Packing Soft Convex Polygons in an Optimized Convex Container. Mobile Netw Appl (2024). https://doi.org/10.1007/s11036-023-02286-5

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