Bimaterial 3D printing using galvanometer scanners

  • Daniel Bandeira
  • Marta PascoalEmail author
  • Beatriz Santos
Research Article


In this work a 3D printing system based on the use of stereolithography and able to print parts made of two materials is studied. The 3D printing problem is divided into two subproblems. First, the problem of locating UV light emitters capable of reaching all areas of the polymer that constitutes the part to be printed is analyzed with the goal of minimizing the number of used emitters. Next, for each layer of the part the selected emitters are assigned to the areas of the polymer to be reached, with the goals of maximizing the angle of incidence of the UV light on the printing plane and minimizing the number of emitters that need to be activated. Integer linear formulations were introduced in an earlier work for both problems. Here these models are revisited and heuristic and exact methods are developed. Finally, the formulations and methods are analyzed for a case study. The results of the computational experiments are presented and discussed.


Set covering problem Biobjective optimization 3D printing Multi-material hybrid objects; laser projection 



This work was developed within the Project PT2020-POCI-SII & DT 17963: NEXT.Parts, Next-Generation of Advanced Hybrid Parts, from the program Portugal 2020, through the COMPETE 2020 – Programa Operacional Competitividade e Internacionalização. The work was also partially supported by the Portuguese Foundation for Science and Technology (FCT) under project Grants UID/MAT/00324/2019 and UID/MULTI/00308/2019.


  1. Bandeira D, Pascoal M (2018) Modeling bimaterial 3D printing using galvanometer scanners. Submitted for publication. Accessed 18 Mar 2019
  2. Bandeira D, Pascoal M, Mateus A, Reis Silva M (2018) Multi-material 3D printing using stereolithography: an optimization approach. Adv Mater Res (To appear)Google Scholar
  3. Burns M (1993) Automated fabrication: improving productivity in manufacturing. Prentice-Hall Inc, Upper Saddle RiverGoogle Scholar
  4. Caprara A, Toth P, Fischetti M (2000) Algorithms for the set covering problem. Ann Oper Res 98(1):353–371MathSciNetCrossRefzbMATHGoogle Scholar
  5. Ehrgott M (2006) Multicriteria optimization. Springer, BerlinzbMATHGoogle Scholar
  6. Gibson I, Rosen D, Stucker B (2015) Additive manufacturing technologies. Springer, New YorkCrossRefGoogle Scholar
  7. Karalekas D, Aggelopoulos A (2003) Study of shrinkage strains in a stereolithography cured acrylic photopolymer resin. J Mater Process Technol 136(1):146–150CrossRefGoogle Scholar
  8. Karp RM (1972) Reducibility among combinatorial problems. In: Miller RE, Thatcher JW, Bohlinger JD (eds) Complexity of computer computations. Springer, Berlin, pp 85–103CrossRefGoogle Scholar
  9. Salmoria G, Ahrens C, Beal V, Pires A, Soldi V (2009) Evaluation of post-curing and laser manufacturing parameters on the properties of somos 7110 photosensitive resin used in stereolithography. Mater Design 30(3):758–763CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Daniel Bandeira
    • 1
  • Marta Pascoal
    • 1
    • 2
    • 3
    Email author
  • Beatriz Santos
    • 1
  1. 1.Department of MathematicsUniversity of Coimbra, EC Santa CruzCoimbraPortugal
  2. 2.Centre for Mathematics of the University of CoimbraCoimbraPortugal
  3. 3.Institute for Systems Engineering and Computers – CoimbraUniversity of CoimbraCoimbraPortugal

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