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Transactions on Engineering Technologies pp 99–115Cite as

An Approach to Modeling of Additive Manufacturing Technologies

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Abstract

Mathematical modeling of additive manufacturing technologies is aimed at improving the performance of device, machine, and mechanism parts. These technologies include stereolithography, electrolytic deposition, thermal and laser-based 3D printing, 3D-IC fabrication technologies, etc. They are booming nowadays, because they can provide rapid low-cost high-accuracy production of 3D items of arbitrarily complex shape (in theory, from any material). However, deformation and strength problems for products manufactured with these technologies yet remain to be solved. The fundamentally new mathematical models considered in the paper describe the evolution of the end product stress-strain state in additive manufacturing and are of general interest for modern technologies in engineering, medicine, electronics industry, aerospace industry, and other fields.

Keywords

  • Additive manufacturing technologies
  • Deformation
  • Growing solids
  • Incompatibility
  • Residual stresses
  • Strength

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Notes

  1. 1.

    It can be shown that on any Riemannian manifold \((\mathfrak{B},\boldsymbol{g})\) there is a unique linear connection ∇ that is compatible with \(\boldsymbol{G}\) and is torsion-free. This connection is Levi-Civita connection.

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Acknowledgements

This work was supported by the RSF under Grant 14-19-01280.

Author information

Authors and Affiliations

  1. Institute for Problems in Mechanics, Vernadsky Ave 101 Bldg 1, Moscow, 119526, Russia

    Alexander V. Manzhirov & Sergei A. Lychev

  2. Bauman Moscow State Technical University, 2nd Baumanskaya Str 5/1, Moscow, 105005, Russia

    Alexander V. Manzhirov & Sergei A. Lychev

  3. National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Kashirskoye shosse 31, Moscow, 115409, Russia

    Alexander V. Manzhirov & Sergei A. Lychev

Authors
  1. Alexander V. Manzhirov
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  2. Sergei A. Lychev
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Corresponding author

Correspondence to Alexander V. Manzhirov .

Editor information

Editors and Affiliations

  1. Multimedia Engineering College of Engioneering, Mokpo National University, Chonnam, Korea, Republic of (South Korea)

    Gi-Chul Yang

  2. IAENG Secretariat, International Association of Engineers, Hong Kong, Hong Kong SAR

    Sio-Iong Ao

  3. Dept of Applied Mathematics & Computing School of Engineering, Cranfield University, Cranfield, Bedfordshire, United Kingdom

    Len Gelman

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© 2015 Springer Science+Business Media Dordrecht

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Manzhirov, A.V., Lychev, S.A. (2015). An Approach to Modeling of Additive Manufacturing Technologies. In: Yang, GC., Ao, SI., Gelman, L. (eds) Transactions on Engineering Technologies. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9804-4_7

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  • DOI: https://doi.org/10.1007/978-94-017-9804-4_7

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-017-9803-7

  • Online ISBN: 978-94-017-9804-4

  • eBook Packages: EngineeringEngineering (R0)

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