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The Radial Natural Neighbours Interpolators Extended to ElastoplastiCity

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Book cover Progress on Meshless Methods

Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 11))

Considering a small strain formulation a Radial Natural Neighbour Interpolator method is extended to the elastoplastic analysis. Resorting to the Voronoï tessellation the nodal connectivity is obtained. The Delaunay triangulation supplies the integration background mesh. The improved interpolation functions based on the Radial Point Interpolators are provided with the delta Kronecker property, easing the imposition of the essential and natural boundary conditions. The Newton-Raphson method is used for the solution of the nonlinear system of equations and an Hill yield surface is considered. Benchmark examples prove the high accuracy and convergence rate of the proposed method.

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Author information

Authors and Affiliations

  1. Associate Professor, Faculty of Engineering of the University of Porto — FEUP Rua Dr. Roberto Frias, Porto, 4200-465, Portugal

    LÙcia Maria Jesus Simas de Dinis

  2. Departamento de Engenharia Mecânica e Gestão Industrial, Faculdade de Engenharia da Univer-sidade do Porto, Rua Dr. Roberto Frias, Porto, 4200-465, Portugal

    Renato Manuel Natal Jorge

  3. Researcher, Institute of Mechanical Engineering — IDMEC Rua Dr. Roberto Frias, Porto, 4200-465, Portugal

    Jorge Belinha

Authors
  1. LÙcia Maria Jesus Simas de Dinis
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  2. Renato Manuel Natal Jorge
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  3. Jorge Belinha
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Corresponding author

Correspondence to LÙcia Maria Jesus Simas de Dinis .

Editor information

Editors and Affiliations

  1. Departamento de Engenharia Mecânica e Gestão Industrial, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, Porto, 4200-465, Portugal

    A. J. M. Ferreira

  2. University of California Davis, California, USA

    E. J. Kansa

  3. Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL, 60616, USA

    G. E. Fasshauer

  4. Instituto Superior Técnico, DECivil/ICIST, TU Lisbon, Portugal

    V. M. A. Leitão

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de Dinis, L.M.J.S., Jorge, R.M.N., Belinha, J. (2009). The Radial Natural Neighbours Interpolators Extended to ElastoplastiCity. In: Ferreira, A.J.M., Kansa, E.J., Fasshauer, G.E., Leitão, V.M.A. (eds) Progress on Meshless Methods. Computational Methods in Applied Sciences, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8821-6_11

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  • DOI: https://doi.org/10.1007/978-1-4020-8821-6_11

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-8820-9

  • Online ISBN: 978-1-4020-8821-6

  • eBook Packages: EngineeringEngineering (R0)

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