The radial natural neighbours interpolators extended to elastoplasticity. (English) Zbl 1157.74049

Ferreira, A. J. M. (ed.) et al., Progress on meshless methods. Invited papers based on the presentations at the 2nd ECCOMAS thematic conference on meshless methods, Porto, Portugal, July 9–11, 2007. Dordrecht: Springer (ISBN 978-1-4020-8820-9/hbk). Computational Methods in Applied Sciences (Springer) 11, 175-198 (2009).
Summary: Considering a small-strain formulation, we extend the radial natural neighbour interpolator method 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 essential and natural boundary conditions. The Newton-Raphson method is used for the solution of nonlinear system of equations, and an Hill yield surface is considered. Benchmark examples prove the high accuracy and convergence rate of the proposed method.
For the entire collection see [Zbl 1151.65003].


74S30 Other numerical methods in solid mechanics (MSC2010)
74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
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