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A natural neighbour method based on Fraeijs de Veubeke variational principle for materially non-linear problems

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Abstract

The natural neighbour method can be considered as one of many variants of the meshless methods. In the present paper, a new approach based on the Fraeijs de Veubeke (FdV) functional, which is initially developed for linear elasticity, is extended to the case of geometrically linear but materially non-linear solids. The new approach provides an original treatment to two classical problems: the numerical evaluation of the integrals over the domain A and the enforcement of boundary conditions of the type u i  =  ũ i on S u . In the absence of body forces (F i  =  0), it will be shown that the calculation of integrals of the type \({\int\nolimits_A \cdot {\rm d}A}\) can be avoided and that boundary conditions of the type u i  =  ũ i on S u can be imposed in the average sense in general and exactly if ũ i is linear between two contour nodes, which is obviously the case for ũ i  =  0.

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Authors and Affiliations

  1. Dalian University of Technology, 116023, Dalian, China

    Xiang Li

  2. ArGEnCo Department, University of Liège, Liège, Belgium

    Xiang Li, Serge Cescotto & Barbara Rossi

Authors
  1. Xiang Li
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  2. Serge Cescotto
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  3. Barbara Rossi
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Correspondence to Xiang Li.

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Li, X., Cescotto, S. & Rossi, B. A natural neighbour method based on Fraeijs de Veubeke variational principle for materially non-linear problems. Acta Mech Sin 25, 83–93 (2009). https://doi.org/10.1007/s10409-008-0200-z

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  • DOI: https://doi.org/10.1007/s10409-008-0200-z

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