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Structural Engineering and Mechanics
  Volume 14, Number 6, December 2002 , pages 713-732

Point interpolation method based on local residual formulation using radial basis functions
G.R. Liu , L. Yan, J.G. Wang and Y.T. Gu

    A local radial point interpolation method (LRPIM) based on local residual formulation is presented and applied to solid mechanics in this paper. In LRPIM, the trial function is constructed by the radial point interpolation method (PIM) and establishes discrete equations through a local residual formulation, which can be carried out nodes by nodes. Therefore, element connectivity for trial function
and background mesh for integration is not necessary. Radial PIM is used for interpolation so that singularity in polynomial PIM may be avoided. Essential boundary conditions can be imposed by a straightforward and effective manner due to its Delta properties. Moreover, the approximation quality of the radial PIM is evaluated by the surface fitting of given functions. Numerical performance for this
LRPIM method is further studied through several numerical examples of solid mechanics.
Key Words
     meshless method; radial basis function; point interpolation; background integration.
Center for Advanced Computation in Engineering Science, Department of Mechanical and Production Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260

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