A meshfree radial point interpolation method (RPIM) for three-dimensional solids

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Upper bound solution to elasticity problems: A unique property of the linearly conforming point interpolation method (LC‐PIM) (2008, background): “polynomial basis functions [7] and radial basis functions (RBFs) [8, 11].”
An enriched radial point interpolation method (e-RPIM) for analysis of crack tip fields (2010, methodology): “Therefore, RPIM has been successfully used in the analysis of solids, fluids and composite materials [2,24].”
A linearly conforming point interpolation method (LC‐PIM) for three‐dimensional elasticity problems (2007, methodology): “polynomial PIM using polynomial basis functions [8–10] and radial PIM (RPIM) using radial basis functions [11, 12].”
Dispersion analysis of the meshfree radial point interpolation method for the Helmholtz equation (2009, methodology): “For computations in the field of structural mechanics, the RPIM has been successfully applied [32, 33].”
A LINEARLY CONFORMING POINT INTERPOLATION METHOD (LC-PIM) FOR 2D SOLID MECHANICS PROBLEMS (2005, background): “These values of parameters have been found to perform well for most problems [Wang and Liu, 2002b; Liu, 2002; Liu et al., 2005].”
The natural neighbour radial point interpolation method: dynamic applications (2009, methodology): “The RPIM was also successfully extended to the three-dimensional (3D) analysis ( Liu et al. , 2005”