Factors affecting accuracy of radial point interpolation meshfree method for 3-D solid mechanics

Abstract

Recently, the radial point interpolation meshfree method has gained popularity owing to its advantages in large deformation and discontinuity problems, however, the accuracy of this method depends on many factors and their influences are not fully investigated yet. In this work, three main factors, i.e., the shape parameters, the influence domain size, and the nodal distribution, on the accuracy of the radial point interpolation method (RPIM) are systematically studied and conclusive results are obtained. First, the effect of shape parameters (R, q) of the multi-quadric basis function on the accuracy of RPIM is examined via global search. A new interpolation error index, closely related to the accuracy of RPIM, is proposed. The distribution of various error indexes on the R-q plane shows that shape parameters q ∈ [1.2, 1.8] and R ∈ [0, 1.5] can give good results for general 3-D analysis. This recommended range of shape parameters is examined by multiple benchmark examples in 3D solid mechanics. Second, through numerical experiments, an average of 30–40 nodes in the influence domain of a Gauss point is recommended for 3-D solid mechanics. Third, it is observed that the distribution of nodes has significant effect on the accuracy of RPIM although it has little effect on the accuracy of interpolation. Nodal distributions with better uniformity give better results. Furthermore, how the influence domain size and nodal distribution affect the selection of shape parameters and how the nodal distribution affects the choice of influence domain size are also discussed.