A node-based smoothed radial point interpolation method with linear strain fields for vibration analysis of solids

This paper presents a high-order node-based smoothed radial point interpolation method (NS-RPIM) with linear strain fields in smoothing domains. The linear smoothed strains are constructed by complete order of polynomial functions and normalized with reference to the central point of the smoothing region. The new NS-RPIM is one order higher than those of the existing methods which use piecewise constant strains. This high-order method still uses linear displacements within each triangular background cell, but linear strains are created over smoothing domains using the pick-out theory. Because the smoothed strain and the compatible strain within a local region are equal in an integral sense, the unknown parameters in the reconstructed strain functions can be determined uniquely by using three linearly independent weight functions. The numerical verification and computational efficiency are investigated and compared with the standard node-based smoothing models. It is found that the linear strain NS-RPIM shows improvement on both the convergence and computational efficiency in terms of error norm in displacement and is temporally stable. Since no spurious non-zero energy mode appears, this approach can be employed directly for the vibration analysis of solids.