Edge-based Smoothed Point Interpolation Method (ES-PIM)

Abstract

In Chapter 6, we have presented the node-based smoothed PIM (NS-PIM), and examined the properties of various NS-PIM models. These NS-PIM models are softer models, spatially stable, having nonzero-energy modes, work very well for static mechanics problems, and have very important upper bound and super-convergence properties in the strain energy [1][2][3][4][5][6][7][8]. However, the NS-PIM was found temporally instable [7-10], when applied to solve dynamic problems. Such instability is often observed at higher energy level as spurious (nonphysical) nonzero-energy modes in the free vibration analysis of (stable and constrained) solids. Our studies have found that the cause of such instability is the "overly-soft" nature of these models introduced by the node-based smoothing operations. The authors believe that any method that has upper bound property can have spurious modes at a higher energy level and hence may suffer from the instability for solving dynamic problems. Therefore, for dynamic analysis of solid and structures, we need alternatives or special treatments to install temporal stability for these overly-soft models.In this chapter, we introduce another important S-PIM model called edgebased smoothed point interpolation method or ES-PIM, which has been found both spatially and temporally stable, and works well for both static and dynamic problems [9,10]. It is found also that the ES-PIM can produce much more accurate results compared to the NS-PIM and FEM using the same mesh [9][10][11][12][13][14][15][16][17][18][19][20][21]. The ES-PIM models are usually stiffer models with very "close-to-exact" stiffness. In particular the linear ES-PIM-Tr3 is found as one of the best linear models, and is regarded as a "star performer" among all the linear models.