A node-based partly smoothed point interpolation method (NPS-PIM) for dynamic analysis of solids

Abstract

Traditional finite element method (FEM) using linear triangular element is overly-stiff and generally natural frequencies calculated would be too high. The newly developed node-based smoothed point interpolation method (NS-PIM) has overly-soft stiffness, which makes it provide natural frequencies smaller than the exact ones and has the problem of temporally instability. So this work proposed a node-based partly smoothed point interpolation method (NPS-PIM) by combing the ideas of both FEM and NS-PIM through node-based partly strain smoothing operation. Owing to the properly constructed stiffness, detailed numerical study has shown that the NPS-PIM not only successfully overcomes the temporal instability existing in the NS-PIM, but also provides more accurate results than both FEM and NS-PIM models. The use of linear triangular background cells makes the present method very competitive for solving practical engineering problems with complicated shapes.