A nesting cell-based smoothed radial point interpolation method with two-level smoothed strains for static, free and forced vibration analysis of solids

Abstract

In this paper, a nesting cell-based smoothed radial point interpolation method with two-level smoothed strains (CS-RPIM-N) is presented for static, free and forced vibration analysis of solids. In the present method, displacement fields are constructed using the radial basis function augmented by polynomial. To improve the accuracy of the CS-RPIM, two-level sub-domains based on the triangular background integration cells are designed and used to construct the two-level smoothed strains. Each two-level sub-domains includes the triangular background cell itself and four equal-area triangular sub-cells. The discretized system equations are constructed by the Generalized smoothed Galerkin (GS-Garlerkin) weak form and Richardson extrapolation method. The accuracy, efficiency and stability of the present method are assessed by virtue of several numerical examples for the problems involving static, free and forced vibration analysis of solids. The numerical results reveal that the CS-RPIM-N stands out and achieves better performance compared to other existing approaches in the literature.