The meshless radial point interpolation method with ρ∞-Bathe implicit time discretization algorithm for transient elastodynamic analysis.

In this work the novel ρ ∞ -Bathe direct time integration algorithm is combined with the classical meshless radial point interpolation method to solve transient elastodynamic problems. The present combined numerical approach makes the best use of high computation accuracy of the RPIM in spatial discretization and high numerical stability of the ρ ∞ -Bathe method in temporal discretization. In addition, we theoretically show the total dispersion error of the obtained numerical solutions in transient elastodynamic analysis can be split into the spatial error and temporal error, which respectively show the monotonic convergence property with respect to the decreasing element sizes and time integration steps. The relationship among the spatial discretization error, temporal discretization error and total numerical error is also characterized in a simple and elegant form. The present study can explain theoretically why the present combined numerical approach possesses the important monotonic convergence property in solving transient elastodynamic problems. Due to this attractive property, the quality of the numerical solutions can be monotonically improved by directly using the decreasing time steps as long as a relatively reasonable spatial discretization is employed. Three typical numerical experiments are conducted to demonstrate that the important monotonic convergence property for transient elastodynamic analysis indeed can be achieved by the present combined numerical approach, hence the proposed combined numerical approach has a wide prospect for tackling very complex transient elastodynamic problems, such as the wave propagation in anisotropic media and laminated composite structures. [ABSTRACT FROM AUTHOR]