Completeness of corrective smoothed particle method for linear elastodynamics

Two different solution algorithms of the corrective smoothed particle method (CSPM) are developed and examined with linear elastodynamic problems. One is to use the corrective first derivative approximations to solve the stress-based momentum equations, with stresses evaluated from the strains. This is an approach that has widely been adopted in smoothed particle hydrodynamics (SPH) methods. The other is new, in which the corrective second derivative approximations are used to directly solve the displacement-based Navier equations. The former satisfies the nodal completeness condition but lacks integrability; on the contrary, the latter is truly complete. Numerical tests show that the latter outperforms the former as well as other existing SPH methods, as expected.