Mixed Smoothed Particle Hydrodynamics Method for Planar Elasticity Problems

This study presents a mixed smoothed particle hydrodynamics (SPH) model to solve static elasticity problems. In this method, the quadratic differential governing equations of the problems are written as a system of first-order differential equations based on the displacements and stresses. The higher accuracy can be achieved mostly due to the elimination of the second derivatives required for the discretization of the quadratic governing equations of the test problems. The accuracy of the proposed approach was compared with the standard SPH method (Shao and Lo in Adv Water Resour 26(7):787-800, 2003), the newly higher-order SPH Laplacian model (Shobeyri in J Sci Technol Trans Civ Eng 43(4):791-805, 2019), and a mixed MLS (moving least squares) method. The results show the superiority of the SPH mixed model over the other models, especially the standard approach due to its inherent properties.