Modified finite particle method: applications to elasticity and plasticity problems

Meshless methods are widely investigated and successfully implemented in many applications, including mechanics, fluid-dynamics, and thermo-dynamics. Within this context, this paper introduces a novel particle approach for elasticity, namely the modified finite particle method (MFPM), derived from existing projection particle formulations, however presenting second-order convergence rates when used to solve elastic boundary value problems. The formulation is discussed and some applications to bi-dimensional elastic and elasto-plastic problems are presented. The obtained numerical results confirm the accuracy of the method, both in elasticity and in plasticity applications.