A Modified Finite Particle Method: multidimensional elasto-statics and dynamics.

Particle methods are a class of numerical methods that belong to the family of meshless methods and
are not based on an underlying mesh or grid, but rather on any general distribution of particles. They are
nowadays widely applied in many fields, including, for example, solid mechanics, fluid dynamics, and
thermodynamics.
In this paper, we start from the original formulation of the so-called modified finite particle method
(MFPM) and develop a novel formulation. In particular, after discussing the position of the MFPM in the
context of the existing literature on meshless methods, and recalling and discussing the 1D formulation and
its properties, we introduce the novel formulation along with its extension to the approximation of 2D and
3D differential operators. We then propose applications of the discussed methods to some elastostatic and
elastodynamic problems. The obtained results confirm the potential and the flexibility of the considered
methods, as well as their second-order accuracy, proposing MFPM as a viable alternative for the simulation
of solids and structures. Copyright © 2014 John Wiley & Sons, Ltd.