A modified finite particle method: Multi-dimensional statics and dynamics

We present the so-called Modified Finite Particle Method (MFPM), that is a recent methodology of approximation of differential operators, based on the projection of the Taylor series of a function u(x) on a set of projection functions. In particular, we discuss the generalization of MFPM formulation to the multi-dimensional case, extending the methodological procedure adopted for the one-dimensional case. Moreover, we address the extension to dynamics and solve problems with an explicit time integration scheme. Finally, we apply the MFPM to an elasto-statics (a perforated plate under tension) and two elasto-dynamics (a two-dimensional bar under a quasi-impulsive load and a quarter of an annulus under a sinusoidal body load) benchmarks. When an analytical solution is available we calculate the corresponding convergence orders of the error, always obtaining the expected second-order accuracy