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 ...

Equilibrium of masonry-like vaults treated as unilateral membranes: where mathematics meets history

In this paper, we study the equilibrium of masonry vaults, assuming that the material has infinite friction and no cohesion (i.e. it is No-Tension in the sense of Heyman). With Heyman's assumptions, the equilibrium of a structure composed of this ideal masonry material, can be studied with limit analysis. In particular, the present study is concerned with the application of the safe theorem of limit analysis to masonrylike vaults, that is, curved constructions modelled as continuous unilatera...

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

Un modello di danno fragile per mezzi porosi: esempi di applicazione

Si presenta un approccio accoppiato per modellare il danneggiamento indotto da sollecitazioni idrauliche e meccaniche in ammassi rocciosi. Il danneggiamento del materiale è legato alla formazione a scala microstrutturale di diverse famiglie di fratture parallele, annidate una nell’altra, ciascuna caratterizzata da una propria orientazione e spaziatura. La semplicità della geometria delle fratture permette di esprimere analiticamente la variazione di porosità e di permeabilità causate dal prog...