A semi-analytical approach for the dynamics of the stone arch

Abstract

A semi-analytical approach is proposed for modelling the plane dynamics of a stone arch, treated as a system of rigid elements with friction and unilateral contacts at each joint. By generalising the method proposed in a previous paper, the analytical approach is firstly applied to the plane dynamics of a rectangular block simply supported on a moving base. In this case, where the contact although sometimes extended is unique, dynamics is formulated as a frictional contact problem, and conditions for onset of motion according to various mechanisms are fully analytically identified; moreover, criteria for evaluating contact reactions during either smooth or non-smooth dynamics are outlined. The method is then extended to the case of the arch, where each element is characterised at most by a double extended contact; criteria for the onset of motion and evaluation for each element of contact reactions during the dynamic evolution are then identified. The approach proposed constitutes a first step for performing dynamic analysis through either an event-driven or a time-stepping numerical procedure.