Dynamic modelling structure of hinge-controlled masonry arches and 2D accelerations

Engineering efficiency is paramount for the introduction of novel systems and formats of analysis. This work extends an accessible and efficient analysis platform by combining the kinematic equilibrium approach of limit analysis with the single degree of freedom nature of a hinge-controlled masonry arch to perform dynamic modelling of applied two-dimensional acceleration vectors. Utilising ideal conditions, minimum work-paths are formulated to describe the work required to drive the arch to collapse. Then, assuming conservative work allows the formation of a spatial description of kinetic energy, and ultimately the establishment of the time domain for constant 2D accelerations. A dynamic time incremental analysis structure is then formulated based upon the assumption of constant acceleration for each time step. This dynamic model propagates the centroid displacement and kinetic energy through an applied acceleration sequence. Lastly, the dynamic model under ideal conditions is tested for validity through half-cycle collapse domain benchmark and the conservation of energy.