In the present work we describe a procedure for determining the ground acceleration that activates the in-plane mechanism of a wall panel with openings. The method, based on the assumption that the material is unilateral (namely a No-Tension material in the sense of Heyman), leans on the kinematic theorem of limit analysis. By working with the kinematic theorem, we admit singular strains representing concentrated fractures; in other words we allow for strong discontinuities in the displacements. In recent papers we adopted finite elements with strong discontinuities and search for local minima of the energy (in proximity of equilibrium trajectories) by minimizing the energy through descent, both with respect to the displacements and with respect to the position of the jump set. In this paper we propose a similar, though simplified, strategy to explore compatible mechanisms having free discontinuities. The numerical implementation of the proposed approach is discussed through illustrative examples, on examining collapse mechanisms of masonry structures subject to vertical and seismic loads.

Antonio Fortunato, Fernando Fraternali, Maurizio Angelillo