Masonry domes under complex loading conditions: a shell-based static limit analysis approach

A shell-based static limit analysis approach is proposed for the structural assessment of masonry domes subject to complex loading conditions, such as involving horizontal forces or differential settlements of the supports. The problem formulation resorts to the statics of shells and to the shell stress resultants on the dome mid-surface to characterize the equilibrated and statically admissible stress states in the dome. By exploiting differential or integral shell equilibrium conditions, alongside classical Heyman’s assumptions, collapse and minimum-thrust analysis problems are formulated. Finite difference or finite volume discretization strategies are discussed to arrive at their discrete counterparts, which are efficiently solved as second-order cone programming problems. Numerical simulations are presented, dealing with the pseudo-static seismic analysis of spherical and catenary domes subject to uniformly or linearly distributed horizontal accelerations along the height of the dome, and with the minimum-thrust analysis of spherical domes under non-standard distributions of support differential settlements. The obtained results prove the computational merit of the proposed framework.