  A static limit analysis approach is proposed for assessing the collapse
capacity of axisymmetric masonry domes subject to horizontal forces. The
problem formulation is based on the sound theoretical framework provided by the
classical statics of shells. After introducing the shell stress tensors on the
dome mid-surface, integral equilibrium equations are enforced for its typical
part. Heyman's assumptions of infinite compressive and vanishing tensile
strengths are made, with cohesionless friction behavior governing the shear
strength, to characterize the admissible stress states in the dome. An original
computational strategy is developed to address the resulting static limit
analysis problem, involving the introduction of a mesh on the dome mid-surface,
the interpolation of the physical components of the shell stress tensors on the
element boundaries, and the imposition of equilibrium and admissibility
conditions respectively for the elements and at the nodes of the mesh. The
descending discrete convex optimization problem is solved by standard and
effective optimization tools, automatically providing collapse multiplier of
horizontal forces, incipient collapse mechanism and expected crack pattern.
Convergence analysis, validation with experimental results available in the
literature, and parametric analyses with respect to geometric parameters and
friction coefficient, are presented for spherical and ellipsoidal masonry
domes, proving the reliability of the proposed approach for estimating the
pseudo-static seismic resistance of masonry domes.
