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A static limit analysis approach is proposed for assessing the collapsecapacity of axisymmetric masonry domes subject to horizontal forces. Theproblem formulation is based on the sound theoretical framework provided by theclassical statics of shells. After introducing the shell stress tensors on thedome mid-surface, integral equilibrium equations are enforced for its typicalpart. Heyman's assumptions of infinite compressive and vanishing tensilestrengths are made, with cohesionless friction behavior governing the shearstrength, to characterize the admissible stress states in the dome. An originalcomputational strategy is developed to address the resulting static limitanalysis problem, involving the introduction of a mesh on the dome mid-surface,the interpolation of the physical components of the shell stress tensors on theelement boundaries, and the imposition of equilibrium and admissibilityconditions respectively for the elements and at the nodes of the mesh. Thedescending discrete convex optimization problem is solved by standard andeffective optimization tools, automatically providing collapse multiplier ofhorizontal forces, incipient collapse mechanism and expected crack pattern.Convergence analysis, validation with experimental results available in theliterature, and parametric analyses with respect to geometric parameters andfriction coefficient, are presented for spherical and ellipsoidal masonrydomes, proving the reliability of the proposed approach for estimating thepseudo-static seismic resistance of masonry domes.

Collapse capacity of masonry domes under horizontal loads: A static limit analysis approach