An isogeometric collocation method for the static limit analysis of masonry domes under their self-weight

A novel isogeometric collocation method is proposed for the static limit analysis of axially-symmetric masonry domes subject to their self-weight. A shell-based static formulation is employed, alongside Heyman's assumptions on masonry, to characterize the equilibrated and statically admissible stress states in the dome. As a distinctive feature of the approach, a vector stress function is introduced, generating point-wise self-equilibrated shell stress resultants in the dome. Accordingly, the classical minimum-thrust problem is formulated in terms of the unknown vector stress function, and the static admissibility conditions are enforced as the only optimization constraint. NURBS-based isogeometric analysis is adopted to accomplish the need for an accurate geometric description of the dome and a high-order continuous interpolation of the vector stress function. A discrete minimum-thrust problem is derived as a linear programming problem, with the static admissibility conditions checked at suitable collocation points. Instrumental to its solution is the computation of a particular solution of the equilibrium equations, which is obtained by an isogeometric collocation method. By a mechanical interpretation of the dual optimization problem, the settlement mechanism of the dome corresponding to its minimum-thrust state is also computed. Numerical results, dealing with a thorough convergence analysis, parametric analyses on spherical and ogival domes with parameterized geometry, and the real case of the Taj Mahal central dome are presented to prove the computational merit of the proposed approach.