Semianalytical Lower-Bound Limit Analysis of Domes and Vaults

Featured Application The possible application of the work is in the forecast of the stability of masonry or concrete structures. The result is very useful in addressing the restoration and interpreting the results of the experimental monitoring of the structures during their lifetime. The nonlinear analysis conducted by means of the upper-bound theorem of the limit design allows for evaluating the response to different randomly variable and unknown load paths giving the overall safety factor. In this way, the real-life behavior of the structures can be addressed by practitioners that must monitor and restore the art structures. The calculation of the collapse load of spherical domes is addressed using a semianalytical approach under the hypothesis of small displacements and perfect plasticity. The procedure is based on the numerical approximation of the self-stress that represents the projection of the balance equilibrium null space on a finite dimensional manifold. The so-obtained self-equilibrated stress span is superimposed onto a finite-element linear elastic solution to the prescribed loads yielding to the statically admissible set accordingly to Melan's theorem. The compatibility of the stress with the constitutive law of the material was enforced using a linearized limit domain in terms of generalized stress, namely, axial force and bending moment along the local spherical curvilinear coordinates. The procedure was tested with reference to numerical and experimental data from the literature, confirming the accuracy of the proposed method. A comparison with the literature confirms that the buckling load was much greater than the two plastic collapse loads calculated through the proposed procedure and reported in the quoted literature.