Numerical methods for the lower bound limit analysis of masonry arches

The present paper deals with the problem of stability of masonry arches. In particular, the problem is approached invoking the lower bound theorem of Limit Analysis; thus, the existence of a thrust-line entirely contained in the thickness of the arch ensures that the arch does not collapse under the assigned load. With this aim, the Milankovitch theory [8]of the problem of the equilibrium of the arches is provided in a general framework, regardless of the shape of the arch and of the nature of the applied loads. Here, in order to formulate the lower bound limit analysis problem in general context, the Milankovitch’s theory is reviewed, formulating the problem of the determination of the thrust-line in a form suitable for the implementation in numerical procedures. In particular, the thrust curve is approximated by polynomial functions that are solved employing the Point Collocation Method [10]. Moreover, an optimization procedure is formulated for determining admissible equilibrium minimum and maximum thrust solutions. For the special case of a circular arch subjected to vertical load, the numerical procedure is assessed comparing the results obtained by the Collocation technique with the corresponding closed form solutions of the equilibrium problem.