Singular stress fields for masonry-like vaults

Abstract

In the present paper, we apply the theorems of limit analysis to vaults modeled as masonry-like materials, that is, unilateral continuous bodies. On allowing for singular stresses, we consider statically admissible stress field concentrated on surfaces lying inside the masonry. Such structures are unilateral membranes, whose geometry is described a la Monge , and the equilibrium of them, under vertical loads, is formulated in the Pucher form. The problem is reduced to pere roca a single partial differential equation of the second order where the shape f and the stress function F appear symmetrically. The unilateral restrictions require that the membrane surface lies in between the extrados and intrados surfaces of the vault and that the stress function be concave. Such a constraint is, in general, not satisfied on a given shape for given loads: in such a case, the shape has to be modified to fit the constraint. In a sense, the unilateral assumption renders the membrane an underdetermined structure that must adapt its shape in order to satisfy the unilateral restrictions. A number of simple examples are presented to illustrate how the method works

Static Analysis of Cross Vaults: The Case of the Cathedral of Casertavecchia

“…The method, put forward in by Angelillo, Fortunato in the paper [4], and applied to simple vaults by Angelillo et al in [1] and to spiral stairs by Angelillo in [2], leans on the use of singular stresses concentrated on surfaces (membranes), on the Monge representation through a function f of the membrane surface, and on the Pucher formulation of membrane equilibrium.…”

“…Some iterative procedures based on the alternate applications of this two dual approaches starting from f or from F, are proposed and exploited in a recent paper (see [1]) in the case of domes. Here we use simply the approach based on the assignment of a restricted class of stress functions F.…”

“…We describe the shell surface S a la Monge, in the form (1), that is in terms of a continuous function f depending on…”

“…If f is piecewise quadratic and of the form (13), taking into account (11), the equilibrium equation (6), written inside Ω 1 and Ω 2 (that is excluding the diagonals) gives the two algebraic conditions…”

Fast Kinematic Limit Analysis of FRP Reinforced Masonry Vaults Through a New Genetic Algorithm Nurbs-Based Approach

“…The recently developed computational methods for masonry vaults, simple or reinforced, can be classified into two broad categories: the Finite Element methods developed both for nonlinear incremental analysis [8] and for limit analysis [9], and the thrust network methods [10][11] directly based on a lower bound formulation [12]. Practical application of these methods requires skilled users and, in the case of thrust network methods, the definition of an equilibrium surface for the vault, which is a priori unknown.…”