| dc.description.abstract | Masonry is one of the oldest construction materials used by man and still
widespread worldwide. Historic buildings with a masonry structure are generally
admirable engineering works with paramount socio-economic value
and profile of cultural heritage. Despite their high durability when compared
to other types of structures (e.g., concrete or steel structures) the masonry
structures are especially vulnerable to settlements so that an accurate predictions
of their capacity against settlements is of some importance. In the
last decades, intensive research has been carried out to develop numerical
models with different degrees of complexity able to describe the non-simple
behavior of masonry structures under external loads and settlements, but
the theme is still open and there is not yet a universally recognized analysis
method applicable to any kind of problem.
This dissertation focuses on fracture mechanisms in unilateral masonry-like
structures on spreading abutments. Structures composed of unilateral masonry
like material are, usually, modelled as a multibody composed of both
rigid or elastic blocks, with unilateral no-friction contact condition. However,
in this dissertation I present a new approach in which the multibody
is composed of a mixed elastic-rigid (i.e., pseudo-rigid) material with unilateral
friction contacts subjected to a Principle of Maximum Dissipation. The
key contributions of this dissertation consist, on one hand, in introducing a
vanishing “fictitious” elasticity useful to give mathematical convergence of
the problem and, on the other hand, in taking into account frictional sliding
of the blocks with an associative flow rule (i.e., Tresca law). This last assumption
implies a normal dilatancy (in real cases essentially due to the roughness
of the contact), which gives a useful interpretation of real frictional joints, and
produces a frictional contact problem which is expressed through an elliptic
variational inequality formulation and can be treated as a standard Convex
Optimization Problem.
In this setting, two approaches are implemented: a Piecewise Elastic-Rigid
Displacement approach and a Continuous Elastic-Rigid displacement approach.
The first approach reduces the Convex Optimization Problem to a
Linear Programming Problem, via a block-based approximation, the second
one reduces the Convex to a Second-Order Cone Optimization Problem via
a FEM-like approximation. Three applications to real structural engineering
problems are presented in order to highlight the features, the reliability and
the innovation of the proposed method from both a methodological and a
practical viewpoint emphasizing the contribution to the issue. [edited by Author] | it_IT |
