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In this paper, an innovative strengthening system for masonry walls made of externally bonded Fabric-Reinforced Cementitious Matrix (FRCM) is presented. Due to the good mechanical properties and the compatibility with the architectural heritage, the FRCM is an adequate alternative to the use of Fiber-Reinforced Polymer (FRP) composites and other traditional techniques. The proposed system is applied to the strengthening of a classical architectural typology in cultural heritage architecture, which is the “in falso” masonry: a load-bearing wall built over a masonry vault, and hence without a direct load path to the ground. A research program, characterized by an experimental campaign, has been started in order to devise and verify an optimal strengthening system that assures for the masonry wall a structural behavior similar to a “wall beam”, so to prevent progressive collapses when the underlying masonry vault loses its carrier function. In particular, rather than the canonical application, consisting in widespread application to the whole surface of the masonry wall, an innovative intervention made of “Green Tape” of composites has been designed and verified by a specifically designed experimental set-up. The main objective of the research is to propose a reinforcement strategy not detrimental to unmovable artistic assets and tied to the safety and robustness of the architectural heritage.

Thermography is a non-destructive and non-contact technique allowing, without taking samples, gaining information about several aspects of heritage buildings. This contribution presents the last phase of a research path, started with laboratory tests and now aimed at a real case of great cultural value, which involved the use of the thermal imaging camera to unveil in-depth defects and the wall texture, hidden by valuable plasters or frescoes, in order to correlate the quality of the masonry to its mechanical properties. For this, a method has been devised, made of an original integration of thermographic and post-processing techniques, and recently was applied for the first time to a real case study: the Italian Templar church of San Bevignate, part of an architectural complex from the 13th century located in the city of Perugia. The opportunity to establish the masonry quality of a historical building using non-destructive testing (NDT) represents a little-known possibility to frame not only important factors for the conservation of the frescoes but also information on the seismic vulnerability of historical masonry architectures in order to preserve the artefact from being damaged during the surveys and to plan any effective intervention of restoration and structural reinforcement.

The use of equivalent beam models to estimate the dynamical characteristics of complex tall buildings has been investigated by several authors. The main reason is the structural response estimation to stochastic loads, such as wind and earthquake, using a reduced number of degrees of freedom, which reduces the computational costs and therefore gives the designer an effective tool to explore a number of possible structural solutions. In this paper, a novel approach to calibrate the mechanical and dynamical features of a complete 3D Timoshenko beam, i.e., describing bending, shear and torsional behavior, is proposed. This approach is based on explicitly considering the sub-structures of the tall building. In particular, the frames, shear walls and lattice sub-systems are modeled as equivalent beams, constrained by means of rigid diaphragms at different floors. The overall dynamic features of the tall building are obtained by equating the deformation energy of an equivalent sandwich beam with that of the selected sub-structures. Finally, the 3D Timoshenko equivalent beam parameters are calibrated by minimizing a suitable function of modal natural frequencies and static displacements. The closed form modal solution of the equivalent beam model is used to obtain the response to stochastic loads.

Several masonry structures of cultural and historical interest are made with a non-periodic masonry material. In the case of periodic textures, several methods are available to estimate the strength of the masonry; however, in the case of non-periodic masonry, few methods are available, and they are frequently difficult to use. In the present paper we propose using discontinuity layout optimization (DLO) to estimate the failure load and mechanism of a masonry wall made with non-periodic texture. We developed a parametric analysis to account for the main features involved in the estimation of failure: in particular we considered three different textures (periodic, quasi-periodic, and chaotic), variable height-to-width ratio of the wall (from 0 to 3) and of the blocks (from 0.25 to 1), different mechanical properties of mortar joints and blocks, and possible presence of a load on the top. The results highlight the importance of the parameters considered in the analysis, both on the values of the failure load and on the failure mechanism. Therefore, it is found that DLO can be an useful and affordable method in order to assess the mechanical strength of masonry wall made with non-periodic textures.

The paper first gives a rigorous proof of existence and highlights proprieties of the eigenvalues and eigenfunctions for a bounded body with peridynamical Dirichlet boundary conditions. In particular, the mechanical behavior of the body is described by mixed local and nonlocal operators where, for the latter, the regional fractional Laplacian is used. The dynamics of the1-dimensional case is thereafter analyzed. More precisely, the previous results are applied to analyze the evolutionary problem which corresponds to free oscillations of a bar taking also into account the damping effects. A peculiar numerical approach is finally proposed to solve both the eigenvalue problem and the time evolution problem. Comparisons with classical local models and super- and sub-critical behaviors are highlighted.

The use of fractional models to analyse nonlocal behaviour of solids has acquired great importance in recent years. The aim of this paper is to propose a model that uses the fractional Laplacian in order to obtain the equation ruling the dynamics of nonlocal rods. The solution is found by means of numerical techniques with a discretisation in the space domain. At first, the proposed model is compared to a model that uses Eringen’s classical approach to derive the differential equation ruling the problem, showing how the parameters used in the proposed fractional model can be estimated. Moreover, the physical meaning of the model parameters is assessed. The model is then extended in dynamics by means of a discretisation in the time domain using Newmark’s method, and the responses to different dynamic conditions, such as an external load varying with time and free vibrations due to an initial deformation, are estimated, showing the difference of behaviour between the local response and the nonlocal response. The obtained results show that the proposed model can be used efficiently to estimate the response of the nonlocal rod both to static and dynamic loads.

In the present paper we propose a model describing the nonlocal behavior of an elastic body using a peridynamical approach. Indeed, peridynamics is a suitable framework for problems where discontinuities appear naturally, such as fractures, dislocations, or, in general, multiscale materials. In particular, the regional fractional Laplacian is used as the nonlocal operator. Moreover, a combination of the fractional and classical Laplacian operators is used to obtain a better description of the phenomenological response in elasticity. We consider models with linear and nonlinear perturbations. In the linear case, we prove the existence and uniqueness of the solution, while in the nonlinear case the existence of at least two nontrivial solutions of opposite sign is proved. The linear and nonlinear problems are also solved by a numerical approach which estimates the regional fractional Laplacian by means of its singular integral representation. In both cases, a numerical estimation of the solutions is obtained, using in the nonlinear case an approach involving a random variation of an initial guess of the solution. Moreover, in the linear case a parametric analysis is made in order to study the effects of the parameters involved in the model, such as the order of the fractional Laplacian and the mixture law between local and nonlocal behavior.

In this paper, we present some applications of the multivariate sampling Kantorovich operators \\(S_w\\) to seismic engineering. The mathematical theory of these operators, both in the space of continuous functions and in Orlicz spaces, show how it is possible to approximate/reconstruct multivariate signals, such as images. In particular, to obtain applications for thermographic images a mathematical algorithm is developed using MATLAB and matrix calculus. The setting of Orlicz spaces is important since allow us to reconstruct not necessarily continuous signals by means of \\(S_w\\). The reconstruction of thermographic images of buildings by our sampling Kantorovich algorithm allow us to obtain models for the simulation of the behavior of structures under seismic action. We analyze a real world case study in term of structural analysis and we compare the behavior of the building under seismic action using various models.