Analysis of masonry vaults as a topology optimization problem

Congreso celebrado en la Escuela de Arquitectura de la Universidad de Sevilla desde el 24 hasta el 26 de junio de 2015.An innovative approach is proposed to analyze 3D masonry vaults, assuming masonry to behave as a linear elastic no‐tension material. Masonry is replaced by a suitable equivalent orthotropic material with spatially varying elastic properties and negligible stiffness in any direction along which tensile stresses must be prevented. An energy‐based algorithm is implemented to define the distribution and the orientation of the equivalent material for a given load, minimizing the potential energy so as to achieve a purely compressive state of stress. The algorithm is embedded within a numerical procedure that performs a non‐incremental analysis under given loads. The collapse load of masonry structural elements can also be predicted running a sequence of independent analyses. The capabilities of the approach in predicting the crack pattern in typical masonry vaults are also shown

Optimal strengthening of masonry arch bridges with externally bonded reinforcing layers

Strengthening is a natural step following a failed bridge assessment. Referring to masonry bridges, a numerical tool is presented to find the optimal distribution of reinforcement to be externally bonded to two-dimensional elastic no-tension structural elements, with the aim of maximizing their overall stiffness. Notwithstanding the non-linearity of the adopted material model, no incremental procedure is needed to prescribe equilibrium of the strengthened element. Indeed, the same minimization procedure handles both the energy-based solution of the no-tension elastic body and the topology optimization problem that distributes the optimal reinforcement. A few numerical simulations are presented to assess the capabilities of the proposed procedure in defining the optimal reinforcement layouts for masonry arches and arch bridges, subjected to gravity loads and resting on fixed or elastic foundations. Designers can exploit the tool to sketch a preliminary layout of the FRP strengthening, which should be subsequently detailed according to technical codes

Analysis of no-tension structures under monotonic loading through an energy-based method

An approach is proposed to estimate the collapse load of linear elastic isotropic no-tension 2D solids. The material is replaced by a suitable equivalent orthotropic material with spatially varying local properties. A non-incremental energy-based algorithm is implemented to define the distribution and the orientation of the equivalent material, minimizing the potential energy so as to achieve a compression-only state of stress. The algorithm is embedded within a numerical procedure that evaluates the collapse mechanisms of structural elements under monotonic loading. The accuracy of the method is assessed through comparisons with the “exact” results predicted by limit analysi

Design of the optimal fiber-reinforcement for masonry structures via topology optimization

AbstractA novel approach for the rational positioning of fiber reinforcements on masonry structures based on topology optimization is presented. Due to the brittle behavior of masonry, the minimization of the strain energy cannot be implemented to generate truss-like layouts that may be interpreted as strut-and-tie models in the discontinuity regions of reinforced concrete structures. To cope with the brittleness of brickwork, the optimal problem can be conveniently reduced to the minimization of the amount of reinforcement required to keep tensile stresses in any masonry element below a prescribed threshold. A strength criterion recently proposed for masonry is employed, based on a lower bound limit analysis homogenization model (Milani, 2011) and relying upon a discretization of ¼ of any unit cell by six CST elements. Thanks to the limited number of variables involved, closed form solutions for the masonry macroscopic strength domain can be obtained. This criterion is implemented into the multi-constrained discrete formulation of the topology optimization algorithm, to locally control the stress field over the design domain. For comparison, the phenomenological Tsai–Wu strength criterion for anisotropic solids is also implemented.The contribution discusses three sets of numerical results, addressing the fiber-reinforcement of some benchmark masonry walls. The optimal reinforcement layouts are found to be affected by the choice of the masonry strength criterion only to a limited extent, as far as failure in the masonry element is mainly due to tensile stresses. Contrary to intuition, placing the reinforcing fibers along the direction of the principal tensile stresses in masonry is also found to be not necessarily the most effective solution, for certain geometries and load conditions

Funicular analysis of symmetric arches with finite friction accounting for stereotomy

In this contribution the funicular analysis of symmetric masonry arches is performed by accounting for stereotomy, as well as for the presence of Coulomb’s friction at the interfaces between the voussoirs. The classical thrust network analysis approach is then enhanced by removing the hypothesis that the friction coefficient is infinite. The procedure presented here handles networks with any topology, fixed plane projection and loads applied at the nodes, whose equilibrium conditions are managed by exploiting the force density method. At each joint, a set of local constraints is enforced to restrain the shear-to-normal component ratio of the force between two adjacent voussoirs. The minimization/maximization of the horizontal thrusts, formulated in terms of applicate of the restrained nodes, is achieved by solving the corresponding multi-constrained minimization/maximization problem through sequential convex programming. The results obtained via this funicular method are validated by means of a graphical procedure based on the lower bound theorem of limit analysis, known as Durand-Claye method, by considering a masonry arch with nonconventional stereotomy

Fast stability analysis of masonry domes and vaults subjected to gravity-induced loads

This paper presents two different (semi)analytical methods for the limit analysis of masonry structures, i.e., a static approach known as “stability area method”, theoretically framed within the lower bound theorem of limit analysis, and a kinematic approach, based on the upper bound theorem. The analysis is conducted on case studies of masonry domes and vaults subjected to a vertical load applied at the crown. The collapse load is obtained by considering different hypotheses on the masonry tensile and compressive strengths. The results are compared with those deriving from experimental tests available in the literature

Analysis of 3D no-tension masonry-like walls

The no-tension model can be used in the analysis of structures made of brittle materials to obtain a preliminary description of their mechanical behavior. The model is based on the assumption that the stress tensor is negative semi–definite, and depends linearly upon elastic strains. Notwithstanding the simplicity of this model, serious numerical problems are found even in the analysis of elementary cases. To overcome this kind of instabilities, some robust numerical approaches have been proposed in the last decades. Most of them resort to incremental strategies of non–linear finite element analysis. Alternatively, the no–tension assumption can be handled through the minimization of a suitable form of the elastic strain energy. A numerical method was proposed in that seeks the equilibrium of two-dimensional no–tension bodies through the minimization of the potential energy. Following this approach an equivalent optimization problem was formulated in and implemented in to investigate the in–plane and out–of–plane behavior of masonry walls through simplified 2D models. Assuming masonry to behave as a linear elastic no–tensionmaterial, a numericalmethod is introduced to analyze 3D masonry structural elements, with special attention to masonry walls. Masonry is replaced by an equivalent orthotropic material with spatially varying elastic properties. Using an interpolation typical of Topology Optimization, the stiffness of the equivalent material is given negligible values in any direction along which tensile stresses must be prevented. An energy-based optimization algorithm defines the distribution and the orientation of the equivalent material for a given load, so as to obtain a purely compressive state of stress throughout the element. A regular mesh of eight node finite elements is used to speed up the sensitivity analysis. The capabilities of the approach in predicting no–tension stress solutions in masonry walls with openings of different shape is shown. The effect of settlements is investigated as well. The collapse load of walls subject to horizontal actions is predicted by running a sequence of independent analyses on the same discrete model, to investigate both their in–plane and out-of–plane behavior

MUSiC : a model-unspecific search for new physics in proton-proton collisions at root s=13TeV

Results of the Model Unspecific Search in CMS (MUSiC), using proton-proton collision data recorded at the LHC at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 35.9 fb(-1), are presented. The MUSiC analysis searches for anomalies that could be signatures of physics beyond the standard model. The analysis is based on the comparison of observed data with the standard model prediction, as determined from simulation, in several hundred final states and multiple kinematic distributions. Events containing at least one electron or muon are classified based on their final state topology, and an automated search algorithm surveys the observed data for deviations from the prediction. The sensitivity of the search is validated using multiple methods. No significant deviations from the predictions have been observed. For a wide range of final state topologies, agreement is found between the data and the standard model simulation. This analysis complements dedicated search analyses by significantly expanding the range of final states covered using a model independent approach with the largest data set to date to probe phase space regions beyond the reach of previous general searches.Peer reviewe

Search for new particles in events with energetic jets and large missing transverse momentum in proton-proton collisions at root s=13 TeV

A search is presented for new particles produced at the LHC in proton-proton collisions at root s = 13 TeV, using events with energetic jets and large missing transverse momentum. The analysis is based on a data sample corresponding to an integrated luminosity of 101 fb(-1), collected in 2017-2018 with the CMS detector. Machine learning techniques are used to define separate categories for events with narrow jets from initial-state radiation and events with large-radius jets consistent with a hadronic decay of a W or Z boson. A statistical combination is made with an earlier search based on a data sample of 36 fb(-1), collected in 2016. No significant excess of events is observed with respect to the standard model background expectation determined from control samples in data. The results are interpreted in terms of limits on the branching fraction of an invisible decay of the Higgs boson, as well as constraints on simplified models of dark matter, on first-generation scalar leptoquarks decaying to quarks and neutrinos, and on models with large extra dimensions. Several of the new limits, specifically for spin-1 dark matter mediators, pseudoscalar mediators, colored mediators, and leptoquarks, are the most restrictive to date.Peer reviewe

Measurement of prompt open-charm production cross sections in proton-proton collisions at root s=13 TeV

The production cross sections for prompt open-charm mesons in proton-proton collisions at a center-of-mass energy of 13TeV are reported. The measurement is performed using a data sample collected by the CMS experiment corresponding to an integrated luminosity of 29 nb(-1). The differential production cross sections of the D*(+/-), D-+/-, and D-0 ((D) over bar (0)) mesons are presented in ranges of transverse momentum and pseudorapidity 4 < p(T) < 100 GeV and vertical bar eta vertical bar < 2.1, respectively. The results are compared to several theoretical calculations and to previous measurements.Peer reviewe