26 research outputs found
Generalized Korn's inequality and conformal Killing vectors
Korn's inequality plays an important role in linear elasticity theory. This
inequality bounds the norm of the derivatives of the displacement vector by the
norm of the linearized strain tensor. The kernel of the linearized strain
tensor are the infinitesimal rigid-body translations and rotations (Killing
vectors). We generalize this inequality by replacing the linearized strain
tensor by its trace free part. That is, we obtain a stronger inequality in
which the kernel of the relevant operator are the conformal Killing vectors.
The new inequality has applications in General Relativity.Comment: 8 page
IoT sensors for modern structural health monitoring. A new frontier
The problem of determining the structural safety level of buildings and civil engineering infrastructures (CEIs) is raising growing concern worldwide. Most of the reinforced concrete constructions have a design life not greater than 100 years, and today it is necessary to face the problem of assessing their level of safety and structural integrity. Such problem is even more pressing when a construction is subjected to extreme environmental conditions. The long-term goal of this study is the realization of wireless low- cost devices, and a data management software, for the structural health monitoring of buildings and CEIs, with remotely controlled sensors embedded in, or installed on, the structural elements, to measure stresses together with accelerations. Once equipped with such system, each construction can become part of the Internet of Things, permitting users and authorities to be alerted in case structural safety is diminished or compromised. A crucial aspect is the unaltered preservation of measurement data over time, which cannot just rely on third parties, and for which it is necessary the exploitation of suitable data-protection technologies. This study have been carried out by experimental testing and validation, both in lab and on site, of the monitoring devices designed and realized. Results show that it is possible to realize low-cost monitoring systems, and related installation techniques, for integration in every new or existing buildings and CEIs
Permanent monitoring of thin structures with low-cost devices
Recently, structural monitoring technology invested in methodologies that give direct information on structures' stress state. Optic fibers, strain gauges, pressure cells give real-time data on the stress condition of a structural element, often determining the area where peak stresses have been reached, with a clear advantage over other less direct monitoring methodologies, such as, e.g., the use of accelerometers and inverse analysis to estimate internal forces. In addition, stresses can be recorded in a data log for analysis after a loading event, as well as for taking into account the lifelong stress state of the structure. Beams and columns of a reinforced concrete frame can be effectively monitored for flexural loads. Differently, thin shells are most of their lifespan under membrane regime, and, when properly designed, they rarely move to the bending regime. Our proposal is to monitor the stress in thin structures by small-sized low- cost devices able to record the stress history at key locations, sending alerts when necessary, with the aim of ensuring safety against the risk of collapse, or simply to perform maintenance/repairing activities. Such devices are realized with cheap off-the-shelf electronics and traditional strain gauges. The application examples are given as laboratory tests performed on a reinforced concrete plate, a masonry panel, and a steel beam. Results shows that the permanent monitoring control of stresses can be conveniently carried out on new structures using low-cost devices of the type we designed and realized in-house
Exact solutions for linearly electroelastic plate-like bodies
A three-dimensional, explicit and exact solution is derived for a transversely Isotropic, linearly electroelastic body in the form of a right cylinder of arbitrary cross section, being simply supported and connected to ground over its lateral boundary, and subject to an arbitrary distribution of force and charge over its end faces. When electric phenomena are ignored, this solution reduces to the solution given in for linearly elastic plate-like bodies
On morphoelastic rods
Morphoelastic rods are thin bodies which can grow and can change their intrinsic curvature and torsion. We deduce a system of equations that rule accretion and remodeling in a morphoelastic rod by combining balance laws involving non-standard forces with constitutive prescriptions filtered by a dissipation principle that takes into account both standard and non-standard working. We find that, as in the theory of three-dimensional bulk growth proposed [DiCarlo, A and Quiligotti, S. Mech Res Commun 2002; 29: 449-456], it is possible to identify a universal coupling mechanism between stress and growth, conveyed by an Eshelbian driving force
On Variational Approaches to Plate Models
The three basic functionals of potential energy, complementary energy and Hellinger-Prange-Reissner are used to obtain a rational derivation of Reissner-Mindlin plate models, starting from the three-dimensional theory. We show that the models so obtained are instances of the same plate theory; nevertheless, due to the different constitutive relations governing their response, they mimic the three-dimensional behaviour in three different manners
Lie Groups and the Compatibility Conditions for Continua with Rigid Structure
A derivation of the compatibility conditions for a continuum with rigid structure undergoing finite deformations is proposed. The geometry of the Lie group of frame changes is used. The compatibility conditions are deduced by requiring the involutiveness of a distribution associated to the strain: their relationship with the Maurer-Cartan equations of the group of frame changes is demonstrated. Applications to micropolar and Cauchy continua are given
On the Design of Superstable Prestressed Frameworks
The strength and stiffness of prestressed lattices, and their mechanical behavior, depend strongly on the underlying graph and the nodal conformation geometry. A special class of structures is that of superstable frameworks, that is, prestressed frameworks which are stable independently of material properties and level of prestress. After reviewing the main related notions and results in rigidity theory, we exploit the characterization of superstability for generic configurations to establish a construction for superstable systems on a given number of nodes generically placed in two or three dimensions