Linear Pantographic Sheets: Existence and Uniqueness of Weak Solutions

The well-posedness of the boundary value problems for second gradient elasticity has been studied under the assumption of strong ellipticity of the dependence on the second placement gradients (see, e.g., Chambon and Moullet in Comput. Methods Appl. Mech. Eng. 193:2771–2796, 2004 and Mareno and Healey in SIAM J. Math. Anal. 38:103–115, 2006). The study of the equilibrium of planar pantographic lattices has been approached in two different ways: in dell’Isola et al. (Proc. R. Soc. Lond. Ser. A 472:20150, 2016) a discrete model was introduced involving extensional and rotational springs which is also valid in large deformations regimes while in Boutin et al. (Math. Mech. Complex Syst. 5:127–162, 2017) the lattice has been modelled as a set of beam elements interconnected by internal pivots, but the analysis was restricted to the linear case. In both papers a homogenized second gradient deformation energy, quadratic in the neighbourhood of non deformed configuration, is obtained via perturbative methods and the predictions obtained with the obtained continuum model are successfully compared with experiments. This energy is not strongly elliptic in its dependence on second gradients. We consider in this paper also the important particular case of pantographic lattices whose first gradient energy does not depend on shear deformation: this could be considered either a pathological case or an important exceptional case (see Stillwell et al. in Am. Math. Mon. 105:850–858, 1998 and Turro in Angew. Chem., Int. Ed. Engl. 39:2255–2259, 2000). In both cases we believe that such a particular case deserves some attention because of what we can understand by studying it (see Dyson in Science 200:677–678, 1978). This circumstance motivates the present paper, where we address the well-posedness of the planar linearized equilibrium problem for homogenized pantographic lattices. To do so: (i) we introduce a class of subsets of anisotropic Sobolev’s space as the most suitable energy space E relative to assigned boundary conditions; (ii) we prove that the considered strain energy density is coercive and positive definite in E; (iii) we prove that the set of placements for which the strain energy is vanishing (the so-called floppy modes) must strictly include rigid motions; (iv) we determine the restrictions on displacement boundary conditions which assure existence and uniqueness of linear static problems. The presented results represent one of the first mechanical applications of the concept of Anisotropic Sobolev space, initially introduced only on the basis of purely abstract mathematical considerations

Potential for building Façade-integrated solar thermal collectors in a highly urbanized context

Development of technologies, materials, support systems, and coatings has made the integration of solar thermal systems into the building envelope increasingly possible. Solar thermal collectors can either be directly integrated, substituting conventional roof or façade covering materials, or constitute independent devices added to a roof or façade structure. Aimed at estimating the real effectiveness of building-integrated solar systems for domestic heat water (DHW) production or for heating integration, when horizontal or inclined pitches on buildings are not applicable, the authors analyze a case study with different scenarios, taking into account the issues connected to a highly urbanized context in the Mediterranean climate. A GIS model was used for estimating the energy balance, while the real producibility of the simulated systems was calculated by a dynamic hourly simulation model, realized according to ISO 52016. The savings in terms of primary energy needs obtained by installing solar thermal systems on the facade are presented, and the differences between the cases in which the system is used for DHW production only and for space heating too are distinguished and discussed. The evaluated potential is quantified in the absence of roof collectors, despite their high potential in the Mediterranean region, in order to better appreciate the effects induced by integrated facade systems

Discrete and continuous models of linear elasticity: history and connections

This paper tracks the development of lattice models that aim to describe linear elasticity of solids and the field equations of which converge asymptotically toward those of isotropic continua, thus showing the connection between discrete and continuum. In 1759, Lagrange used lattice strings/rod dynamics to show the link between the mixed differential-difference equation of a one-dimensional (1D) lattice and the partial differential equation of the associated continuum. A consistent three-dimensional (3D) generalization of this model was given much later: Poincaré and Voigt reconciled the molecular and the continuum approaches at the end of the nineteenth century, but only in 1912 Born and von Kármán presented the mixed differential- difference equations of discrete isotropic elasticity. Their model is a 3D generalization of Lagrange’s 1D lattice and considers longitudinal, diagonal and shear elastic springs among particles, so the associated continuum is characterized by three elastic constants. Born and von Kármán proved that the lattice equations converge to Navier’s partial differential ones asymptotically, thus being a formulation of continuous elasticity in terms of spatial finite differences, as for Lagrange’s 1D lattice. Neglecting shear springs in Born–Kármán’s lattice equals to Navier’s assumption of pure central forces among molecules: in the limit, the lattice behaves as a one-parameter isotropic solid (“rari-constant” theory: equal Lamé parameters, or, equivalently, Poisson’s ratio υ = 1/4). Hrennikoff and McHenry revisited the lattice approach with pure central interactions using a plane truss; the equivalent Born–Kármán’s lattice in plane stress in the limit tends to a continuum with Poisson’s ratio υ = 1/3. Contrary to McHenry–Hrennikoff’s truss, Born–Kármán’s lattice leads to a “free” Poisson’s ratio bounded by its “limit’ bound (υ = 1/4 for plane strain or 3D elasticity; υ = 1/3 for plane stress elasticity). Unfortunately, Born–Kármán’s lattice model does not comply with rotational invariance principle, for non-central forces. The consistent generalization of Lagrange’s lattice in 3D was achieved only by Gazis et al. considering an elastic energy that depends on changes in both lengths and angles of the lattice. An alternative consistent three-parameter elastic lattice is the Hrennikoff’s, with additional structure in the cell. We also discuss the capability of nonlocal continuous models to bridge the gap between continuum isotropic elasticity at low frequencies and lattice anisotropic elasticity at high frequencies

Influence of Installation Conditions on Heating Bodies Thermal Output: Preliminary Experimental Results☆

Abstract Heating bodies are thermodynamic systems whose heat output is strongly dependent on boundary conditions and in about a century several attempts have been made for its experimental determination. To this aim, at the beginning of 60s, in Europe different national standards were adopted (e.g. in 1967 in Italy the UNI 6514/1967). At European level, the EN 442-1:2014 and EN 442-2:2014 allows the heating body heat output estimation with an expanded uncertainty lower than 1% and they are now accepted in various international markets. The EN 442 also allows heat output calculation in operating conditions different from standard ones by employing theoretical-experimental correlations that, by their nature, are not able to include any possible actual operating condition. In fact, in actual operating conditions the heating body heat output depends on several factors, among which: i) installation position with respect to the wall and the floor; ii) presence grid/shelf/niche or an obstruction caused by curtains on the heating body; iii) thermo-fluid-dynamic condition variations (inlet flow rate and temperature); iv) hydraulic connections. Radiators represent the most spread heating body (installed since the end of '800) and in the last decades different radiators typologies have been proposed on the market, characterized by different materials, sizes, shapes, etc. In the present paper the authors present the preliminary result of an experimental campaign on field for the heat output measurement of different radiators typologies (cast iron, aluminum) as a function of different installation and operating conditions. The influence on the heating body performance and the associate technical-economical consequences in terms of heat cost allocation accuracy have been investigated

A novel measurement method for accurate heat accounting in historical buildings

Nowadays, two different heat accounting methods are available: the direct method, based on heat meters, and the indirect one, based on heat cost allocators. Unfortunately, in existing buildings, due to the plant configuration, heat meters are often technically unfeasible or not cost efficient, whereas heat cost allocators can be easily installed in almost all conditions. At the same time, the indirect method relies on a high number of interconnected devices with installation and operative conditions often variable within the same building and influencing the on-field metrological performances. In this paper, the authors propose a novel "hybrid" method for accurate heat accounting combining the advantages of indirect method with the higher accuracy typical of direct methods. The proposed method has been experimented at INRIM, the primary metrology institute in Italy, assessing the on-field performance in a virtual eight-apartments building. The experimental results show that the proposed method always presents improved accuracy. (C) 2020 Elsevier Ltd. All rights reserved

Wearable Devices to Improve Physical Activity and Reduce Sedentary Behaviour: An Umbrella Review

Background: Several systematic reviews (SRs), with and without meta-analyses, have investigated the use of wearable devices to improve physical activity, and there is a need for frequent and updated syntheses on the topic. Objective: We aimed to evaluate whether using wearable devices increased physical activity and reduced sedentary behaviour in adults. Methods: We conducted an umbrella review searching PubMed, Cumulative Index to Nursing and Allied Health Literature, the Cochrane Library, MedRxiv, Rxiv and bioRxiv databases up to February 5th, 2023. We included all SRs that evaluated the efficacy of interventions when wearable devices were used to measure physical activity in adults aged over 18 years. The primary outcomes were physical activity and sedentary behaviour measured as the number of steps per day, minutes of moderate to vigorous physical activity (MVPA) per week, and minutes of sedentary behaviour (SB) per day. We assessed the methodological quality of each SR using the Assessment of Multiple Systematic Reviews, version 2 (AMSTAR 2) and the certainty of evidence of each outcome measure using the GRADE (Grading of Recommendations, Assessment, Development, and Evaluations). We interpreted the results using a decision-making framework examining the clinical relevance and the concordances or discordances of the SR effect size. Results: Fifty-one SRs were included, of which 38 included meta-analyses (302 unique primary studies). Of the included SRs, 72.5% were rated as ‘critically low methodological quality’. Overall, with a slight overlap of primary studies (corrected cover area: 3.87% for steps per day, 3.12% for MVPA, 4.06% for SB) and low-to-moderate certainty of the evidence, the use of WDs may increase PA by a median of 1,312.23 (IQR 627–1854) steps per day and 57.8 (IQR 37.7 to 107.3) minutes per week of MVPA. Uncertainty is present for PA in pathologies and older adults subgroups and for SB in mixed and older adults subgroups (large confidence intervals). Conclusions: Our findings suggest that the use of WDs may increase physical activity in middle-aged adults. Further studies are needed to investigate the effects of using WDs on specific subgroups (such as pathologies and older adults) in different follow-up lengths, and the role of other intervention components

A nonlinear Lagrangian particle model for grains assemblies including grain relative rotations

International audienceWe formulate a discrete Lagrangian model for a set of interacting grains, which is purely elastic. The considered degrees of freedom for each grain include placement of barycenter and rotation. Further, we limit the study to the case of planar systems. A representative grain radius is introduced to express the deformation energy to be associated to relative displacements and rotations of interacting grains. We distinguish inter‐grains elongation/compression energy from inter‐grains shear and rotations energies, and we consider an exact finite kinematics in which grain rotations are independent of grain displacements. The equilibrium configurations of the grain assembly are calculated by minimization of deformation energy for selected imposed displacements and rotations at the boundaries. Behaviours of grain assemblies arranged in regular patterns, without and with defects, and similar mechanical properties are simulated. The values of shear, rotation, and compression elastic moduli are varied to investigate the shapes and thicknesses of the layers where deformation energy, relative displacement, and rotations are concentrated. It is found that these concentration bands are close to the boundaries and in correspondence of grain voids. The obtained results question the possibility of introducing a first gradient continuum models for granular media and justify the development of both numerical and theoretical methods for including frictional, plasticity, and damage phenomena in the proposed model