Some results on thermal stress of layered plates and shells by using Unified Formulation

This work presents some results on two-dimensional modelling of thermal stress problems in multilayered structures. The governing equations are written by referring to the Unified Formulation (UF) introduced by the first author. These equations are obtained in a compact form, that doesn't depend on the order of expansion of variables in the thickness direction or the variable description (layer-wise models and equivalent single layers models). Classical and refined theories based on the Principle of Virtual Displacements (PVD) and advanced mixed theories based on the Reissner Mixed Variational Theorem (RMVT) are both considered. As a result, a large variety of theories are derived and compared. The temperature profile along the thickness of the plate/shell is calculated by solving the Fourier's heat conduction equation. Alternatively, thermo-mechanical coupling problems can be considered, in which the thermal variation is influenced by mechanical loading. Exact closed-form solutions are provided for plates and shells, but also the applications of the Ritz method and the Finite Element Method (FEM) are presented

Best theory diagrams for cross-ply composite plates using polynomial, trigonometric and exponential thickness expansions

This paper presents Best Theory Diagrams (BTDs) employing combinations of Maclaurin, trigonometric and exponential terms to build two-dimensional theories for laminated cross-ply plates. The BTD is a curve in which the least number of unknown variables to meet a given accuracy requirement is read. The used refined models are Equivalent Single Layer and are obtained using the Unified Formulation developed by Carrera. The governing equations are derived from the Principle of Virtual Displacement (PVD), and Navier-type closed form solutions have been obtained in the case of simply supported plates loaded by a bisinuisoidal transverse pressure. BTDs have been constructed using the Axiomatic/Asymptotic Method (AAM) and genetic algorithms (GA). The influence of trigonometric and exponential terms in the BTDs has been studied for different layer configurations, length-to-thickness ratios, and stresses. It is shown that the addition of trigonometric and exponential expansion terms to Maclaurin ones may improve the accuracy and computational cost of refined plate theories. The combined use of CUF, AAM and GA is a powerful tool to evaluate the accuracy of any structural theory

Multiobjective Best Theory Diagrams for cross-ply composite plates employing polynomial, zig-zag, trigonometric and exponential thickness expansions

This paper presents Best Theory Diagrams (BTDs) for plates considering all the displacement and stress components as objectives. The BTD is a diagram in which the minimum number of terms that have to be used to achieve the desired accuracy can be read. Maclaurin, zig-zag, trigonometric and exponential expansions are employed for the static analysis of cross-ply composite plates. The Equivalent Single Layer (ESL) approach is considered, and the Unified Formulation developed by Carrera is used. The governing equations are derived from the Principle of Virtual Displacements (PVD), and Navier-type closed-form solutions are adopted. BTDs are obtained using the Axiomatic/Asymptotic Method (AAM) and genetic algorithms (GA). The results show that the BTD can be used as a tool to assess the accuracy and computational efficiency of any structural models and to draw guidelines to develop structural models. The inclusion of the multiobjective capability extends the BTD validity to the recognition of the role played by each output parameter in the refinement of a structural model

A note on the computation of geometrically defined relative velocities

We discuss some aspects about the computation of kinematic, spectroscopic, Fermi and astrometric relative velocities that are geometrically defined in general relativity. Mainly, we state that kinematic and spectroscopic relative velocities only depend on the 4-velocities of the observer and the test particle, unlike Fermi and astrometric relative velocities, that also depend on the acceleration of the observer and the corresponding relative position of the test particle, but only at the event of observation and not around it, as it would be deduced, in principle, from the definition of these velocities. Finally, we propose an open problem in general relativity that consists on finding intrinsic expressions for Fermi and astrometric relative velocities avoiding terms that involve the evolution of the relative position of the test particle. For this purpose, the proofs given in this paper can serve as inspiration.Comment: 8 pages, 2 figure

Seyfert's Sextet: A Slowly Dissolving Stephan's Quintet?

We present a multiwavelength study of the highly evolved compact galaxy group known as Seyfert's Sextet (HCG79: SS). We interpret SS as a 2-3 Gyr more evolved analog of Stephan's Quintet (HCG92: SQ). We postulate that SS formed by sequential acquisition of 4-5 primarily late-type field galaxies. Four of the five galaxies show an early-type morphology which is likely the result of secular evolution driven by gas stripping. Stellar stripping has produced a massive/luminous halo and embedded galaxies that are overluminous for their size. These are interpreted as remnant bulges of the accreted spirals. H79d could be interpreted as the most recent intruder being the only galaxy with an intact ISM and uncertain evidence for tidal perturbation. In addition to stripping activity we find evidence for past accretion events. H79b (NGC6027) shows a strong counter-rotating emission line component interpreted as an accreted dwarf spiral. H79a shows evidence for an infalling component of gas representing feedback or possible cross fueling by H79d. The biggest challenge to this scenario involves the low gas fraction in the group. If SS formed from normal field spirals then much of the gas is missing. Finally, despite its advanced stage of evolution, we find no evidence for major mergers and infer that SS (and SQ) are telling us that such groups coalesce via slow dissolution.Comment: 70 pages, 19 figures, 15 tables - accepted for publication in the Astronomical Journa

An axiomatic/asymptotic evaluation of best theories for isotropic metallic and functionally graded plates employing non-polynomic functions

This paper presents Best Theory Diagrams (BTDs) constructed from various non-polynomial terms to identify best plate theories for metallic and functionally graded plates. The BTD is a curve that provides the minimum number of unknown variables necessary to obtain a given accuracy or the best accuracy given by a given number of unknown variables. The plate theories that belong to the BTD have been obtained using the Axiomatic/Asymptotic Method (AAM). The different plate theories reported are implemented by using the Carrera Unified Formulation (CUF). Navier-type solutions have been obtained for the case of simply supported plates loaded by a bisinusoidal transverse pressure with different length-to-thickness ratios. The BTDs built from non-polynomial functions are compared with BTDs using Maclaurin expansions. The results suggest that the plate models obtained from the BTD using nonpolynomial terms can improve the accuracy obtained from Maclaurin expansions for a given number of unknown variables of the displacement field

Modeling the influence of MgSO4 invariant points on multiphase reactive transport process during saline soil evaporation

In the present work, we modeled a laboratory experiment where a sand column saturated with a MgSO4 solution is subject to evaporation. We used a compositional formulation capable of representing the effect of geochemistry on flow and transport for concentrated solutions under extreme dry conditions. The model accounts for the water sink/sources terms due to hydrated mineral dissolution/precipitation and the occurrence of invariant points, which prescribe the water activity. Results show that the occurrence of the invariant points at the top of the domain could affect the vapor flux at the column top and salt precipitation along the column. In fact, the invariant points occurrence could explain the spatial fluctuation on the salt precipitates formation. Results also suggest that the complex hydrochemical interactions occurring during soil salinization, including osmotic effects, are crucial not only to understand the salt precipitation, but also the evaporation rate.Fil: Gamazo, P.. Universidad de la Republica; Uruguay. Universidad Politecnica de Catalunya; EspañaFil: Saaltink, M. W.. Universidad Politecnica de Catalunya; EspañaFil: Carrera, J.. Instituto de Diagnóstico Ambiental y Estudios del Agua; EspañaFil: Slooten, L. J.. Instituto de Diagnóstico Ambiental y Estudios del Agua; EspañaFil: Bea, Sergio Andrés. Universidad Nacional del Centro de la Provincia de Buenos Aires. Rectorado. Instituto de Hidrología de Llanuras - Sede Azul; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Tandil; ArgentinaFil: Gran, M.. Universidad Politecnica de Catalunya; Españ