Classical Analytical Models Research Articles

Turbulent universality and the drift velocity at the interface between two homogeneous fluids

The drift velocity U0 at the interface between two homogeneous turbulent fluids of arbitrary relative densities in differential mean motion is considered. It is shown that an analytical expression for U0 follows from the classical scaling for these flows when the scaling is supplemented by standard turbulent universality and symmetry assumptions. This predicted U0 is the weighted mean of the free-stream velocities in each fluid, where the weighting factors are the square roots of the densities of the two fluids, normalized by their sum. For fluids of nearly equal densities, this weighted mean reduces to the simple mean of the free-stream velocities. For fluids of two widely differing densities, such as air overlying water, the result gives U0 ≈ αV∞, where α ≪ 1 is the square root of the ratio of the fluid densities, V∞ is the free-stream velocity of the overlying fluid, and the denser fluid is assumed nearly stationary. Comparisons with two classical laboratory experiments for fluids in these two limits and with previous numerical simulations of flow near a gas–liquid interface provide specific illustrations of the result. Solutions of a classical analytical model formulated to reproduce the air–water laboratory flow reveal compensating departures from the universality prediction, of order 15% in α, including a correction that is logarithmic in the ratio of dimensionless air and water roughness lengths. Solutions reproducing the numerical simulations illustrate that the logarithmic correction can arise from asymmetry in the dimensionless laminar viscous sublayers.

Improved analytical modeling and system performance evaluation of deep coaxial borehole heat exchanger with segmented finite cylinder-source method

The deep borehole heat exchanger is attracting more and more attention due to its higher performance. But there is no suitable analytical model for its fast simulation and system design. Classic analytical models of borehole heat exchangers (BHEs), assume that the initial soil temperature and heat flux of the borehole wall are uniform. Those makes them not applicable to deep borehole systems in which geothermal gradient is dominant. This study introduced and formulated a segmented finite cylinder-source model (SFCS), which can provide an accurate simulation tool. Data of distributed thermal response test and finite difference model are used for model comparison. A comprehensive comparative study is implemented to identify the performance differences between the classical and the new model. It is shown from simulation results that the newly proposed SFCS model can better describe the water as well as soil temperature field, especially for deeper borehole systems. In addition, three new influencing factors, namely pipe sizing ratio, inlet thermal flow rate and initial soil temperature distribution function, are introduced for system performance evaluation. Some valuable findings are identified, which can promote a better system design and achieve a higher system performance.

Probabilistic corrosion time initiation modelling in reinforced concrete structures using the BEM

Abstract The reinforcement’s depassivation in reinforced concrete structures occurs when the chloride concentration at the reinforcement’s interface reaches the threshold content. The depassivation phenomenon starts the propagation period, in which huge mechanical degradation processes are triggered. Moreover, it is well established that the propagation period is considerably shorter than the initiation period. Therefore, the accurate prediction of the corrosion time initiation is a major issue in structural durability domain. This study presents a transient formulation based on the Boundary Element Method (BEM) for the corrosion time initiation assessment. The diffusion fields evaluated by the BEM are utilized into a probabilistic framework, which enables the assessment of probabilistic values for corrosion time initiation. Therefore, the formulation handles properly the uncertainties in this problem, which is largely subjected to randomness. Three applications are presented. The robustness and accuracy of the proposed approach over classical analytical models are highlighted.

Cohesive-zone analyses with stochastic effects, illustrated by an example of kinetic crack growth

Cohesive-zone models of fracture are traditionally implemented using a deterministic failure criterion, with crack advance occurring when the work done against crack-tip tractions reaches a critical level. There are, however, many physical phenomena where crack growth is controlled by stochastic events ahead of the crack. These can include kinetic crack growth, stress-corrosion cracking, and void nucleation. In this paper, we show how a cohesive-zone model might be adapted to describe such stochastic phenomena. In particular, we have chosen to model kinetic crack growth by assuming that the probability of local failure, or bond rupture, depends on the difference between the level of local work done against the cohesive tractions and the equilibrium toughness of the interface. We have shown that if the cohesive parameters are within a range appropriate for linear-elastic fracture mechanics (LEFM), and the possibility of failure is limited to the crack tip, then the model accurately reproduces a classical analytical model for kinetic crack growth, with the crack velocity having an exponential relationship with respect to the level of the energy-release rate above a threshold. As with all cohesive-zone models, a transition between toughness-controlled fracture and strength-controlled fracture occurs as the cohesive length is increased. However, it is further noted that if failure is not limited to the crack tip, but is allowed to occur anywhere ahead of the crack tip, then the length scale controlling the crack velocity changes from the mesh size to the cohesive length. This mesh-independent result is associated with diffuse damage ahead of the crack tip. From a physical perspective, such a damage zone could correspond to a situation with a low activation energy for bond rupture, or to one where the a crack grows in response to spatially diffuse stochastic process in a damage zone such as void nucleation, crazing or micro-cracking.

Analytical Far-Zone Calculation of the Field Radiated From an Equilateral Triangular Aperture

This communication contributes to the classical analytical models for computing the radiated electromagnetic fields from an aperture with a canonical shape by means of the equivalence principle. Analytical closed-form expressions are presented for the radiation pattern generated by the modes of an equilateral triangular aperture. The derived formulation is based on the use of a well-known equivalence principle, which provides the radiated far-field from the transversal field at the aperture. This equivalence principle, as well as the formulation of the modal field functions associated with an equilateral triangular aperture, are briefly described. The equivalence principle is then applied to these modal field functions to evaluate the closed-form expressions for the integrals required to obtain the radiation pattern associated with each mode. Different examples are shown, where the analytical results achieved by the formulation derived in this communication when compared with those provided by commercial software packages based on different numerical approaches show a very good agreement.

Obtaining G12 and Xt using mixed ANNs based on matrix and fiber properties

This study aimed to create ANN architectures capable of modeling the shear modulus (G12) and longitudinal ultimate tensile strength (Xt) of unidirectional composites. The trained and tested ANNs are used to obtain these mechanical properties. Based on the properties of the fiber, matrix, and their volumetric fraction, this analysis will use the lowest possible number of fiber- and matrix-related properties. To that end, data were collected from the literature and divided into a training and test set for cross-validation. Seven different architecture types were developed, changing their inputs and adding analytical models parallel to the analysis so that three were used to obtain G12 and four to obtain Xt. Classic analytical models, such as the Halpin-Tsai and rule of mixtures, were used to construct the mixed ANNs and serve as a reference for comparison purposes.

A soft computing approach for estimating the specific heat capacity of molten salt-based nanofluids

Despite the promising potential of nanofluids as heat transfer and energy storage media, determination of their thermal behavior and properties need significant experimentation. Considering the relatively high costs of such fluids and the time-consuming procedures for synthesizing them and measuring their characteristics, machine learning techniques can be powerful tools for simulating their behaviors in the unstudied combinations of operating conditions. In this study, a machine learning model has been developed for the first time in the literature - to simulate and predict the specific heat capacity of a molten nitrate salt mixture seeded with silica, alumina and titania nanoparticles. A multilayer perceptron neural network (ANN) was selected among 1920 ANNs with different architectural features. With a prediction R2 value of 0.9998, the suggested model was found to provide much superior predictions (and validated against experimental data) as compared to the classic analytical models. The model developed in this study can, therefore, be used for estimating the values of specific heat capacity for nanofluid samples - based on the temperature and mass fraction of the nanoparticles, as well as the average (or nominal size) of the nanoparticles. The soft-computing technique itself was evaluated under extreme training conditions and it was found that the algorithm can adapt to new data sets with maximum MAPE of 2% and can enable excellent quality of predictions (R2 > 0.95) when trained with <300 data points.

Vibration Analysis and Dynamic Characterization of Structural Glass Elements with Different Restraints Based on Operational Modal Analysis

Given a series of intrinsic features of structural glass systems (i.e., material properties, type of restraints, operational conditions, etc.), special care should be spent at the design stage, to ensure appropriate fail-safe requirements, but also in the service life of these innovative building components and assemblies. In this paper, the dynamic characterization of simple monolithic glass elements is presented, based on non-destructive laboratory experiments and Operational Modal Analysis (OMA) techniques, including Finite Element (FE) numerical simulations, classical analytical models, and video-tracking approaches. It is shown, in particular, how the actual restraint condition (i.e., flexibility of supports, with respect to ideal boundaries) can affect the vibration parameters of a given glass member (frequency and damping capacity). This turns out in possible variations of its overall structural performance, including stress-strain-related effects, hence suggesting the need for even further dedicated studies and methods for the reliable analysis and design of structural glass assemblies and complex systems under dynamic loads.

Design of commercial hexagonal honeycombs of equal out-of-plane shear moduli

In the present paper the hexagonal honeycombs with double vertical walls (commercial), which usually are used as cores in sandwich plates, and the rigid skin effect are considered. Loaded in out-of-plane shear, the core is designed to have an identical macroscopic behavior in both planes, that is G13 = G23. Using a general parameterization of their geometry and imposing the necessary conditions together with some restrictions, the relations between geometrical parameters are first sought analytically in some simplified hypotheses. Then, considering a 3D finite element model and the optimization module in ANSYS, the more accurate geometry representation of the possible out-of-plane isotropic commercial honeycombs and their effective elastic constants were obtained. The numerical results are discussed by comparing them to the ones given by the classic analytical models. The results provide new insights into understanding the mechanics of honeycombs and designing new types of cellular materials which may fulfill some supplementary conditions than the existing ones.

Morphological and textural evolution of the prismatic ultrastructure in mollusc shells: A comparative study of Pinnidae species

Molluscan shells, exhibiting a variety of complex three-dimensional architectures, are an exemplar model system to study biogenic mineral formation by living organisms. Recent studies have demonstrated that the deposition process of some shell ultrastructures can be described using classical analytical models borrowed from materials physics, which were developed to predict the structural evolution of man-made and geological polycrystalline composite assemblies. In the current study, we use this newly developed capacity to quantitatively describe the morphogenesis of the prismatic ultrastructure in three shells from the bivalve family Pinnidae towards establishing a correlation between structure, texture, growth kinetics, topology and phylogeny of the species. Using data collected by electron microscopy, synchrotron-based microtomography, electron backscatter diffraction analysis (EBSD) and X-ray diffraction we demonstrate that the prismatic ultrastructures in Pinnidae are formed following either ideal or triple-junction-controlled kinetics, which are shown to be closely linked to the morphological and topological characteristics, as well as crystallographic texture of these biocomposites. The experimental and analytical framework presented in this comparative study can serve as an additional tool for classifying molluscan shell ultrastructures on the levels of structural and textural morphogenesis. Statement of SignificanceThe ability to quantitatively describe the structural evolution of the prismatic architecture in mollusc shells is used for the first time to derive and compare between analytical parameters that define the growth kinetics and morphological and topological evolution during the growth of three shells from the family Pinnidae from two different genera. Furthermore, these parameters are linked to the evolution of crystallographic texture in the studied architectures. The developed experimental and analytical framework not only enables us to quantitatively describe species-specific growth mechanisms but also suggests a direct correlation between the evolution of morphology and texture.

An analytical model of double scattering for SAR imaging of urban structures

An analytical solution of double scattering for urban structures is proposed. This model is based on geometrical optics (GO) and first order small slope approximation (SSA1), thus has a wider scope of application than classical analytical models. In our model, the surface of building is assumed to be smooth and the ground is regarded as Gauss rough surface, then a closed form can be obtained. The radar cross section (RCS) and SAR images of double scattering for buildings surrounded by grass are simulated respectively. By comparing the real and simulated images, it shows that this model can accurately exhibit the effects of aspect angle on the double scattering feature in SAR image. This model is believed to possess great value in SAR image simulation and feature extraction of urban scene for its easy implementation and clear physical interpretation.

Establishment of non-Fourier heat conduction model for an accurate transient thermal response in wet fins

In this work, transient heat transfer response of wet fins is carried out using both Fourier and non-Fourier heat conduction models. The separation of variables is used to establish a classical analytical model defining the actual transient thermal response. The present analysis has been focused and generalized for both longitudinal and pin fins under isothermal and convective base conditions. During the analysis, the instantaneous efficiency has been introduced with both Fourier and non-Fourier heat conduction models in fins operating under dehumidifying conditions. The analysis shows for a significant deviation in temperature response with the non-Fourier heat conduction as compared with that of the Fourier model. The effect of different design variables and fin surface conditions is reported. From the present analysis it becomes apparent that the instantaneous fin efficiency for wet fin surface is always less than the dry one and the condensation of vapor on the fin surface amplifies the non-Fourier heat conduction. Hence, the present analysis of non-Fourier heat transfer for determining the performance parameters of wet fins would help to have actual design information under transient behavior conditions.

Coseismic Stress and Strain Field Changes Investigation Through 3‐D Finite Element Modeling of DInSAR and GPS Measurements and Geological/Seismological Data: The L'Aquila (Italy) 2009 Earthquake Case Study

AbstractWe investigate the L'Aquila 2009 earthquake (AQE,Mw6.3, Italy) through a 3‐D Finite Element (FE) mechanical model based on the exploitation of ENVISAT DInSAR and GPS measurements and an independently generated fault model. The proposed approach mainly consists of (a) the generation of a 3‐D fault model of the active structures involved in the sequence and those neighboring to them, benefiting of a large geological and seismological data set; (b) the implementation of the generated 3‐D fault model in a FE environment, by exploiting the elastic dislocation theory and considering the curved fault geometry and the crustal heterogeneities information; and (c) the optimization of the seismogenic crustal blocks model parameters in order to reproduce the geodetic measurements. We show that our modeling approach allows us to well reproduce the coseismic surface displacements, including their significant asymmetric pattern, as shown by the very good fit between the modeled ground deformations and the geodetic measurements. Moreover, a comparative analysis between our FE model results and those obtained by considering a classical analytical (Okada) model, for both the surface displacements and the Coulomb stress changes, has been performed. Our model permits to investigate the coseismic stress and strain field changes relevant to the investigated volume and their relationships with the surrounding geological structures; moreover, it highlights the very good correlation with the seismicity spatial distribution. The retrieved stress field changes show different maxima: (a) at few kilometers depth, within the main event surface rupture zone; (b) at depths of 5–9 km in correspondence of main event hypocentral area, along the SW dipping Paganica Fault System (PFS); and (c) at depths of 12–14 km, in correspondence of the largest aftershock hypocentral area, along a steep segment of an underlying east dipping basal detachment. Moreover, the main event hypocenter is localized in a region of high‐gradient strain field changes, while a deeper volumetric dilatation lobe involves the largest aftershock zone. From these findings, we argue that the AQE hanging wall downward movement along the steep portion of PFS might have been modulated by the underlying basal detachment; on the other hand, the coseismic eastward motion of the PFS footwall might have triggered further slip on the OS, thus releasing the largest aftershock on an independent source. The retrieved stress and strain field changes, which support the active role of the OS, have been also validated through a comparative analysis with those obtained from independent geological, seismological, and GPS measurements.

Seismic Capacity Evaluation of Interior Shear Keys for Highway Bridges

ABSTRACTInterior shear keys commonly serve as structural fuses to control damage in substructures under seismic loads. To evaluate the seismic capacity of interior shear keys, six specimens with the main variables were tested. Three failure modes of the interior shear key specimens were observed during the tests. Moreover, different analytical models corresponding to the three failure modes and an empirical formula were developed to estimate the seismic capacity of the specimens. Compared with the experimental results, the improved methods provided a more accurate prediction of the load-carrying capacity than the classical analytical models.

Synergy from reproductive division of labor and genetic complexity drive the evolution of sex.

Computer experiments that mirror the evolutionary dynamics of sexual and asexual organisms as they occur in nature were used to test features proposed to explain the evolution of sexual recombination. Results show that this evolution is better described as a network of interactions between possible sexual forms, including diploidy, thelytoky, facultative sex, assortation, bisexuality, and division of labor between the sexes, rather than a simple transition from parthenogenesis to sexual recombination. Diploidy was shown to be fundamental for the evolution of sex; bisexual reproduction emerged only among anisogamic diploids with a synergistic division of reproductive labor; and facultative sex was more likely to evolve among haploids practicing assortative mating. Looking at the evolution of sex as a complex system through individual-based simulations explains better the diversity of sexual strategies known to exist in nature, compared to classical analytical models.

Finite element modeling of grain size effects on the ultrasonic microstructural noise backscattering in polycrystalline materials

The correlation between ultrasonic wave propagation and polycrystalline microstructures has significant implications in nondestructive evaluation. An original numerical approach using the finite element method to quantify in both time and frequency domains the ultrasonic noise scattering due to the elastic heterogeneity of polycrystalline microstructures is presented. Based on the reciprocity theorem, it allows the scattering evaluation using mechanical data recorded only on the boundary of polycrystal instead of within its volume and is applicable to any polycrystalline aggregate regardless of its crystallographic or morphological characteristics. Consequently it gives a more realistic and accurate access of polycrystalline microstructures than the classical analytical models developed under the assumption of single scattering and the Born approximation.The numerical approach is proposed within the same unified theoretical framework as the classical analytical models, so it is possible to validate it in the cases of idealized microstructures for which the considered analytical models remain relevant. As an original result, assuming single phase, untextured and equiaxed microstructures, two-dimensional (2D) theoretical formulas are developed and a frequency-dependent coefficient is found compared to the classical three-dimensional (3D) formulas. 2D numerical simulations are then performed for idealized microstructures composed of hexagonal grains with a uniform grain-size. Three grain sizes are considered herein and involve different scattering regions. Good comparisons are obtained between theoretical and numerical estimates of the backscattering coefficient, which validate the numerical approach. Effects of the grain boundary orientations are analyzed by modeling an irregular hexagonal grain morphology and a random grain morphology generated by an established Voronoi approach. The origin of the significant oscillation level of backscattering is then investigated and discussed.

Frictional analysis of pipe-slurry-soil interaction and jacking force prediction of rectangular pipe jacking

Predictive model and formula of jacking force has been well-established for circular pipe jacking in the past decades. However, the frictional mechanism of pipe–soil–slurry and jacking force prediction of rectangular pipe jacking has not well been understood. Nowadays, the rectangular pipe jacking is widely used, because of its over 20% larger effective usable area than that of circular pipe as underground facilities, with the same cross-sectional area. Nevertheless, the corresponding prediction models of thrust of rectangular pipe jacking are lacking. In order to further understand the frictional mechanism of slurry rectangular pipe jacking, five classical analytical calculation models have been proposed, considering the pipe–soil–slurry interaction, and prediction formulas are obtained. Then, 3D finite difference method was introduced to estimate the jacking force by using FLAC3D. Finally, three case studies have been carried out to validate the proposed models. The results show that the numerical and theoretical results have good consistency, and what is more, the measured jacking force can be well included within the ranges of analytical models presented in this paper, which can improve the thrust prediction of rectangular pipe jacking.

A Receptance Coupling Approach to Optimally Tune and Place Absorbers on Boring Bars for Chatter Suppression

A receptance coupling based method to optimally tune and place a tuned mass damper (TMD) on slender boring bars is presented. The boring bar and the TMD are treated as separate substructures. Substructural receptances are synthesized while optimizing TMD parameters as well as its location on the bar to target an increase in dynamic stiffness of the boring bar to improve chatter-free cutting conditions. Simulation based results with the proposed approach agree with classical analytical models reported in the literature. Methods presented are generalizable and can be extended to other slender cantilevered tools to increase their resistance against chatter vibrations.

A deterministic model of electron transport for electron probe microanalysis

Within the last decades significant improvements in the spatial resolution of electron probe microanalysis (EPMA) were obtained by instrumental enhancements. In contrast, the quantification procedures essentially remained unchanged. As the classical procedures assume either homogeneity or a multi-layered structure of the material, they limit the spatial resolution of EPMA. The possibilities of improving the spatial resolution through more sophisticated quantification procedures are therefore almost untouched. We investigate a new analytical model (M1-model) for the quantification procedure based on fast and accurate modelling of electron-X-ray-matter interactions in complex materials using a deterministic approach to solve the electron transport equations. We outline the derivation of the model from the Boltzmann equation for electron transport using the method of moments with a minimum entropy closure and present first numerical results for three different test cases (homogeneous, thin film and interface). Taking Monte Carlo as a reference, the results for the three test cases show that the M1-model is able to reproduce the electron dynamics in EPMA applications very well. Compared to classical analytical models like XPP and PAP, the M1-model is more accurate and far more flexible, which indicates the potential of deterministic models of electron transport to further increase the spatial resolution of EPMA.

Impact of renewable energy sources on steady-state stability of weak AC/DC systems

In recent years, the penetration of renewable resources into AC power systems has increased tremendously, creating a significantly impact on the latter's operations and stability. In this respect, it is also important to gain a basic analytical understanding of such impact on the steady-state stability of power systems with electrically weak AC/DC interconnections, but such works are not very evident in the literature. Therefore, a classical analytic model of the single and multi-infeed HVDC system which now incorporates renewable resources is proposed. Then the well-established concept of voltage sensitivity of the AC/DC interconnection is applied to analyze the impact of the renewable resources on the steady-state stability of these composite system models, as well as on the influence of system conditions and parameters. This impact is also compared with that arising from other types of shunt devices alternatively connected at the same AC/DC interconnection, therefore their relative beneficial or negative impacts will also be benchmarked.