Wide Range Of Aspect Ratios Research Articles

Elastoplastic Buckling Analysis of Plates Involving Free Edges by Deformation Theory of Plasticity

In this paper, elastoplastic buckling of rectangular plates with different boundary conditions is investigated. Differential governing equations of plate are obtained on the basis of general loading and according to deformation theory (DT) of plasticity. Various loading conditions such as uniaxial, biaxial and shear are studied. The employed material is AL7075T6 which is usually used in the aerospace industry. A wide range of aspect ratios and plate thicknesses are investigated. The generalized differential quadrature method (GDQ) is used as the numerical method to analysis the problem. The obtained results using deformation theory of plasticity are in good agreement with experimental data. An extensive parametric study for the effects of different aspects ratios, loading ratios, transverse shear deformations, thickness ratios and various boundary conditions on the buckling coefficient are presented.

Análisis de las irreversibilidades en colectores solares de placas planas no isotérmicos para calentamiento de aire utilizando un modelo adimensional

The dimensionless model developed and validated by Baritto and Bracamonte (2012) for the thermal behavior of flat plate solar collector without glass cover is improved by adding the entropy balance equation in a dimensionless form. The model is solved for a wide range of aspect ratios and mass flow numbers. A parametric study is developed and the distribution of internal irreversibilities along the collector is analyzed. The influence of the design parameters on the entropy generation by fluid friction and heat transfer is analyzed and it is found that for certain combinations of these parameters optimal thermodynamic operation can be achieved.

Cell Morphodynamics via Phase Field Dynamics Model

Cell motion is a complex biological process that involves the cooperative interactions between the cytoskeleton and cell membrane, and these interactions generally include these interactive energies generated from the surface tension and the bending elastic energy of the cell membrane, the "protrusive" and "contractile" forces separately driven by actin polym- erization into cytoskeletons and myosin contraction, and the adhesion between the cell and the substrate. Herein, one compu- tational model based on the phase field method and the reaction-diffusion model is subsequently developed to describe this complicated biological process, coupling the cell movement and cell morphologenis with the dynamic behaviors of actin assemble into actin filaments, the physiological functions of myosin, and the interaction between the cell and the substrate. In the computational model for cell motion, the moving boundary with physical membrane properties is proposed to numerically solve the problem involved in the computational efficiency. The fish keratocytes, fast moving cells that maintain their mor- phology, are applied in the present study, and the related system parameters are chosen. The steady state and movement ve- locity of cells are obtained with a wide range of aspect ratios and movement velocities in the computational model, which are found to be well in agreement with the associated experimental results in vitro. In addition, the dependences of the movement velocity and the steady state of the cells are in detail studied on system parameters that are the concentrations of the actin and myosin, as well as the actin rate constants. It will be straightforward to extend this method to more complicated systems, such as cell contraction, cell division, and cell movement in actin flow and shear flow. Keywords cell motion; cell morphology; actin; myosin; phase field method

RADIATION BOUNDARY CONDITIONS FOR THE HELMHOLTZ EQUATION FOR ELLIPSOIDAL, PROLATE SPHEROIDAL, OBLATE SPHEROIDAL AND SPHERICAL DOMAIN BOUNDARIES

One of the most popular radiation boundary conditions for the Helmholtz equation in exterior 3-D regions has been the sequence of operators developed by Bayliss et al.1 for computational domains with spherical exterior boundaries. The present paper extends those spherical operators to triaxial ellipsoidal boundaries by utilizing two mathematical constructs originally developed for ellipsoidal acoustic infinite elements.2 The two constructs are: (i) a radial/angular coordinate system for ellipsoidal geometry, and (ii) a convergent ellipsoidal radial expansion for exterior fields, analogous to the classical spherical multipole expansion. The ellipsoidal radial and angular coordinates are smooth generalizations of the traditional radial and angular coordinates used in spherical, prolate spheroidal and oblate spheroidal systems. As a result, all four coordinate systems and their corresponding radiation boundary conditions are included within this single ellipsoidal system, varying smoothly from one to the other. The geometric flexibility of this system enables the exterior boundary of the computational domain to closely circumscribe objects with a wide range of aspect ratios, thereby reducing the size and cost of 3-D computational models.

Modeling of Gray Gas Radiation With Different Shapes of Heat Source in Three-Dimensional Enclosures

This article deals with performance evaluation of the discrete ordinates method in terms of its capacity to provide accurate results in solving radiation mode problems with different complexities. The problem formulation is done keeping in view the heat transfer process in an evaporator used in a coal-based thermal power station. The hot gas mass in the evaporator is assumed to be a heat source with two different shapes, spherical and conical. The evaporator walls that are covered with a water cooling jacket are modeled with a convective boundary condition. The gas is assumed to be gray and absorbing–emitting. The solution of the radiative transport equation is carried out using the discrete ordinates method. Parametric studies are performed for a wide range of aspect ratio, extinction coefficient, and convective heat transfer coefficient. The code is validated by comparing the result of discrete ordinates method with the exact and the discrete transfer method for nonradiative as well as radiative equilibrium conditions.

Evaluation of Reynolds stress, k-ε and RNG k-ε turbulence models in street canyon flows using various experimental datasets

In this study the Reynolds-averaged Navier-Stokes computational fluid dynamics methodology is used, which has proved to be a powerful tool for the simulations of the airflow and pollutant dispersion in the atmospheric environment. The interest is focused on the urban areas and more specifically on the street canyons, several types of which are examined in order to evaluate the performance of various turbulence models, including a Reynolds-stress model and variations of the k-e model. The results of the two-dimensional simulations are compared with measurements from a diversity of independent street canyon experimental datasets, covering a wide range of aspect ratios, free stream velocities and roughnesses. This way more general and reliable conclusions can be reached about the applicability, accuracy and ease of use of each turbulence model. In this work, the renormalization group k-e presented better results in most cases examined, while the Reynolds-stress model did not stand up for the expectations and also exhibited convergence problems.

Hydrodynamic interaction of roll stabilizing wings

The paper presents an investigation of hydrodynamic interaction of roll stabilizing wings, based on a special vortex system and known experimental results.Introducing a finite equivalent length of free tip vortices behind the leading wing allows to determine the downwash angle and lift force of the following wing over a wide range of aspect ratios and intervals between the wings.An example of applying the obtained results is considered in calculations of a roll damping moment generated by lift forces of the Short Wings Roll Stabilizer (SWIRS), installed on a high-speed ship.

Report on Microgravity Experiments of Marangoni Convection Aboard International Space Station

This paper reports some important results obtained from a series of microgravity experiments on the Marangoni convection that takes place in liquid bridges. This project, called Marangoni Experiment in Space (MEIS), started from August 22, 2008 as the first science experiment on the Japanese Experimental Module “KIBO” at the ISS. Two series of experiments, MEIS-1 and 2, were conducted in 2008 and 2009, respectively. The experimental methods used are explained in some detail. The maximum size of the liquid bridge that could be realized during these experiments was 30 mm in diameter and 60 mm in length, giving an aspect ratio of 2.0. The results are obtained for a wide range of aspect ratios of the liquid bridges, including the values that cannot be reached in 1 g experiments, and therefore, they provide indispensable amount of data for the study of instability mechanisms of the Marangoni convection.

Qualitative Equivalence Between Electrical Percolation Threshold and Effective Thermal Conductivity in Polymer/Carbon Nanocomposites

In this study, a qualitative equivalence between the electrical percolation threshold and the effective thermal conductivity of composites filled with cylindrical nanofillers has been recognized. The two properties are qualitatively compared on a wide range of aspect ratios, from thin nanoplatelets to long nanotubes. Statistical continuum theory of strong-contrast is utilized to estimate the thermal conductivity of this type of heterogeneous medium, while the percolation threshold is simultaneously evaluated using the Monte Carlo simulations. Statistical two-point probability distribution functions are used as microstructure descriptors for implementing the statistical continuum approach. Monte Carlo simulations are carried out for calculating the two-point correlation functions of computer generated microstructures. Finally, the similarities between the effective conductivity properties and percolation threshold are discussed.

Steel silos with different aspect ratios: I — Behaviour under concentric discharge

The current European standards for the design of thin-walled metal silos require the designer to use a complex combination of rules covering many different aspects of loading, structural behaviour and strength. Each individual rule was often developed autonomously, usually with implicit and undocumented conservative assumptions. When combined, the overall factor of safety of a designed silo may be significantly different from that guaranteed by the standard, making it difficult to reproduce the design rules in a numerical calculation that does not include the same implicit assumptions. This paper explores the behaviour of five thin-walled cylindrical silos with stepwise-varying wall thickness and aspect ratios varying from very squat to very slender, all custom-designed for and analysed under the EN 1991–4 concentric discharge loading condition. The aspect ratio plays a deciding role in both the behaviour and design of silos, and it is important to ascertain that a finding that is valid for one is transferable to the others. The nonlinear finite element analyses reveal that the computed load factor exceeds the partial safety factor in design by a large factor over a wide range of aspect ratio, suggesting that the overall design process is particularly conservative. The reasons for these discrepancies are explored. This paper is the first of a pair. The second paper explores the behaviour of the same set of example silos under the EN 1991–4 eccentric discharge loads, with fundamentally different conclusions.

The granular column collapse as a continuum: validity of a two-dimensional Navier–Stokes model with a μ(I)-rheology

AbstractThere is a large amount of experimental and numerical work dealing with dry granular flows (such as sand, glass beads, etc.) that supports the so-called $\ensuremath{\mu} (I)$-rheology. The reliability of the $\ensuremath{\mu} (I)$-rheology in the case of complex transient flows is not fully ascertained, however. From this perspective, the granular column collapse experiment provides an interesting benchmark. In this paper we implement the $\ensuremath{\mu} (I)$-rheology in a Navier–Stokes solver (Gerris) and compare the resulting solutions with both analytical solutions and two-dimensional contact dynamics discrete simulations. In a first series of simulations, we check the numerical model in the case of a steady infinite two-dimensional granular layer avalanching on an inclined plane. A second layer of Newtonian fluid is then added over the granular layer in order to recover a close approximation of a free-surface condition. Comparisons with analytical and semi-analytical solutions provide conclusive validation of the numerical implementation of the $\ensuremath{\mu} (I)$-rheology. In a second part, we simulate the unsteady two-dimensional collapse of granular columns over a wide range of aspect ratios. Systematic comparisons with discrete two-dimensional contact dynamics simulations show good agreement between the two methods for the inner deformations and the time evolution of the shape during most of the flow, while a systematic underestimation of the final run-out is observed. The experimental scalings of spreading of the column as a function of the aspect ratio available from the literature are also recovered. A discussion follows on the performances of other rheologies, and on the sensitivity of the simulations to the parameters of the $\ensuremath{\mu} (I)$-rheology.

Stretch-induced stress patterns and wrinkles in hyperelastic thin sheets

Wrinkles are commonly observed in stretched thin sheets and membranes. This paper presents a numerical study on stretch-induced wrinkling of hyperelastic thin sheets based on nonlinear finite element analyses. The model problem is set up for uniaxial stretching of a rectangular sheet with two clamped ends and two free edges. A two-dimensional stress analysis is performed first under the plane-stress condition to determine stretch-induced stress distribution patterns in the elastic sheets, assuming no wrinkles. As a prerequisite for wrinkling, development of compressive stresses in the transverse direction is found to depend on both the length-to-width aspect ratio of the sheet and the applied tensile strain in the longitudinal direction. A phase diagram is constructed with four different distribution patterns of the stretch-induced compressive stresses, spanning a wide range of aspect ratio and tensile strain. Next, an eigenvalue analysis is performed to find the potential buckling modes of the elastic sheet under the prescribed boundary conditions. Finally, a nonlinear post-buckling analysis is performed to show evolution of stretch-induced wrinkles. In addition to the aspect ratio and tensile strain, it is found that the critical condition for wrinkling and the post-buckling behavior both depend sensitively on the sheet thickness. In general, wrinkles form only when both the magnitude and the distribution area of the compressive stresses are sufficiently large. The wrinkle wavelength decreases with increasing strain, in good agreement with the prediction by a scaling analysis. However, as the tensile strain increases, the wrinkle amplitude first increases and then decreases, eventually flattened beyond a moderately large critical strain, in contrast to the scaling analysis.

The Minimum Q for Spheroidally Shaped Objects: Extension to Cylindrically Shaped Objects and Comparison to Practical Antennas

The classic work of Chu and others has been extended to determine the minimum radiation Q for the TM case of electrically small antennas contained within a spheroid (prolate and oblate) with no energy stored inside. The results of numerical calculations have been used to give an analytic formula that can be used to determine the electrically small bound on Qr as a function of aspect ratio for prolate and oblate spheroids. These formulas have been used to develop a lower bound for antennas contained within a cylinder, and a comparison has been made to several practical antennas as a function of aspect ratio. An antenna suggested by Wheeler is shown to have the best (lowest), Qr of the antennas examined over a wide range of aspect ratios.

Aspect ratio dependent buckling mode transition in single-walled carbon nanotubes under compression

Using molecular dynamics simulations, we study axial compressive behavior of single-walled carbon nanotubes (SWCNTs) with a wide range of aspect ratios (length to diameter ratio). It is shown that the difference in aspect ratio leads to distinct buckling modes in SWCNTs. Small-aspect-ratio SWCNTs primarily exhibit shell buckling; they switch to a column buckling mode with increasing aspect ratio. Further compression of the already column buckled large-aspect-ratio SWCNTs results in a shell buckling. This shell buckling mode is distinct from that of small-aspect-ratio SWCNTs in that it originates from the column buckling induced bending deformation. The transition strain from column buckling to shell buckling of large-aspect-ratio SWCNTs is predicted using an analytical expression. The underlying mechanism is discussed by analyzing the variation of C-C bond lengths and angles.

Analysis of Piezoelectric Energy Harvesters of a Moderate Aspect Ratio With a Distributed Tip Mass

Various mathematical beam models have been proposed for the efficient analysis of a piezoelectric energy harvester (PEH) and carrying out parameter study but there appears no beam model suitable for a PEH of a moderate width-to-length aspect ratio with a distributed tip mass, and so, moderate width-to-length aspect ratios and distribution effects of a tip mass over a finite length will be mainly focused on in the present beam analysis. To deal with a wide range of aspect ratios, the material coefficients appearing in the constitutive equations of a PEH beam will be interpolated by those of the limiting plane-strain and plane-stress conditions. The key idea in the interpolation is to derive the interpolation parameter analytically by using the fundamental frequency of a cantilevered beam of moderate aspect ratios. To deal with the distribution effects of a tip mass over a finite length, the use of a set of polynomial deflection shape functions is proposed in the assumed mode approach. The equations to predict the electrical outputs based on the proposed enhanced beam model are explicitly expressed in template forms, so one can calculate the outputs easily from the forms. The validity and accuracy were checked for unimorph and bimorph PEHs by comparing the results from the developed beam model, the conventional beam model, and a three-dimensional finite element model. The comparisons showed substantial improvements by the developed model in predicting the electrical outputs.

Viscous lock-exchange in rectangular channels

In a viscous lock-exchange gravity current, which describes the reciprocal exchange of two fluids of different densities in a horizontal channel, the front between two Newtonian fluids spreads as the square root of time. The resulting diffusion coefficient reflects the competition between the buoyancy-driving effect and the viscous damping, and depends on the geometry of the channel. This lock-exchange diffusion coefficient has already been computed for a porous medium, a two-dimensional (2D) Stokes flow between two parallel horizontal boundaries separated by a vertical height H and, recently, for a cylindrical tube. In the present paper, we calculate it, analytically, for a rectangular channel (horizontal thickness b and vertical height H) of any aspect ratio (H/b) and compare our results with experiments in horizontal rectangular channels for a wide range of aspect ratios (1/10 to 10). We also discuss the 2D Stokes–Darcy model for flows in Hele-Shaw cells and show that it leads to a rather good approximation, when an appropriate Brinkman correction is used.

Two-dimensional cylindrical plasma for intermediate gas pressures

A two-dimensional hydrodynamic model for a bounded plasma cylinder is developed. This model establishes a bridge between the two limiting cases presented by Godyak and Sternberg (2008 Plasma Sources Sci. Technol. 17 0250042): the diffusion-controlled regime and the free-fall regime. An analysis of the bounded plasma cylinder with arbitrary aspect ratios and arbitrary collisionality is presented. Plasma parameters relevant in applications are found for a wide range of aspect ratios and collisionality.

The effect of particle inertia on triaxial ellipsoids in creeping shear: From drift toward chaos to a single periodic solution

The motion of inertial, triaxial ellipsoids in creeping shear flow is explained for a wide range of aspect ratios and Stokes numbers (St, quantifying particle inertia). Particle inertia induces a drift toward rotation around the shortest axis, with this axis aligned with the vorticity axis of the flow. For aspect ratio combinations in a certain region, this periodic state is unstable for low St and the particle moves in a chaotic manner. At higher St, the instability is stabilized and one single final periodic motion is well defined also for (in the limit of St=0) unstable aspect ratios.

Lock-exchange experiments with an autocatalytic reaction front

A viscous lock-exchange gravity current corresponds to the reciprocal exchange of two fluids of different densities in a horizontal channel. The resulting front between the two fluids spreads as the square root of time, with a diffusion coefficient reflecting the buoyancy, viscosity, and geometrical configuration of the current. On the other hand, an autocatalytic reaction front between a reactant and a product may propagate as a solitary wave, namely, at a constant velocity and with a stationary concentration profile, resulting from the balance between molecular diffusion and chemical reaction. In most systems, the fluid left behind the front has a different density leading to a lock-exchange configuration. We revisit, with a chemical reaction, the classical situation of lock-exchange. We present an experimental analysis of buoyancy effects on the shape and the velocity of the iodate arsenous acid autocatalytic reaction fronts, propagating in horizontal rectangular channels and for a wide range of aspect ratios (1/3 to 20) and cylindrical tubes. We do observe stationary-shaped fronts, spanning the height of the cell and propagating along the cell axis. Our data support the contention that the front velocity and its extension are linked to each other and that their variations scale with a single variable involving the diffusion coefficient of the lock-exchange in the absence of chemical reaction. This analysis is supported by results obtained with lattice Bathnagar-Gross-Krook (BGK) simulations Jarrige et al. [Phys. Rev. E 81, 06631 (2010)], in other geometries (like in 2D simulations by Rongy et al. [J. Chem. Phys. 127, 114710 (2007)] and experiments in cylindrical tubes by Pojman et al. [J. Phys. Chem. 95, 1299 (1991)]), and for another chemical reaction Schuszter et al. [Phys. Rev. E 79, 016216 (2009)].

Computational model for cell morphodynamics.

We develop a computational model, based on the phase-field method, for cell morphodynamics and apply it to fish keratocytes. Our model incorporates the membrane bending force and the surface tension and enforces a constant area. Furthermore, it implements a cross-linked actin filament field and an actin bundle field that are responsible for the protrusion and retraction forces, respectively. We show that our model predicts steady state cell shapes with a wide range of aspect ratios, depending on system parameters. Furthermore, we find that the dependence of the cell speed on this aspect ratio matches experimentally observed data.