Revisiting the 1954 Suspension Experiments of R. A.Bagnold

In 1954 R. A. Bagnold published his seminal findings on the rheological properties of a liquid-solid suspension. Although this work has been cited extensively over the last fifty years, there has not been a critical review of the experiments. The purpose of this study is to examine the work and to suggest an alternative reason for the experimental findings. The concentric cylinder rheometer was designed to measure simultaneously the shear and normal forces for a wide range of solid concentrations, fluid viscosities and shear rates. As presented by Bagnold, the analysis and experiments demonstrated that the shear and normal forces depended linearly on the shear rate in the 'macroviscous' regime; as the grain-to-grain interactions increased in the 'grain-inertia' regime, the stresses depended on the square of the shear rate and were independent of the fluid viscosity. These results, however, appear to be dictated by the design of the experimental facility. In Bagnold's experiments, the height (h) of the rheometer was relatively short compared to the spacing (t) between the rotating outer and stationary inner cylinder (h/t=4.6). Since the top and bottom end plates rotated with the outer cylinder, the flow contained two axisymmetric counter-rotating cells in which flow moved outward along the end plates and inward through the central region of the annulus. At higher Reynolds numbers, these cells contributed significantly to the measured torque, as demonstrated by comparing Bagnold's pure-fluid measurements with studies on laminar-to-turbulent transitions that pre-date the 1954 study. By accounting for the torque along the end walls, Bagnold's shear stress measurements can be estimated by modelling the liquid-solid mixture as a Newtonian fluid with a corrected viscosity that depends on the solids concentration. An analysis of the normal stress measurements was problematic because the gross measurements were not reported and could not be obtained

Strength of Materials

Strength of materials is the science of engineering methods for calculating the strength, rigidity and durability of machine and structure elements. Elements of mechanical engineering and building structures during operation are subjected to the force action of different nature. These forces are either applied directly to the element or transmitted through joint elements. For normal operation of engineering structure or machine, each element must be of such sizes and shapes that it can withstand the load on it, without fracture (strength), not changing in size (rigidity), retaining its original shape (durability). Strength of materials is theoretical and experimental science. Experiment – theory – experiment – such is the dialectic of the development of the science of solids resistance to deformation and fracture. However, the science of strength of materials does not cover all the issues of deformable bodies mechanics. Other related disciplines are also involved: structural mechanics of core systems, elasticity theory and plasticity theory. Strength of materials is general engineering science, in which, on the basis of experimental data concernimg properties of materials, on one hand, and rules of theoretical mechanics, physics and higher mathematics, on the other, the general methods of calculating rational sizes and shapes of engineering structures elements, taking into account the size and character of loads acting on them are studied. Strength of materials tasks are solved by simple mathematical methods, with a number of assumptions and hypotheses, as well as with the use of experimental data. Strength of materials has independent importance, as the subject, knowledge of which are required for all engineering specialties. It is the basis for studying all sections of structural mechanics, the basis for studying the course of machine parts, etc. Strength of materials is the scientific basis of engineering calculations, without which at rescent time it is impossible to design and create all the variety of modern mechanical engineering and civil engineering structures. The peculiarity of this course book is its focus on performing the term paper in strength of materials, which includes 14 tasks covering the entire course. The manual summarizes the main material for the topic of each task, outlines the statement of the task, and examples of solutions. The appendices provide the example of term paper structure (title page, contents, example of solving the task) and reference materials needed for its performance. All this will contribute to deeper course learning and independent performance of the term paper.INTRODUCTION...5 How to choose the task ...6 1. BASIC CONCEPTS OF STRENGTH OF MATERIALS ...7 2. CENTRAL TENSION AND COMPRESSION OF DIRECT RODS (BARS) ...13 Task 1 Strength calculation and displacement determination under tension and compression...19 Example of solving the task 1 Strength calculation and displacement determination under tension and compression ...22 Task 2 Calculation of statically indeterminate rod (bar) system under tensile-compression ...26 Example of solving the task 2 Calculation of statically indeterminate rod (bar) system under tensilecompression ...29 3. GEOMETRIC CHARACTERISTICS OF PLANE SECTIONS ...33 Task 3 Determination of axial moments of inertia of plane sections ...37 Example of solving the task 3 Determination of axial moments of inertia of plane sections ...40 4. SHEAR. TORSION ...43 Task 4 Shaft calculation for torsion...47 Example of solving the task 4 Shaft calculation for torsion (strength and rigidity) ...50 5. COMPLEX STRESSED STATE ...55 Task 5 Analysis of plane stressed state ...58 Example of solving the task 5 Analysis of plane stressed state ...60 6. STRAIGHT TRANSVERSE BENDING ...65 Task 6 Drawing the diagrams of shear (cutting) force and bending moment for cantilever beam ...76 Example of solving the task 6 Drawing the diagrams of shear (cutting) force and bending moment for cantilever beam ...79 Task 7 Diagraming of shear (cutting) force and bending moment for simply supported beam ...82 Task 8 Strength calculation under the bending of beams ...85 Task 9 Calculation for strength and determining displacements during the bending of beams ...85 Example of solving the task 7 and 8 Diagraming of shear (cutting) force and bending moment for simply supported beam. Strength calculation under the bending of beams ...88 7. DETERMINATION OF DISPLACEMENTS UNDER BENDING ...94 Example of solving the task 9 by the method of initial parameters ...108 Example of solving the task 9 by Mohr method ...110 8. STATICALLY INDETERMINATE SYSTEMS ...114 Task 10 Calculation of statically indeterminate frame ...120 Example of solving the task 10 using the force method ...123 Example of solving the task 10 by the metod of minimum potential energy of deformation ...128 9. EVALUATION OF STRESSES AND DISPLACEMENTS AT OBLIQUE BENDING ...130 Task 11 Choosing the beam section at oblique bending deformation ...134 Example of solving the task 11 Choosing the beam section at oblique bending deformation ...137 10. JOINT ACTION OF BENDING WITH TORSION ...144 Task 12 Calculation of the shaft for bending with torsion...146 Example of solving the task 12 Calculation of the shaft for bending with torsion ...149 11. STABILITY OF CENTRALLY-COMPRESSED RODS ...154 Task 13 Calculation of stability of compressed rod ...160 Example of solving the task 13 Calculation of stability of compressed rod ...162 12. DYNAMIC LOADS. DETERMINING IMPACT STRESSED AND DISPLACEMENTS ...165 Task 14 Determining maximum dynamic stresses and displacements under the impact ...169 Example of solving the task 14.1 ...172 Example of solving the task 14.2 ...175 List of references and recommended literature ...178 Annexes ...179 MAIN DEFINITIONS OF STRENGTH OF MATERIALS ...187 MAIN FORMULAS OF STRENGTH OF MATERIALS ...191 PERSONALITIES ...195 MAIN SYMBOLS OF STRENGTH OF MATERIALS ...230 UKRAINIAN-ENGLISH VOCABULARY OF BASIC TERMS ...23

The Ray Bundle method for calculating weak magnification by gravitational lenses

We present here an alternative method for calculating magnifications in gravitational lensing calculations -- the Ray Bundle method. We provide a detailed comparison between the distribution of magnifications obtained compared with analytic results and conventional ray-shooting methods. The Ray Bundle method provides high accuracy in the weak lensing limit, and is computationally much faster than (non-hierarchical) ray shooting methods to a comparable accuracy. The Ray Bundle method is a powerful and efficient technique with which to study gravitational lensing within realistic cosmological models, particularly in the weak lensing limit.Comment: 9 pages Latex, 8 figures, submitted to MNRA

Application of an expert system shell in the preliminary design of offshore supply vessels

This paper presents the application of expert system programming in preliminary ship design with particular emphasis on offshore supply vessels. Instead of using one of the conventional programming expert system languages, the system is developed using an expert system shell, Leonardo. The design program is written in such a way that it is user friendly as well as giving the user full control over the progress of the design. The algorithms developed in this system are based on extensive research on existing offshore supply vessels

From 3D Point Clouds to Pose-Normalised Depth Maps

We consider the problem of generating either pairwise-aligned or pose-normalised depth maps from noisy 3D point clouds in a relatively unrestricted poses. Our system is deployed in a 3D face alignment application and consists of the following four stages: (i) data filtering, (ii) nose tip identification and sub-vertex localisation, (iii) computation of the (relative) face orientation, (iv) generation of either a pose aligned or a pose normalised depth map. We generate an implicit radial basis function (RBF) model of the facial surface and this is employed within all four stages of the process. For example, in stage (ii), construction of novel invariant features is based on sampling this RBF over a set of concentric spheres to give a spherically-sampled RBF (SSR) shape histogram. In stage (iii), a second novel descriptor, called an isoradius contour curvature signal, is defined, which allows rotational alignment to be determined using a simple process of 1D correlation. We test our system on both the University of York (UoY) 3D face dataset and the Face Recognition Grand Challenge (FRGC) 3D data. For the more challenging UoY data, our SSR descriptors significantly outperform three variants of spin images, successfully identifying nose vertices at a rate of 99.6%. Nose localisation performance on the higher quality FRGC data, which has only small pose variations, is 99.9%. Our best system successfully normalises the pose of 3D faces at rates of 99.1% (UoY data) and 99.6% (FRGC data)

Transient Fragments in Outbursting Comet 17P/Holmes

We present results from a wide-field imaging campaign at the Canada-France-Hawaii Telescope to study the spectacular outburst of comet 17P/Holmes in late 2007. Using image-processing techniques we probe inside the spherical dust coma and find sixteen fragments having both spatial distribution and kinematics consistent with isotropic ejection from the nucleus. Photometry of the fragments is inconsistent with scattering from monolithic, inert bodies. Instead, each detected fragment appears to be an active cometesimal producing its own dust coma. By scaling from the coma of the primary nucleus of 17P/Holmes, assumed to be 1.7 km in radius, we infer that the sixteen fragments have maximum effective radii between ~ 10 m and ~ 100 m on UT 2007 Nov. 6. The fragments subsequently fade at a common rate of ~ 0.2 mag/day, consistent with steady depletion of ices from these bodies in the heat of the Sun. Our characterization of the fragments supports the hypothesis that a large piece of material broke away from the nucleus and crumbled, expelling smaller, icy shards into the larger dust coma around the nucleus.Comment: 41 pages, 12 figures. Accepted for publication by the Astronomical Journal

Influence of the Nose Radius on the Machining Forces Induced during AISI-4140 Hard Turning: A CAD-Based and 3D FEM Approach

The present study investigated the performance of three ceramic inserts in terms of the micro-geometry (nose radius and cutting edge type) with the aid of a 3D finite element (FE) model. A set of nine simulation runs was performed according to three levels of cutting speed and feed rate with respect to a predefined depth of cut and tool nose radius. The yielded results were compared to the experimental values that were acquired at identical cutting conditions as the simulated ones for verification purposes. Consequently, two more sets of nine simulations each were carried out so that a total of 27 turning simulation runs would adduce. The two extra sets corresponded to the same cutting conditions, but to different cutting tools (with varied nose radius). Moreover, a prediction model was established based on statistical methodologies such as the response surface methodology (RSM) and the analysis of variance (ANOVA), further investigating the relationship between the critical parameters (cutting speed, feed rate, and nose radius) and their influence on the generated turning force components. The comparison between the experimental values of the cutting force components and the simulated ones demonstrated an increased correlation that exceeded 89%. Similarly, the values derived from the statistical model were in compliance with the equivalent FE model values due to the verified adequacy