Effect Of Shape Variation Research Articles

Hemodynamic characteristics of flow around a deformable stenosis

Clinical studies reported that some vulnerable stenoses deformed their shape in a blood vessel based on flow condition. However, the effects of shape variation on flow characteristics remain unclear. The flow characteristics are known to affect vulnerable stenosis rupture and fractional flow reserve (FFR) value which has been widely used as a diagnostic tool for stenosis. Vulnerable stenosis rupture occurs when the structural stress exerted on a fibrous cap exceeds its tolerable threshold. The stress magnitude is determined from the spatial distribution of static pressure around the stenosis. In the present study, the static pressure distribution and the FFR value in deformable stenosis were investigated with related other flow characteristics. Two phantom models were fabricated to mimic deformable and nondeformable stenoses using polydimethylsiloxane. The flow characteristics were observed under a steady-flow condition at three Reynolds numbers (Re=500, 1000, 1500) using a particle image velocimetry. The pressure drop across the stenosis models were measured using a pressure sensor to determine effects of shape deformation on FFR value. Shape variations and jet deflections were clearly observed in the deformable stenosis model, and the effective severity of the stenosis increased up to 17.2%. The shape variations of deformable stenosis model increased the static pressure difference at the upstream and downstream sides of the stenosis. The pressure drop across the deformable stenosis model was significantly higher than that of the nondeformable stenosis model. The present results substantiate that stenosis deformability should be carefully considered to diagnose the rupture of vulnerable stenosis.

Effects of shape variations on the energy metabolism of the sand cricket Gryllus firmus: a geometric morphometric analysis

Respiration and energy metabolism are key processes in animals, which are severely constrained by the design of physical structures, such as respiratory structures. Insects have very particular respiratory systems, based on gas diffusion across tracheae. Since the efficiency of the tracheal respiratory system is highly dependent on body shape, the pattern of morphological variation during ontogeny could have important metabolic consequences. We studied this problem combining through-flow respirometry and geometric morphometrics in 88 nymphs of the sand cricket, Gryllus firmus. After measuring production in each individual, we took digital photographs and defined eight landmarks for geometric morphometric analysis. The analysis suggested that ontogenic deformations were mostly related to enlargement of the abdomen, compared to thorax and head. We found that (controlling for body size) metabolic variables and especially resting metabolism are positively correlated with a shape-component associated to an elongation of the abdomen. Our results are in agreement with the mechanics of tracheal ventilation in orthopterans, as gas circulation occurs by changes in abdominal pressures due to abdominal contractions and expansions along the longitudinal axis.

Architecturally modified Al–DRA composites: the effect of size and shape of the DRA rods on fracture behavior

Architectural modification of aluminum matrix composites is considered as an efficient method to improve fracture toughness. Al–DRA (Al–Al/SiC/20p) composites were fabricated via “powder extrusion–casting–ingot extrusion” route with structures similar to that of reinforced concrete, so that DRA rods were surrounded by unreinforced aluminum. The effects of variation in shape, size, and number of DRA rods on fracture behavior of Al–DRA composites were investigated. Composites containing DRA rods with hexagonal cross-section exhibited higher resistance to crack initiation and growth, in comparison to those containing circular rods. In the case of hexagonal rods, increasing the number of rods (reducing the rods’ cross-section surface) led to further enhancement of fracture toughness. Fracture surface observations of all samples revealed the existence of desirable cohesion between rods and the surrounding matrix. The remained sharp and unblunted corners of hexagonal DRA rods caused stress concentration and microcrack formation upon loading. Hence, plastic deformation constraint of aluminum ligament between rods was alleviated, which, in turn, led to further energy consumption during the fracture process.

Size and shape of the resection surface geometry of the osteoarthritic knee in relation to total knee replacement design

This study examines the resection surface geometry of the femur, tibia, and patella in relation to the design of total knee implants. Using a technique known as principal component analysis (PCA), the variation in the resection geometry of the knee was summarized. Of the total variation of the knee, 58 per cent was due to variation in size and 14 per cent was due to varying femoral intercondylar notch width. A PCA was performed on each bone separately and it was found that 60 per cent, 76 per cent and 71 per cent of variation was due to size for the femur, tibia, and patella respectively. Femoral and tibial size were highly correlated (r = 0.95) while patellar size had poorer correlation with both femoral and tibial size (r < 0.7). Simple linear dimensions (femoral epicondylar width or tibial mediolateral width) were reliable indicators of knee size. The effect of shape variation, which is generally not accounted for in implant design, was measured. The resected surfaces of each subject were compared with a model of the resection surfaces of the knee which varied in size but not shape. The maximum overhang and underhang of the model on the resection surfaces were measured. There was average maximum model overhang of 3.6 mm and underhang of 3.9 mm in the femur, 2.3 mm overhang and 1.9 mm underhang in the tibia, and 2.6 mm overhang and 2.5 mm underhang in the patella. The maximum coverage that an implant can be expected to provide for a population is quantified. Implant designs which include some shape as well as size variation improve on the implant fit.

Buckling of Externally Pressurized Prolate Ellipsoidal Domes

Details are given of a numerical and experimental study into buckling of steel ellipsoidal domes loaded by static external pressure. A range of geometries and thicknesses of domes is examined, as is the influence of different boundary conditions. Shells are examined on the basis of having the same mass. The main focus of the study is on prolate domes, i.e., those taller than a hemisphere of the same base radius. Numerical predictions are confirmed by pressurizing six laboratory scale prolate domes to destruction. Details are given of the manufacture and test procedure for the domes. The adverse effects of variations in shape and wall thickness are discussed, and finite element predictions are made for geometrically imperfect domes. Correlation between the two sets of results is good. Numerically and experimentally obtained results are related to the current design codes: ASME Boiler and Pressure Vessel Code, Sec. 8, Division 2 (described hereon as ASME VIII), PD5500, and ECCS recommendations (ASME B&amp;PV Code, 2004 ed., Sec. 8, Division 2, New York, NY; BSI 2003 “Published Document PD5500: Specification for Unfired Pressure Vessels,” BSI London; European Convention for Constructional Steelwork Recommendations, 1988 “Buckling of Stell Shells-European Recommendations,” ECCS-TWG 8.4, 4th ed., Brussels), which at present make no provision for prolate domes. Suggestions are made for the possible inclusion of such domes into the standards.

Swelling and Shrinking Dynamics of Nematic Elastomers Having Global Director Orientation

We reveal that the swelling and shrinking of monodomain nematic elastomers in solvents exhibit unusual kinetics owing to the presence of shape and volume variation modes with markedly different rates. A change in the degree of nematic order caused by temperature (T) jumps drives a spontaneous macroscopic deformation along the director as well as a change in the chemical potential of the solvent inside the gel. The former yields an almost instantaneous shape variation, whereas the latter induces a slow volume variation governed by the diffusion of polymer networks, such as the swelling of isotropic gels. The markedly different rates of these two modes yield unique kinetics of swelling and shrinking: (1) a pronounced over- or undershoot of the gel dimensions is observed in the direction where the effect of shape variation on the dimensions counters that of the volume variation, and (2) a large dimensional change (more than 50% of the total change) occurs immediately after the T-jumps in the direction along which the effects of the two modes on the dimensions harmonize.

Characteristics of Beam-Based Flexure Modules

The beam flexure is an important constraint element in flexure mechanism design. Nonlinearities arising from the force equilibrium conditions in a beam significantly affect its properties as a constraint element. Consequently, beam-based flexure mechanisms suffer from performance tradeoffs in terms of motion range, accuracy and stiffness, while benefiting from elastic averaging. This paper presents simple yet accurate approximations that capture the effects of load-stiffening and elastokinematic nonlinearities in beams. A general analytical framework is developed that enables a designer to parametrically predict the performance characteristics such as mobility, over-constraint, stiffness variation, and error motions, of beam-based flexure mechanisms without resorting to tedious numerical or computational methods. To illustrate their effectiveness, these approximations and analysis approach are used in deriving the force–displacement relationships of several important beam-based flexure constraint modules, and the results are validated using finite element analysis. Effects of variations in shape and geometry are also analytically quantified.

Effect of shape variations on the structure and crystallography of directionally solidified [formula omitted]-α eutectic composites

Master ingots of the {gamma}/{gamma}{prime}-{alpha} alloy with chemical composition: Ni-31.01Mo-6.43Al-0.01W-0.006C-0.001S (wt.%) were prepared in a vacuum inducing furnace by melting high-purity metals under an argon atmosphere and casting in copper chill molds. These ingots were machined to rods of 12 {times} 10{sup {minus}3} m diameter. Directional solidification was performed under an argon atmosphere in a modified Bridgman-type solidification apparatus. During steady-state growth of the {gamma}/{gamma}{prime}-{alpha} eutectic composite the interfibre spacing varies with the growth rate according to the relation {lambda} = KR{sup {minus}0.5}, where K is calculated to be 4.71 {times} 10{sup {minus}9} m{sup 1.5}s{sup {minus}0.5}. The gradual contraction in the solidifying cross section decreases the number of the eutectic grains increases the interfibre spacing and causes coarsening and fiber-lamella transformations of the reinforcing phase. The phases grow in the growth direction and the preferred {l_brace}100{r_brace}{sub {gamma}/{gamma}{prime}}{parallel}{l_brace}100{r_brace}{sub {alpha}} orientation relationship is maintained between the matrix and reinforcing phase. The growth direction is parallel to the ingot axis for the matrix but deviates from this axis for the reinforcing phase.

A Method for Calculating the Michell and Havelock Integrals

A method is suggested for analyzing and calculating the Michell and Havelock integrals. In place of the corresponding integral expressions, infinite series are proposed that do not require many terms for accuracy. Shape dependence is presented by way of products of integral functions that define the ship. It is thus possible to analyze the effect of shape variation by varying these functions without integrating them. Velocity dependence is linear with respect to integral functions that are shape-independent and hence suitable for tabulation. Values afforded by the Michell and Havelock integrals are to an extent tied to wave resistance. It is believed that to the same extent the method proposed herein is especially apt for (i) the systematic analysis of ship series and (ii) computer-aided shape design.

Design Sensitivity Analysis in Structural Mechanics. III. Effects of Shape Variation

Abstract The dependence of static response and eigenvalues on the shape of plates and plane elastic solids is characterized. Shape of elastic bodies is taken as the design variable. The material derivative idea of continuum mechanics is used to obtain expressions for directional derivatives of displacement fields and eigenvalues with respect to a transformation function that defines a shape variation. The result is used to obtain explicit and computable expressions for variations of integral functionals that arise in structural optimization problems.

The effect of hydrofluoric acid on quartz shape-Fourier grain shape analysis

Fourier grain shape analysis of quartz grains in sediment has been applied to a wide variety of sedimentological problems. Mineralogically pure samples of quartz are required to eliminate the effects of shape variation due to non-quartz minerals. Hydrofluoric acid treatments of samples, which enables the identification feldspar contaminant grains, has been shown to have no significant effect on the shape of quartz particles, as measured by the first twenty terms of a closed-form Fourier Series.

Effect of shape variations on the structure of directionally solidified Al-Al3Ni composites

The effect on structure of some of the possible changes in shape of directionally solidified Al-Al3Ni eutectic composites has been studied for two growth conditions. The shape changes investigated included both contraction and divergence in cross-section of the grown part, as well as 90 deg bends in the center-line of the composites. The experimental results showed that contractions in the solidifying cross section do not seriously affect the growth of composites, apart from some coarsening of the structure near the surface. Fiber branching took place in the case of gradual divergence in the solidifying cross section with the fibers deviating from the general growth direction by an angle determined by the shape of equitemperature contours during solidification. Sharp changes in growth direction, 90 deg bend, gave rise to nucleation of new grains of considerable misorientation and hypoeutectic alloys nucleated primary aluminum phase before the eutectic structure was established. The relatively large under cooling needed for nucleation gave rise to high local growth rates in the 90 deg bend area. As the Al3Ni fibers grow at right angles to equitemperature contours during solidification, it is concluded that control of the composite structure can be achieved by controlling the growth conditions and mold design. Molten alloy-graphite reactions resulted in the formation of aluminum carbides which were more extensive at higher temperatures and longer exposure times.

The effect of shape variations during growth on the morphology ofin-situ eutectic composites

An experimental investigation has been conducted of the influence onin-situ eutectic composite microstructures of both gradual and abrupt changes in cross-sectional area, both with and without simultaneous changes in growth direction, and of the effects of changes in growth direction at constant cross-section. Alloys of the binary (Al-Ni and ternary Al-Cu-Ni) eutectic were chosen to eliminate the effects of microsegregation and these were grown under a variety of conditions of growth rate and temperature gradient, consistent with those used for off-eutecticin-situ composites, and in apparatus generally used for that work and described previously. As well as the expected variation in lamellae or inter-rod spacing with changes of cross-section, abrupt decreases in crosssectional growth area coupled with changes in growth direction produced a multigrain structure of various orientations. Potentially weak zones denuded of lamellae or rod growth were observed when the growth direction deviated beyond a limiting small angle at constant cross-section.

Analogue investigations of electric field distribution and ion trajectories in the field ion microscope

Analytical investigations of the electric field and stress acting on a field ion microscope specimen are based on the assumption that the specimen is smooth, ie the effects of shape variations at the atomic level are not considered. In this paper the possibilities of investigating the corresponding field variations by the use of analogue techniques are discussed, and preliminary experiments on field and trajectory determinations using a resistance network and a two-dimensional field-plotter are described. These techniques are able to give a valuable qualitative idea of the effects arising from various topographical features of the specimen end-form.

Analysis of3NParameters withN−NForces

This investigation has a twofold objective, (a) to examine in some detail the effects of various refinements in the input forces on the binding energy (BE) of the triton and the doublet neutron-deuteron scattering length (a 1/2 ), and (b) to compare the effects of shape variations in the potentials on the evaluation of the same quantities. For this purpose, we calculate the BE and a 1/2 with the inclusion of tensor and core effects individually and collectively and give a comprehensive comparison of these results along with those obtained in earlier investigations by various authors. For the second objective, we present the results for an entirely different shape of the separable potentials (viz., form factors of the type √Q 0 which fulfill certain analyticity requirements on the potentials), and compare these predictions with those based on potentials proposed by Yamaguchi and Yukawa. The effects of the shape variation on the results found from the comparison of these potentials, which agree only approximately on the energy shell, persist even with higher-ranked potentials which agree much more closely on the energy shell as a result of the inclusion of repulsive-core terms. The limitations that the effects of shape variations imply on the reliability of three-body calculations with input two-body forces are discussed.