Center Of Curvature Research Articles

Nonlinear empirical model to simulate displacement-dependent structural behavior of a PWR fuel assembly

A nonlinear model of a pressurized water reactor (PWR) fuel assembly is developed, and its performance is evaluated. The nuclear fuel assembly experiences numerous friction forces developed in the fuel rods and supporting components. Therefore, the fuel assembly deflection generates slips between the structures and develops a nonlinear behavior. The loose joints make it impossible for the rods to share a common center of curvature when the fuel assembly is deflected. In addition, when the fuel assembly is under a high temperature coolant water condition, the slip is activated because of the associated dimensional change. Thus, local and global displacements are introduced to compensate for the slip, and the relationship between the two is explained. Considering the fuel becomes soft when it is deflected, a nonlinear beam model with the varying second moment of area is proposed. The Galerkin discretization method is utilized to solve the nonlinear equation of motion, and an incremental solution is determined based on the linearized equation. Verification examples are provided, and the results are compared to the test data. It is shown that the concept of the model is reasonable and applicable. The developed model could be helpful to understand the nonlinear behavior of a fuel assembly and to predict the responses in case of an accident.

On the possibility of using multi-element phased arrays for shock-wave action on deep brain structures

A noninvasive ultrasound surgery method that relies on using multi-element focused phased arrays is being successfully used to destroy tumors and perform neurosurgical operations in deep structures of the human brain. However, several drawbacks that limit the possibilities of the existing systems in their clinical use have been revealed: a large size of the hemispherical array, impossibility of its mechanical movement relative to the patient’s head, limited volume of dynamic focusing around the center of curvature of the array, and side effect of overheating skull. Here we evaluate the possibility of using arrays of smaller size and aperture angles to achieve shock-wave formation at the focus for thermal and mechanical ablation (histotripsy) of brain tissue taking into account current intensity limitations at the array elements. The proposed approach has potential advantages to mitigate the existing limitations and expand the possibilities of transcranial ultrasound surgery.

Dynamic characteristics of horizontally curved bridges

Horizontally curved bridges have complicated dynamic characteristics because of their irregular geometry and nonuniform mass and stiffness distributions. This paper aims to develop a simplified and practical method for the calculation of the natural frequencies and mode shapes of horizontally curved bridges that would be of interest to bridge engineers for the estimation of the seismic response of these types of bridges. For this purpose, a simple three-degree-of-freedom (3DOF) dynamic model for free vibration equation of this type of bridge has been developed. It is shown that the translational motion of the deck of horizontally curved bridges in the direction that is perpendicular to their axis of symmetry is always coupled with the rotational motion of the deck, regardless of the location of the stiffness center. The model is further exploited to develop closed-form formulas for the estimation of the maximum displacements of the corners of the deck of one-way asymmetric horizontally curved bridges. The accuracy of the model is verified by finite-element model of a horizontally curved bridge prototype in OpenSEES. Finally, the model is utilized to study the influence of the location of the stiffness center with respect to the deck curvature center on the natural frequency and the maximum displacements of the corners of the deck for different curvatures of the deck. The results of free vibration analysis show that the natural frequencies of one-way asymmetric horizontally curved bridges, in general, increase with the increase of the subtended angle of the deck. The results of earthquake response spectrum analysis show that the increase in the subtended angle of one-way asymmetric horizontally curved bridges decreases the radial displacements of the corners of the deck but increases the azimuthal displacement. These two responses both increase with the increase in the distance between the stiffness center and the curvature center.

Laser confocal cylindrical radius measurement method and its system.

This paper proposes a laser confocal cylindrical radius of the curvature measurement (CCRM) method. The CCRM method precisely identifies the positions of the vertex and curvature center of the test cylindrical surface by using the property so that the maximum point of the laser confocal axial intensity curve precisely corresponds to the focus of the laser confocal measurement system, and the accurate distance of these two positions is obtained by the distance measuring instrument, thus achieving the precise measurement of the cylindrical radius. The quadratic fitting method is used to further improve the measurement accuracy. Compared with existing measurement methods, the CCRM method has high measurement precision, simple structure, and strong environmental interference capability, and it is more suitable for engineering applications. Based on the CCRM, the CCRM system is established, and theoretical analysis and preliminary experiments indicate that the relative uncertainty of cylindrical radius measurement is better than 0.045%. Therefore, the CCRM provides an effective approach for the high-precision measurement of cylindrical radius.

Effect of wind gusts on the dynamics of railway vehicles running on a curved track

Due to global warming, there is an increasing number of wind gusts that affect the stability of railway vehicles. A railway vehicle running on a curved track during a wind gust is subjected to multiple forces simultaneously, which include the centrifugal force and forces exerted by the wind gust and cant, and they significantly affect the vehicle’s dynamic characteristics as well as its safety. The forces increase the vibration of carbodies and the risk of derailment and overturning of cars; the effect is worse on irregular tracks. In order to review the phenomenon in detail, a 1/20 scale model of a railway vehicle was built to measure the aerodynamic coefficients in five directions—side force, lift force, roll moment, pitch moment, and yaw moment—through a wind tunnel test. The data collected were applied as external forces to a full-scale railway vehicle model traveling on a curved track. Using a multibody simulation software program, SIMPACK, a railway vehicle was modeled, which was then used in the simulation of the dynamic characteristics and safety of vehicles while traveling on a curved track during a wind gust. Using the actual measured track data from the curved zone, a comparison was made on the dynamic characteristics of the car traveling, with and without a wind gust, on a curved track with a railway curve radius of 599 m; also, the difference was analyzed with the direction of the wind gust blowing from inside and toward the center of curvature. The results showed that in the presence of a wind gust blowing from outside the curvature with an average speed of 25 m/s it is advisable to stop train services on grounds of safety.

Study on performance of bended spiral strand with interwire frictional contact

The present study establishes a solution model of a spiral strand subjected to a bending load, in which the interwire frictional contact and the Poisson's ratio of the wires are considered, and the interwire friction force is automatically achieved. Based on this model, the performance of bended wire rope strand with interwire frictional contact is solved with conjugate gradient method, fast Fourier transform, finite difference method and improved Euler's predictor–corrector method. The effects of the frictional contact, bending load and lay angle on the performance of the bended strand are analyzed. The results show that the consideration of the interwire frictional contact can obtain a larger bending stiffness of the strand compared with a pure bending model. The serious diameter shrinkage of the outside wire due to the effect of Poisson's ratio, the maximum pressure and deformation due to the core-wire contact occur at the furthest part from the curvature center of the bended strand, where the tensile failure and contact fatigue are most likely to happen. Meanwhile, interwire slippage and bending fatigue are liable to happen at the neutral layer. The strand with a large lay angle has a better resistance to bending fatigue but worse tribological properties, compared with a small lay angle strand.

Effect of adaptive motion on cyclic fatigue resistance of R-Endo nickel-titanium file

Aim: The aim of this study is to evaluate R-Endo R3 file's resistance to cyclic fatigue in comparison with continuous rotation movement and Adaptive Motion (AM) movement under dynamic model. Materials and Methods: Forty pieces of R-Endo R3 (25.04) files (lot no: 062011) were included in the study. Cyclic fatigue tests were performed with specifically manufactured dynamic cyclic testing device. The device has an artificially prepared canal with 60° curvature angle and 5 mm curvature radius. The canal inner diameter is 1.5 mm and the center of curvature is located 5 mm coronally from the apex. The files were randomly divided into two groups (n = 20) and the following procedures were performed – Group 1: Rotary motion (RM), Group 2: AM. Time to fracture was recorded and the number of cycles to failure for each instrument was obtained. Statistical analyses were performed using Student's t-test. The statistical significant level was set at P Results: AM group had a significantly higher cyclic fatigue resistance compared with RM group (P Conclusion: Within the limitation of the present study, it was found that Adaptive Motion statistically increases the resistance to cyclic fatigue of R-Endo R3 files, manufactured for retreatment.

Iterating Evolutes and Involutes

This paper concerns iterations of two classical geometric constructions, the evolutes and involutes of plane curves, and their discretizations: evolutes and involutes of plane polygons. In the continuous case, our main result is that the iterated involutes of closed locally convex curves with rotation number one (possibly, with cusps) converge to their curvature centers (Steiner points), and their limit shapes are hypocycloids, generically, astroids. As a consequence, among such curves only the hypocycloids are homothetic to their evolutes. The bulk of the paper concerns two kinds of discretizations of these constructions: the curves are replaced by polygons, and the evolutes are formed by the circumcenters of the triples of consecutive vertices (\(\mathcal {P}\)-evolutes), or by the incenters of the triples of consecutive sides (\(\mathcal {A}\)-evolutes). For equiangular polygons, the theory is parallel to the continuous case: we define discrete hypocycloids (equiangular polygons whose sides are tangent to hypocycloids) and a discrete Steiner point. The space of polygons is a vector bundle over the space of the side directions; our main result here is that both kinds of evolutes define vector bundle morphisms. In the case of \(\mathcal {P}\)-evolutes, the induced map of the base is 4-periodic, and the dynamics reduces to the linear maps on the fibers. We prove that the spectra of these linear maps are symmetric with respect to the origin. The asymptotic dynamics of linear maps is determined by their eigenvalues with the maximum modulus, and we show that all types of behavior can occur: in particular, hyperbolic, when this eigenvalue is real, and elliptic, when it is complex. We also study \(\mathcal {P}\)- and \(\mathcal {A}\)-involutes and prove that the side directions of iterated \(\mathcal {A}\)-involutes of polygons with odd number of sides behave ergodically; this generalizes well-known results concerning iterations of the construction of the pedal triangle. In addition to the theoretical study, we performed numerous computer experiments; some of the observations remain unexplained.

A proposal for a formula of absolute pole velocities between relative poles

In this paper is proposed a vectorial equation that relates the absolute pole velocities of three moving rigid bodies with a planar motion of general type. From this equation, it is possible to obtain a relation between the pole velocities of the three mathematical points, related between them by the Aronhold-Kennedy Theorem. The formula allows the calculation of one of the pole velocities from the other two, being known the angular velocities and accelerations of the moving bodies. It is applicable regardless of whether the instantaneous centers (poles) are located on physical points on the linkage or not. Illustrative examples of the application of the formula on representative planar linkages are included. In the final section, is discussed a similar concept associating a mathematical point to the curvature centers of a point's path, so called centroma.

Mobile mapping systems and spatial data collection strategies assessment in the identification of horizontal alignment of highways

The horizontal alignment of existing highways may be identified by using several terrestrial or aerial geomatics technologies. Such technologies involve different levels of precision and accuracy; hence, different results can be expected. At present, there are no comparisons available between the solutions resulting from the use of different technologies and data sources for the same road alignment.In this investigation, a number of terrestrial mobile mapping techniques and data collection strategies were evaluated. The centerline of a 3.6km section of a highway was used to estimate radii, centers of curvature and orientation of tangents. Two statistical fitting methods were used to back-calculate these parameters, and the results were then compared with as-built alignment data.Terrestrial images from a mobile mapping vehicle were used to determine the centerline, which was also estimated as the average line of the carriageway and pavement edges, and as the average line of the two driving trajectories. Positions were surveyed using low-cost sensors (an integrated GPS-IMU platform, HD webcam). For comparison purposes, aerial orthophotos and a GNSS (high-cost) receiver were used simultaneously. Although the GPS-IMU data and estimated trajectories provided results comparable to those of the GNSS receiver, the use of georeferenced images proved less accurate. The results and comments in the paper should be of use to survey practitioners when they need to select an acquisition methodology appropriate to the desired level of accuracy and in line with budget constraints.

Spiral modes supported by circular dielectric tubes and tube segments

The modal properties of curved dielectric slab waveguides are investigated. We consider quasi-confined, attenuated modes that propagate at oblique angles with respect to the axis through the center of curvature. Our analytical model describes the transition from scalar 2-D TE/TM bend modes to lossless spiral waves at near-axis propagation angles, with a continuum of vectorial attenuated spiral modes in between. Modal solutions are characterized in terms of directional wavenumbers and attenuation constants. Examples for vectorial mode profiles illustrate the effects of oblique wave propagation along the curved slab segments. For the regime of lossless spiral waves, the relation with the guided modes of corresponding dielectric tubes is demonstrated.

Weebles Only Wobble But Eggs Fall Down

SummaryWhy does a roly-poly toy tend to stand upright on its less pointed end while an egg does not? The answer lies in a simple principle that governs the nature of the mechanical equilibrium of a solid of revolution. A roly-poly toy is at a stable equilibrium on its vertex while an egg is at an unstable equilibrium. The roly-poly toy's center of mass is vertically below the center of curvature of its vertex, while for the egg it is the other way around. Although this simple but powerful principle is known, in this article we present a contrasting analysis that not only verifies this principle, but also provides the answer to another interesting question: Is there another simple principle that governs the nature of the equilibrium in the critical situation where the center of curvature of the vertex happens to coincide with the center of mass?

Dean-Taylor flow with convective heat transfer through a coiled duct

Abstract Due to engineering application and its intricacy, flow in a rotating coiled duct has become one of the most challenging research fields of fluid mechanics. In this paper, a spectral-based numerical study is presented for the fully developed two-dimensional flow of viscous incompressible fluid through a rotating coiled rectangular duct. The emerging parameters controlling the flow characteristics are the rotational parameter i.e. the Taylor number, Tr; the Grashof number, Gr; the Prandtl number, Pr and the pressure-driven parameter i.e. the Dean number, Dn. The rotation of the duct about the center of curvature is imposed in both the positive and negative direction and combined effects of the centrifugal, Coriolis and buoyancy forces are investigated, in detail, for two cases of the Dean Numbers, Case I: Dn = 1000 and Case II: Dn = 1500. For positive rotation, we investigated unsteady solutions for 0 ≤ Tr ≤ 500, and it is found that the chaotic flow turns into steady-state flow through periodic or multi-periodic flows, if Tr is increased in the positive direction. For negative rotation, however, unsteady solutions are investigated for − 700 ≤ T r ≤ − 50 , and it is found that the unsteady flow undergoes through various flow instabilities, if Tr is increased in the negative direction. Typical contours of secondary flow patterns and temperature distributions are obtained at several values of Tr, and it is found that the unsteady flow consists of asymmetric two- to eight-vortex solutions. The present study demonstrates the role of secondary vortices on convective heat transfer and it is found that convective heat transfer is significantly enhanced by the secondary flow; and the chaotic flow, which occurs at large Dn’s, enhances heat transfer more effectively than the steady-state or periodic solutions. This study also shows that there is a strong interaction between the heating-induced buoyancy force and the centrifugal-Coriolis instability in the curved channel that stimulates fluid mixing and consequently enhances heat transfer in the fluid.

Simulation of spreading depolarization trajectories in cerebral cortex: Correlation of velocity and susceptibility in patients with aneurysmal subarachnoid hemorrhage.

In many cerebral grey matter structures including the neocortex, spreading depolarization (SD) is the principal mechanism of the near-complete breakdown of the transcellular ion gradients with abrupt water influx into neurons. Accordingly, SDs are abundantly recorded in patients with traumatic brain injury, spontaneous intracerebral hemorrhage, aneurysmal subarachnoid hemorrhage (aSAH) and malignant hemispheric stroke using subdural electrode strips. SD is observed as a large slow potential change, spreading in the cortex at velocities between 2 and 9 mm/min. Velocity and SD susceptibility typically correlate positively in various animal models. In patients monitored in neurocritical care, the Co-Operative Studies on Brain Injury Depolarizations (COSBID) recommends several variables to quantify SD occurrence and susceptibility, although accurate measures of SD velocity have not been possible. Therefore, we developed an algorithm to estimate SD velocities based on reconstructing SD trajectories of the wave-front's curvature center from magnetic resonance imaging scans and time-of-SD-arrival-differences between subdural electrode pairs. We then correlated variables indicating SD susceptibility with algorithm-estimated SD velocities in twelve aSAH patients. Highly significant correlations supported the algorithm's validity. The trajectory search failed significantly more often for SDs recorded directly over emerging focal brain lesions suggesting in humans similar to animals that the complexity of SD propagation paths increase in tissue undergoing injury.

Analysis of albumin Raman scattering registration efficiency from different volume and shape cuvette

The cuvette shape influence on the Raman registration efficiency at small volumes of albumin (0.15-1 ml) using the PLS model was analysed. This paper examines the smallest measurement error RMSE of 3-6 g/l with a correlation coefficient R 2 = 0.95 was achieved for pure Raman spectra extraction by baseline correction with asymmetric least squares smoothing method for aluminum spherical type cuvette-reflectors. Its curvature center was matched with the focal spot of the exciting laser. The error of albumin concentration determination equaled about 5% of albumin normal concentration in a blood plasma using a spherical cuvette with a volume of 0.55 ml. A further decrease of the cuvette volume led to a sharp loss of the method prediction accuracy.

Automatically Determining the Segmentation Lines between Images of Adherent Rice Grains

Abstract. A new strategy for accurately and automatically determining the segmentation lines between images of adherent rice grains was explored based on the characteristics of contour and the techniques of image analysis. The images were captured by using an optical scanner. The original images of touching rice particles were preprocessed by the techniques of image analysis including de-noise, segmentation, and contour extraction. The extracted contours were smoothed by convoluting with Gaussian kernel. The first-derivative of the smoothed vectors was computed to look for the local peaks which corresponded to the segmentation nodes. A radiate triangle region was proposed to determine the confidence region for the potential matching nodes. The direction of radiate region was determined in terms of the axis tilted from the normal through the curvature center. The nodes which fell into the triangle region might become the candidate matching nodes. The splitting line linking between the matching nodes with the shortest distance was considered as the correct splitting path. The results demonstrated that the proposed method could be successfully used to split the images of touching rice particles. Keywords: Confidence region, Image analysis, Matching, Rice particles, Segmentation.

A mathematical analysis of locus of centre of circular curvature of a helix

A mathematical analysis of locus of centre of circular curvature of a helix

Interwire wear and its influence on contact behavior of wire rope strand subjected to cyclic bending load

The present study establishes a solving model for analyzing the interwire wear evolution of a wire rope strand subjected to cyclic bending load, in which the frictional contact and sliding between the wires are considered simultaneously. A wear experiment between the wires is conducted to study the wear behavior of the wires. Meanwhile, the proposed model is verified experimentally. Then the interwire wear and its effect on the contact behavior of the strand are analyzed. The results show that the interwire wear only happens on the side further from the curvature center of the bended strand than its neutral layer, and no wear happens when the wires are apart from each other or the interwire slippage is zero. As the wear process goes on, the wear region extends only along the normal direction of the core-wire contact line, and the maximum wear depth occurs at the middle position between the neutral layer and the furthest location from the curvature center. The contact pressure is distributed uniformly along the normal direction of contact line, but a significant stress concentration and local deformation happen at the position furthest from the curvature center of the bended strand.

Effect of Curvature on Penetration Resistance of Polycarbonate Panels

Three-dimensional transient deformations of clamped flat and doubly curved polycarbonate (PC) panels impacted by a rigid smooth hemispherical-nosed circular cylinder have been numerically studied by the finite-element (FE) method to delineate effects of the panel radius of curvature to its thickness ratio on their penetration resistance. The PC is modeled as thermoelastoviscoplastic with the effective plastic strain rate depending upon the hydrostatic pressure. The effective plastic strain of 3.0 at failure is ascertained by matching for one set of flat panels the computed and the experimental minimum perforation speeds. It is found that a negative curvature (i.e., the center of curvature toward the impactor) of a panel degrades its penetration performance, and the positive curvature enhances it especially for thin panels with thickness/radius of curvature of 0.01. However, the benefit is less evident for panels with the panel thickness/radius of curvature of 0.04 or more. For positively curved thin panels, an elastic hinge forms around the central impacted area during an early stage of deformations, and subsequent deformations occur within this region. No such hinge is observed for flat plates, negatively curved panels of all the thicknesses, and positively curved thick panels. Furthermore, the maximum effective stress induced in regions surrounding the impacted area is less for positively curved panels than that for flat panels. The dominant failure mechanism is found to be the deletion of failed elements due to the effective plastic strain in them exceeding 3.0 rather than due to plug formation. For an example problem, the dependence of the effective plastic strain rate upon the hydrostatic pressure and the consideration of the Coulomb friction at the contact surfaces exhibited minimal effects on the penetration characteristics. This information should be useful for designers of impact-resistant transparent armor, such as an airplane canopy, automobile windshield, and goggles.

Differences of the Curvature Radius and the Curvature Center between Acetabulum and Femoral Head in Dysplastic Hip Joint

Differences of the Curvature Radius and the Curvature Center between Acetabulum and Femoral Head in Dysplastic Hip Joint