Oblique Edge Research Articles

Screw dislocation near a piezoelectric oblique edge crack

The interaction between a screw dislocation and an oblique edge crack in a semi-infinite piezoelectric medium under remote anti-plane mechanical and in-plane electrical loadings is studied in this article. The screw dislocation suffers a finite discontinuity in the displacement and electric potential across the slip plane. The dislocation also has a line force and a line charge along its core. In the framework of linear piezoelectricity theory, the analytical solutions are derived from the complex variable and Schwarz–Christoffel transformation. Furthermore, the electric field, stress field, generalized stress intensity factor, image force and crack extension force are formulated exactly. Numerical calculations are then given graphically for studying the effects of crack length, crack angle and load position on these electric mechanical parameters. Besides, the dislocation solutions proposed here can be served as Green’s functions for the analyses of corresponding piezoelectric cracking or distributed loading problems.

Depth Artifacts Caused by Spatial Interlacing in Stereoscopic 3D Displays

Most spatially interlacing stereoscopic 3D displays display odd and even rows of an image to either the left or the right eye of the viewer. The visual system then fuses the interlaced image into a single percept. This row-based interlacing creates a small vertical disparity between the images; however, interlacing may also induce horizontal disparities, thus generating depth artifacts. Whether people perceive the depth artifacts and, if so, what is the magnitude of the artifacts are unknown. In this study, we hypothesized and tested if people perceive interlaced edges on different depth levels. We tested oblique edge orientations ranging from 2 degrees to 32 degrees and pixel sizes ranging from 16 to 79 arcsec of visual angle in a depth probe experiment. Five participants viewed the visual stimuli through a stereoscope under three viewing conditions: noninterlaced, interlaced, and row averaged (i.e., where even and odd rows are averaged). Our results indicated that people perceive depth artifacts when viewing interlaced stereoscopic images and that these depth artifacts increase with pixel size and decrease with edge orientation angle. A pixel size of 32 arcsec of visual angle still evoked depth percepts, whereas 16 arcsec did not. Row-averaging images effectively eliminated these depth artifacts. These findings have implications for display design, content production, image quality studies, and stereoscopic games and software.

Free vibration analysis of FGM cylindrical shell partially resting on Pasternak elastic foundation with an oblique edge

The free vibration characteristics of FGM cylindrical shells partially resting on elastic foundation with an oblique edge are investigated by an analytical method. The cylindrical shell is partially surrounded by an elastic foundation which is represented by the Pasternak model. An edge of an elastic foundation lies in a plane that is oblique at an angle with the shell axis. The motion of shell is represented based on the first order shear deformation theory (FSDT) to account for rotary inertia and transverse shear strains. The functionally graded cylindrical shell is composed of stainless steel and silicon nitride. Material properties vary continuously through the thickness according to a four-parameter power law distribution in terms of volume fraction of the constituents. The equation of motion for eigenvalue problem is obtained using Rayleigh–Ritz method and variational approach. To validate the present method, the numerical example is presented and compared with the available existing results.

Mixed boundary value problem for quasi-orthotropic elastic plane

The quasi-orthotropic elastic plane in which the characteristic roots of the fundamental differential equation for the orthotropic elastic plane are doubled is investigated for a mixed boundary value problem. One of the main purposes of the present paper is to derive a general solution of a mixed boundary value problem. For the associated stress analysis, a rational mapping function is used and a closed-form stress function is obtained. The stress analysis is hence rigorous for the rational mapping function, which gives a comparative arbitrary configuration. The quasi-orthotropic elastic plane problem includes that of an isotropic elastic plane. As a demonstration of the stress analysis, a half plane with an oblique edge rigid line inclusion in which the rim of the half plane and the principal axis for the orthotropic elasticity coincides is analyzed. A uniform tension is applied over the half plane, and the rigid line inclusion is expressed as a fixed boundary. The homogenous solution of the stress function can be obtained without any integration. Stress distributions and stress intensity factors at the tip of the rigid line inclusion are investigated for Poisson’s ratio. The relationship between the quasi-orthotropic elastic plane and the isotropic elastic plane with respect to stress intensity factors is derived. Stress functions in which the rim of the half plane and the principal axis of the orthotropic elasticity do not coincide are also described.

Oblique edge crack in an orthotropic material under thermal loading

An oblique edge crack in an orthotropic thermoelastic solid under thermal loading is analyzed, and thermally insulated and conductive cracks are considered. The thermal edge crack problem is formulated by the transformed function representation for linear thermoelasticity. The stress intensity factors and energy release rate induced by incompatible thermal strains are obtained, which are dependent on one geometric parameter and three orthotropic material parameters. The explicit dependence on one elastic orthotropic parameter is obtained by the orthotropy rescaling technique, and the influence of the other three parameters is examined numerically. The important influence of the material parameters on the stress intensity factors and energy release rate is discussed.

Una nueva especie de pez del género Hemibrycon (Characiformes: Characidae)

Hemibrycon pautensis (Characiformes, Characidae), a new fish species from Paute River, eastern Ecuador is described. Diagnostic characteristics: eight to nine branched rays in the dorsal fin (vs. six to seven), and 27 - 28 in the anal fin (vs. 16 - 26, except in H. dariensis which presents 22 - 27, in H. metae 26 - 31 and H. jabonero 23 - 28); a no occurrence of dorsal pharyngeal plate (vs. occurrence); a cartilaginous and divided-in-two basihial (vs. an osseous base and a cartilaginous upper part). Hemibrycon pautensis resembles H. metae by its oblique external edge of the pelvic fins. They can be distinguished by the position of the pectoral fins in relation to the snout (38.24-41.6% in H. pautensis vs. 21.21-25.87) and by the position of the pectoral fins in relation to the origin of the dorsal fin (20.95-24.30 in Hemibrycon pautensis vs. 35.89-42.63), and by the number of proximate radials in the pectoral girdle (five in Hemibrycon pautensis vs. three to four). In addition, the geographic distribution of H. metae is restricted to the upper part of the Meta River in Colombia and can be distinguished of H. boquiae by: the number of scales between the lateral-line and the origin of the dorsal fin (eight in H. pautensis vs. 5-7); the distance between the snout and the pelvic fins (38.00-42.90 % in H. pautensis vs. 42.9-46.19%); the pelvic fins length (13.77-17.96% in H. pautensis vs. 10.72-13.21%); and the snout length (21.34-27.88 in H. pautensis vs. 26.92-33.66%).

Quality control of oblique incidence optical coatings based on normal incidence measurement data

We demonstrate selection of reliable approaches for post-production characterization of oblique incidence multilayer optical coatings. The approaches include choice of input information, selection of adequate coating model, corresponding numerical characterization algorithm, and verification of the results. Applications of the approaches are illustrated with post-production characterization of oblique incidence edge filter, oblique incidence beam splitter and oblique incidence 43-layer quarter-wave mirror.

Numerical Evaluation of Stress Intensity Factor for Inclined-Edge Crack Geometry using Singularity Elements

Edge cracks are more dangerous than interior cracks. Free edge close to the crack influences the stress field near the crack tip (since the free edge is traction free).In case of edge crack, the free edge is not only close to the crack, but it intersects the crack. Evaluation of Stress Intensity factor for oblique edge crack geometry is done using commercial FEM software ANSYS and compared with analytical results. The conventional elements always underestimate the sharply rising stress-displacement gradients near the crack tip. Therefore, in order to produce this singularity in stresses and strains Barsoum elements were employed which involves shifting the mid-side nodes to the quarter point locations. It observed that stress intensity factor found by FEM method has good agreement with analytical results.. The singular order of stresses near the interface is a good way of understanding of failure initiation; however, in engineering applications usually the knowledge of singular orders is not enough for the prediction of failure initiation. As an example in the case of homogeneous cracks, the singular order is -1/2 which remains constant irrespective of the surrounding environment and outside loading of the crack. These influential factors are reflected through the associated stress intensity factor of the cracks. Hwu and Kuo [1] have demonstrated several different kinds of examples such as cracks in homogenous isotropic or anisotropic materials, central or edge notches in isotropic materials, interface cracks and interface corners between two dissimilar materials. It is also shown that KI Evaluation Using Displacement etrapolation technique under adaptive dense mesh with Parallel Finite Element gives fairly accurate results [2]. Based upon the analytical solutions obtained previously for the multi-bonded anisotropic wedges and the well-known path-independent H-integral, Hwo and Kuo [3] provided a unified definition and a stable computing approach for the stress intensity factors of interface corners. The stress intensity factor calculations are usually limited to Linear Elastic Fracture Mechanics (LEFM). For a linear elastic material the stress and strain fields ahead of the crack tip are expressed as [4]. The singular order of stresses near the interface is a good way of understanding of failure initiation; however, in engineering applications usually the knowledge of singular orders is not enough for the prediction of failure initiation. As an example in the case of homogeneous cracks, the singular order is -1/2 which remains constant irrespective of the surrounding environment and outside loading of the crack. These influential factors are reflected through the associated stress intensity factor of the cracks. Hwu and Kuo [1] have demonstrated several different kinds of examples such as cracks in homogenous isotropic or anisotropic materials, central or edge notches in isotropic materials, interface cracks and interface corners between two dissimilar materials. It is also shown that KI Evaluation Using Displacement etrapolation technique under adaptive dense mesh with Parallel Finite Element gives fairly accurate results [2]. Based upon the analytical solutions obtained previously for the multi-bonded anisotropic wedges and the wellknown path-independent H-integral, Hwo and Kuo [3] provided a unified definition and a stable computing approach for the stress intensity factors of interface corners. The stress intensity factor calculations are usually limited to Linear Elastic Fracture Mechanics (LEFM). For a linear elastic material the stress and strain fields ahead of the crack tip are expressed as [4].

Stress analysis of quasi-orthotropic elastic plane

The quasi-orthotropic elastic plane in which the characteristic roots of the fundamental differential equation for the orthotropic elastic plane are doubled is investigated. For the associated stress analysis, a rational mapping function is used and a closed-form solution is obtained. Therefore, the stress analysis is rigorous for the rational mapping function. The stress functions can be obtained without any integration. As a demonstration of the stress analysis, a half plane with an oblique edge crack is analyzed. Stress distributions and stress intensity factors are investigated. The relationships between the quasi-orthotropic elastic plane and isotropic plane with respect to the stress intensity factor are investigated. It is also determined that the stress intensity factors for the quasi-orthotropic elastic plane can be calculated from those of the isotropic elastic plane using a similar configuration and loading condition.

How oblique trailing edge of a hydrofoil reduces the vortex-induced vibration

The effect of hydrofoil trailing edge shape on the wake dynamic and flow induced vibration is investigated at high Reynolds number, Re=0.5 × 106–2.9 x 106. Two NACA 0009 hydrofoils with blunt and oblique trailing edges are tested. The velocity field is surveyed with the help of Laser Doppler Velocimetry (LDV), and Particle-Image-Velocimetry, (PIV). Proper-Orthogonal-Decomposition (POD) is used to extract coherent structures from PIV data. Besides, flow induced vibration measurements and high-speed visualization are also performed. A significant reduction of vortex induced vibration is obtained with the oblique trailing edge, in accordance with former reports. High speed videos clearly demonstrate that for both tested hydrofoils, the alternate vortices detach from upper and lower corners of the trailing edge. Due to the oblique truncation, the lower detachment location is shifted upstream with respect to the upper one. Therefore, as the upper vortex rolls up, it coincides with the passage of the lower vortex, leading to their collision. This strong interaction leads to a redistribution of the vorticity, which no more concentrates within the core of Karman vortices. The analysis of the phase locked average of velocity profiles reveals that the oblique truncation leads to a thickening of the core of upper and lower vortices as well as a disorganization of the alternate shedding in the near wake, recovers downstream. We strongly believe that the collision between upper and lower vortices and the resulting vorticity redistribution is the main reason of the vibration reduction obtained with oblique trailing edge. This result paves the way for further optimization of the trailing edge shape.

Application of an orthotropy rescaling method to edge cracks and kinked cracks in orthotropic two-dimensional solids

Oblique edge cracks and kinked cracks in orthotropic materials with inclined principal material directions under inplane loadings are investigated. The Stroh formalism is modified by introducing new complex functions, which recovers a classical solution for a degenerate orthotropic material with multiple characteristic roots. An orthotropy rescaling technique is presented based on the modified Stroh formalism. Stress intensity factors for edge cracks as well as kinked cracks are obtained in terms of solutions for a material with cubic symmetry by applying the orthotropy rescaling method. Explicit expressions of the stress intensity factors for a degenerate orthotropic material are obtained in terms of solutions for an isotropic material. The effects of orthotropic parameter, material orientation, and crack angle on the stress intensity factors for the degenerate orthotropic material are discussed. The stress intensity factors for cubic symmetry materials are calculated from finite element analyses, which can be used to evaluate the stress intensity factors for orthotropic materials. The energy release rate for the kinked crack in an orthotropic material is also obtained.

Oblique edge crack in an anisotropic material under antiplane shear

An oblique edge crack in an anisotropic material under antiplane shear loadings is investigated. The antiplane problems are formulated based on a linear transformation method. An anisotropic solid containing an edge crack subjected to concentrated forces is first considered. The stress intensity factor for the edge crack with concentrated forces is obtained from the solution of the transformed edge crack in an isotropic material which is solved by using conformal mapping technique and complex function theory. The solution of the edge crack under concentrated loads is used to construct the stress intensity factor for the oblique edge crack in the anisotropic material subjected to antiplane distributed loads. Some numerical computations are carried out to calculate the stress intensity factors for the edge crack in inclined orthotropic materials subjected to point forces as well as distributed tractions.

The Analysis and Study of Methods of Calculating Oblique Edge Shear Force

In existent reference material on stamping, a range of application of the calculating formula of shearing force of die of inclined edge is not limited. This gives rise to misunderstanding very easily. Now this paper from different points of view just analyses and discusses the Calculation method for shearing force with different rake angle of inclined edge, so it is very practical and significant.

Error analysis and regression mode of the V‐grooved sample in the atomic force microscope simulation measurement mode by the molecular mechanics

Based on the molecular mechanics, this study uses the two-body potential energy function to construct a trapezoidal cantilever nano-scale simulation measurement model of contact mode atomic force microscopy (AFM) under the constant force mode to simulate the measurement the nano-scale V-grooved standard sample. We investigate the error of offset distance of the cross-section profile when using the probes with different trapezoidal cantilever probe tip radii (9.5, 8.5, and 7.5 A) to scan the peak of the V-grooved standard sample being reduced to one-tenth (1/10) of its size, and use the offset error to inversely find out the regression equation. We analyze how the tip apex as well as the profile of the tip edge oblique angle and the oblique edge angle affects the offset distance. Furthermore, a probe with a larger radius of 9.5 nm is used to simulate and measure the offset error of scan curve, and acquire the regression equation. By the conversion proportion coefficient of size (omega), and revising the size-reduced regression equation during the small size scale, a revised regression equation of a larger size scale can be acquired. The error is then reduced, further enhancing the accuracy of the AFM scanning and measurement.

경계요소법에 의한 방음벽의 성능 평가

Noise barriers are being used more often to solve problems of noise pollution from traffic noise. Several types of noise barriers are being installed to increase the cost-effectiveness of noise barrier installation. In this study, the insertion loss is analyzed to evaluate the effectiveness of the noise barrier by using the BEM. In order to check the validity of the BEM, the BEM and Lam's theoretical analysis are compared with measurement, which is performed in the anechoic chamber for the 1/10 scale-down model, and good agreements are obtained. By using the two dimensional boundary element method, the insertion loss is calculated and analyzed for several typical noise barriers such as the vertical barrier, the barrier with an oblique edge on top, the T-shaped barrier and the barrier with interference device on top. With these analyses, it is possible to design more cost-effective noise barriers appropriate for a particular area.

Una gemma magica con “cavalieri Danubiani”

In this article a magical gem in lapis lazuli is analyzed. It is engraved on both sides and bears an inscription running along the oblique edge. The main side of the gem is divided in 3 sectors where the engraved symbols recall the iconographies well known through the corpus of the Danubian stele: a goddess between two riders; a ritual banquet; a bipodia flanked by two worshipping female figures. Gems with these particular iconographies are very rare and this lapis lazuli can be compared for the complexity of the scenes only with a cornelian gem preserved in the Kunsthistorisches Museum in Wien. The symbols on the other side of the gem are connected to the magical and Gnostic pseudo-Egyptian cultural panorama, as confirmed by the snake Chnoubis around the neck of the bird (Ibis?) depicted standing on a crocodile. It is not difficult to find comparisons among the magical gems for the single elements engraved on the lapis lazuli. Finally, Greek letters are engraved on the large edge of the gem: * CWBAPP — IKVPBH; they are divided by a star realized in a fracture suffered by the stone; in exergue there are the letters IAW in engraved double cartouche. The fact that the solar symbol which divides the Gnostic legend was engraved in the breakage could confirm that the side with the scene of Danubian riders was carved before the other one with magical-Gnostic symbols. Probably the gem was reused with magical purpose between the 2nd and the 3rd century AD.

Stress intensity factors for an oblique edge crack in a coating/substrate system with a graded interfacial zone under antiplane shear

This paper investigates the edge crack problem for a coating/substrate system with a functionally graded interfacial zone under the condition of antiplane deformation. With the interfacial zone being modeled by a nonhomogeneous interlayer having the continuously varying shear modulus between the dissimilar, homogeneous phases of the coated medium, the coating is assumed to contain an edge crack at an arbitrary angle to the interfacial zone. The Fourier integral transform method is used in conjunction with the coordinate transformations of basic field variables. Formulation of the proposed crack problem is then reduced to solving a singular integral equation with a generalized Cauchy kernel. The mode III stress intensity factors are defined and evaluated in terms of the solution to the integral equation. In the numerical results, the values of the stress intensity factors are plotted, illustrating the effects of the crack orientation angle for various material and geometric combinations of the coating/substrate system with the graded interfacial zone.

Stability of Plates with an Oblique Edge Crack under Tension

The stress–strain state and local buckling of thin plates with an oblique edge crack are studied. An expression for critical stresses is derived

T-junction waveguide experiment to characterize left-handed properties of metamaterials

The left-handed property of a metamaterial is demonstrated by measuring the power at the output of a T-junction waveguide loaded with a metamaterial having one edge cut at 45° with respect to the waveguide axis. Both experimental scattering data and numerical results are presented. The metamaterial sample is realized by using a periodic arrangement of wires and split-ring resonators, and the operating frequency is chosen to correspond to a refraction index of about −1. The results show that when the T junction is empty, most of the power is received at the output port directly facing the input port, whereas when it is loaded with the sample of metamaterial, most of the power is received at the output port perpendicular to the input axis. This indicates that the energy is bent by the oblique edge of the sample by an angle of −45° with respect to the normal, which suggests a negative index of refraction.

Lawrence Alma-Tadema and the Modern City of Ancient Rome

This paper argues that Alma-Tadema's representations of the ancient city of Rome can be seen as significant explorations of urban experience, parallel to the more familiar nineteenth-century representations of modern Paris. Alma-Tadema distinguishes clearly between the small-town environment of Pompeian subjects and the metropolitan environment of pictures set in the capital. Using techniques such as oblique viewpoints and edge cropping, Alma-Tadema presents the “shock” experience characteristic of the modern city in urban theory. The late nineteenth-century notion of the city's modernity thus provides a novel perspective on traditional fascination with Rome as the ultimate paradigm for the urban.