Arbitrary Opening Research Articles

Assessment of tensile fatigue limit of notches using sharp and coarse linear elastic finite element models

The aim of the present paper is to provide an efficient numerical technique to evaluate the linear elastic stress parameters to use in an existing fatigue model. The model allows to assess the tensile fatigue limit of components weakened by defects, cracks, sharp as well as blunt notches with an arbitrary notch opening angle. To apply the fatigue model, both the elastic stress concentration factor of the notch and the notch stress intensity factor of the corresponding sharp notch must be evaluated. Therefore, in principle two different linear elastic stress analyses should be performed. The novel technique proposed in the present paper involves only a single linear elastic stress analysis, consisting of a sharp and coarse finite element model: sharp because the notch tip radius is set to zero, and therefore a sharp V-shaped notch is modelled; coarse because coarse patterns of finite elements can be employed. Approximate values of the elastic stress concentration factor and of the notch stress intensity factor calculated from the sharp and coarse finite element model are compared with very accurate estimations obtained from dedicated analyses. To illustrate the fatigue assessment procedure, experimental notch fatigue limits taken from the literature and characterised by a variety of geometrical configurations are compared with theoretical estimations.

Filling transitions in acute and open wedges.

We present numerical studies of first-order and continuous filling transitions in wedges of arbitrary opening angle ψ, using a microscopic fundamental measure density functional model with short-ranged fluid-fluid forces and long-ranged wall-fluid forces. In this system the wetting transition characteristic of the planar wall-fluid interface is always first order regardless of the strength of the wall-fluid potential ɛ(w). In the wedge geometry, however, the order of the filling transition depends not only on ɛ(w) but also on the opening angle ψ. In particular we show that even if the wetting transition is strongly first order the filling transition is continuous for sufficient acute wedges. We show further that the change in the order of the transition occurs via a tricritical point as opposed to a critical end point. These results extend previous effective Hamiltonian predictions which were limited only to shallow wedges.

A quasi-rigorous solution for focusing radially polarized vector beams by an arbitrary opening paraboloid mirror

For focusing of radially polarized vector beams using an arbitrary opening paraboloid mirror, a quasi-rigorous integral representation of light field is derived based on a rigorous vectorial diffraction theory of electromagnetic waves. Under far-field approximation conditions, the derived integrals reduce to the results from vectorial Debye-Wolf diffraction integral. Numerical calculations show that a marked deviation, as represented by evident focal shift, appears for low-aperture paraboloid mirrors, e.g. the maximum focusing semi-angle α below π/9 with the focal length f being 103λ, or below π/6 when f reduces to 102λ. The radial light spot sharpens to be 0.39λ (FWHM) and purely longitudinally polarized when α is close to 115°, while the axial light spot continuously sharpens to be about half wavelength with α approaching π. For an annular paraboloid mirror, it is possible to further compress the radial light spot down to 0.36λ (FWHM).

A singular element for reissner plate bending problem with V-shaped notches

A novel singular finite element is presented to study Reissner plate bending problem with V-shaped notches. Firstly, the expressions of the first four order asymptotic displacement field around the tip of V-shaped notch are derived systematically using William’s eigenfunction series expansion method. Subsequently, the expressions are used to construct a novel displacement mode singular finite element, which can well depict the characteristic of singular stress field around the tip of V-shaped notch having arbitrary opening angle. Combining with conventional finite elements, the novel element can be applied to solve Reissner plate bending problem with V-shaped notches, and mode I, mode II and mode III stress intensity factors can all be determined directly by the coefficients of the asymptotic expansion terms. Finally, four numerical examples are performed to demonstrate the performance of the present method, and the influences of the size and number of export nodes of the singular element on the calculation of bending stress intensity factors are also discussed. Numerical results show that the singular element method is a practical and effective numerical technique for obtaining directly and synchronously mode I, mode II and mode III stress intensity factors without other numerical techniques, such as extrapolation.

Inverse modeling for estimating fluid-overpressure distributions and stress intensity factors from an arbitrary open-fracture geometry

We present a new solution for estimating the fluid overpressure (driving-pressure or net-pressure) acting on the walls of a fracture with an arbitrary opening displacement. In the paper, we first present a forward modeling solution, using Fourier cosine series, for the opening displacement of a fracture subject to an overpressure that varies irregularly along the length of a fracture. By changing the form of the solution, we provide a matrix equation for estimating the Fourier coefficients and thereby obtain the overpressure variation from the fracture geometry. As numerical tests of this inverse analysis, we estimated the overpressure variation from fracture-opening displacements given by well known analytical solutions, and found that this method can be used for overpressure estimates for a variety of fluid-driven fractures. We apply our solutions to a mineral vein hosted by gneiss (West Norway) and conclude from the aperture variation that, at the time of vein formation, the overpressure increased toward the vein tip. We also discuss the physical meaning of the Fourier coefficients by applying our results to man-made hydraulic wing fractures. The results indicate that the coefficients of n = 0 and n = 1 relate to the fluid overpressure and the critical stress intensity factor.

Wicking of a liquid bridge connected to a moving porous surface

AbstractWe study the coupled problem of a liquid bridge connected to a porous surface and an impermeable surface, where the gap between the surfaces is an externally controlled function of time. The relative motion between the surfaces influences the pressure distribution and geometry of the liquid bridge, thus affecting the shape of liquid penetration into the porous material. Utilizing the lubrication approximation and Darcy’s phenomenological law, we obtain an implicit integral relation between the relative motion between the surfaces and the shape of liquid penetration. A method to control the shape of liquid penetration is suggested and illustrated for the case of conical penetration shapes with an arbitrary cone opening angle. We obtain explicit analytic expressions for the case of constant relative speed of the surfaces as well as for the relative motion between the surfaces required to create conical penetration shapes. Our theoretical results are compared with experiments and reasonable agreement between the analytical and experimental data is observed.

The minimum identifying code graphs

Let G be a graph and B(u) be the set of u with all of its neighbors in G. A set S of vertices is called an identifying code of G if, for every pair of distinct vertices u and v, both B(u)∩S and B(v)∩S are nonempty and distinct. A minimum identifying code of a graph G is an identifying code of G with minimum cardinality and M(G) is the cardinality of a minimum identifying code for G. A minimum identifying code graph G of order n is a graph with M(G)=⌈log2(n+1)⌉ having the minimum number of edges. Moncel (2006) [5] constructed minimum identifying code graphs of order 2m−1 for m≥2 and left the same problem but for arbitrary order open. In this paper, we aimed at the construction of connected minimum identifying code graphs in order to solve this problem for integer order greater than or equal to 4. Furthermore, we discussed some related properties.

Endothelial–cardiomyocyte crosstalk enhances pharmacological cardioprotection

Endothelial cells (EC) serve a paracrine function to enhance signaling in cardiomyocytes (CM), and conversely, CM secrete factors that impact EC function. Understanding how EC interact with CM may be critically important in the context of ischemia–reperfusion injury, where EC might promote CM survival. We used isoflurane as a pharmacological stimulus to enhance EC protection of CM against hypoxia and reoxygenation injury. Triggering of intracellular signal transduction pathways culminating in the enhanced production of nitric oxide (NO) appears to be a central component of pharmacologically induced cardioprotection. Although the endothelium is well recognized as a regulator for vascular tone, little attention has been given to its potential importance in mediating cardioprotection. In the current investigation, EC–CM in co-culture were used to test the hypothesis that EC contribute to isoflurane-enhanced protection of CM against hypoxia and reoxygenation injury and that this protection depends on hypoxia-inducible factor (HIF1α) and NO. CM were protected against cell injury [lactate dehydrogenase (LDH) release] to a greater extent in the presence vs. absence of isoflurane-stimulated EC (1.7 ± 0.2 vs. 4.58 ± 0.8 fold change LDH release), and this protection was NO-dependent. Isoflurane enhanced release of NO in EC (1103 ± 58 vs. 702 ± 92 pmol/mg protein) and EC–CM in co-culture sustained NO release during reoxygenation. In contrast, lentiviral mediated HIF1α knockdown in EC decreased basal and isoflurane stimulated NO release in an eNOS dependent manner (517 ± 32 vs. 493 ± 38 pmol/mg protein) and prevented the sustained increase in NO during reoxygenation when co-cultured. Opening of mitochondrial permeability transition pore (mPTP), an index of mitochondrial integrity, was delayed in the presence vs. absence of EC (141 ± 2 vs. 128 ± 2.5 arbitrary mPTP opening time). Isoflurane stimulated an increase in HIF1α in EC but not in CM under normal oxygen tension (3.5 ± 0.1 vs. 0.79 ± 0.15 fold change density) and this action was blocked by pretreatment with the Mitogen-activated Protein/Extracellular Signal-regulated Kinase inhibitor U0126. Expression and nuclear translocation of HIF1α were confirmed by Western blot and immunofluorescence. Taken together, these data support the concept that EC are stimulated by isoflurane to produce important cardioprotective factors that may contribute to protection of myocardium during ischemia and reperfusion injury.

Elastic-Plastic Stress Singularities of Plane V-Notches in Power-Hardening Materials

Extensive studies have been carried out to deal with the stress singularity of V-notch problems in linear elasticity theory. In fact, the plastic deformation consequentially arises in the notch tip region because of the high stress concentration. The solution of linear elasticity is not adequate to explain the fracture failure of V-notch structures. Because of the difficulties of the nonlinear analysis and the singularity behavior, few results are given for the plastic stress singularities of general V-notch structures. In this paper, the plane V-notch structures in a power law hardening materials are considered. The Von Mises yield criterion and the plasticity total theory are adopted when the materials arise in plastic status. Similar to methods used in the elastic analysis, the plastic stress field near V-notch tips is assumed as an asymptotic expansion with respect to the radial coordinate originating from the notch tip. The governing equations of plastic behavior of plane V-notch are transformed to eigenvalue problems of nonlinear ordinary differential equations (ODEs) contained by the stress singularity order and the associated eigenfunctions. Consequently all of the stress singularities who are less than zero and the associated eigenvectors are accurately determined for the plane V-notches with arbitrary opening angle.

Radiations from an Eccentric Coated Cylinder with N Slots

The transverse magnetic (TM) radiation characteristics are investigated for a cylinder with N infinite axial slots of arbitrary opening size and location. The cylinder is a thin circular conductor and coated by an eccentric material. Fields are found by applying the boundary conditions to the cylindrical wave functions. The addition theorem of Bessel functions is used to obtain an infinite series solution in Fourier–Bessel series form. Results are computed by shrinking the generated infinite series to a finite number of terms and compared to other available data. Numerical results in graphical forms for different values are also developed and discussed for small eccentricities.

Spin filtering due to quantum interference in periodic mesoscopic networks

We present several new results, extending our recent proposal of a spin filter based on a tight-binding model for a periodic chain of diamond-like loops [A. Aharony, O. Entin-Wohlman, Y. Tokura, S. Katsumoto, Phys. Rev. B 78 (2008) 125328]. In this filter, the Rashba spin–orbit interaction (which can be tuned by a perpendicular gate voltage) and the Aharonov–Bohm flux (due to a perpendicular magnetic field) combine to select only one propagating ballistic mode. For this mode, the electronic spins are fully polarized along a direction that can be controlled by the electric and magnetic fields and by the electron energy. All the other modes are evanescent. Generalizing the square diamonds into rhombi with arbitrary opening angles, we find that increasing these angles widens the parameter range for efficient filtering. A different gate voltage on the two sides of each rhombus is found to delocalize the electrons for energies on one side of the band center. We also compare our tight-binding model with models which use continuous quantum networks of one-dimensional wires, and find coincidence only when one chooses particular site energies at the nodes of the network.

Fluctuation Theorem for Arbitrary Open Quantum Systems

Based on the observation that the thermodynamic equilibrium free energy of an open quantum system in contact with a thermal environment is the difference between the free energy of the total system and that of the bare environment, the validity of the Crooks theorem and of the Jarzynski equality is extended to open quantum systems. No restrictions on the nature of the environment or on the strength of the coupling between system and environment need to be imposed. This free energy entering the Crooks theorem and the Jarzynski equality is closely related to the Hamiltonian of mean force that generalizes the classical statistical mechanical concept of the potential of mean force.

Comments on the evaluation of the stress intensity factor for a general re-entrant corner in anisotropic bi-materials

This paper illustrates an efficient contour integral procedure to obtain stress intensity factors in combination of the asymptotic analysis with finite element analysis. Note that this set-up is very general: the material can be anisotropic elastic, and the specimen can be built as a bi-material system, notches of arbitrary opening angle can be analyzed ( γ = 0 → crack, γ = 180° → free edge). The purpose of this technical note is to comment on three issues in the notch mechanics: the interpretation of the eigenvalue equation, the definition of stress intensity factors, and the effect of the outer contour location on H-integral evaluations.

RADIATION FROM AN ECCENTRIC COATED CYLINDER WITH SLOTS OF ARBITRARY SIZES AND POSITIONS

The transverse electric (TE) field patterns and characteris- tics are considered for a cylinder with N infinite axialslots of arbitrary opening size and position. The cylinder is a thin circular conductor and covered by an eccentric material. Radiations are determined by applying the boundary conditions to the cylindrical wave functions of the fields. The addition theorem of Bessel functions is employed to find an infinite-series solution in Fourier-Bessel series form. Results are achieved by reducing the produced infinite series to a finite num- ber of terms and judged against other published data. Numerical and graphical results for different values are also presented and discussed for small eccentricities.

Diffraction of the plane wave by a transparent wedge: The Sommerfeld-Malyuzhinets approach

The time-harmonic diffraction of the plane wave by a transparent wedge of an arbitrary opening is examined by the Sommerfeld-Malyuzhinets approach. The velocities of wave propagation inside and outside the wedge are equal. An explicit solution is presented, which is studied asymptotically as kr → ∞ and kr → 0. Bibliography: 2 titles.

Wave losses in the metal-dielectric transmission line with wedge-shaped conductor

We study wave losses in a metal-dielectric wedge-shaped transmission line in the form of a wedge-shaped metal conductor with circular dielectric cap. A distinctive feature of such a line is that it supports one fundamental mode not having the frequency cutoff. It is shown that the longitudinal current of the fundamental mode has a singularity at the rib of a wedge-shaped conductor. This singularity is described analytically. An efficient way for calculating the integrals arising during the losses calculation is proposed. It is pointed out that the mentioned singularity is non-integrable during the losses calculation in the case where the wedge degenerates into an infinitely thin half-plane. Expressions for the wave decay coefficients in a wedge-shaped transmission line in the metal and the dielectric for an arbitrary opening angle of the wedge are found. Structural decay coefficients of the fundamental mode for different dielectric permittivities of the cap and wedge angles are calculated. The results of calculation of losses in the metal and the dielectric in nine of the lower-order modes in a rectangular-wedge line are presented.

Physical Optics Curved-Boundary Dielectric Plate Scattering Formulas for an Accurate and Efficient Electromagnetic Characterization of a Class of Natural Targets

Closed-form representations of the physical optics (PO) field scattered in the far zone by plane penetrable dielectric angular sectors of arbitrary opening angle featuring a conical-section boundary are derived in terms of incomplete cylindrical functions (ICFs). The proposed expressions, possibly in combination with PO formulas for the scattering from polygonal plates, allow one to evaluate the scattering from flat dielectric plates with both convex and concave curved edges in a very efficient manner and constitute a useful tool to improve the accuracy of the geometrical characterization of a class of natural scatterers. In order to check the correctness and computational effectiveness of the proposed scattered-field solutions, comparisons with results obtained by accurate completely numerical PO calculations are provided. Simulation data by the method of moments are also presented to assess the applicability of the PO approximation to the considered sample scattering geometries.

Efficient computation of order and mode of three-dimensional stress singularities in linear elasticity by the boundary finite element method

The Boundary Finite Element Method (BFEM), a novel semi-analytical boundary element procedure solely relying on standard finite element formulations, is employed for the investigation of the orders and modes of three-dimensional stress singularities which occur at notches and cracks in isotropic halfspaces as well as at free edges and free corners of layered plates. After a comprehensive literature review and a concise introduction to the standard three-dimensional BFEM formulation for the static analysis of general unbounded structures, we demonstrate the application of the BFEM for the computation of the orders and modes of two-dimensional and three-dimensional stress singularities for several classes of problems within the framework of linear elasticity. Special emphasis is placed upon the investigation of stress concentration phenomena as they occur at straight free edges and at free corners of arbitrary opening angles in composite laminates. In all cases, the BFEM computations agree excellently with available reference results. The required computational effort is found to be considerably lower compared to e.g. standard Finite Element Method (FEM) computations. In the case of free laminate corners, numerous new results on the occurring stress singularities are presented. It is found that free-corner problems generally seem to involve a more pronounced criticality than the corresponding free-edge situations.

A closed‐form analysis of material and geometry effects on stress singularities at unsymmetric bimaterial notches

AbstractAn important issue in the mechanics of adhesive bonds is the knowledge of local mechanical fields. In the present study, an asymptotic analysis of the stress fields near an unsymmetric bimaterial notch with arbitrary opening angle is performed. Using the complex potential method, the order of the singularity of the stress fields at a notch tip can be determined in closed‐form analytical manner, so that the dependency of the occurring singularity exponents on geometry and material properties can be studied systematically.

Problems of heat conduction for an angular region with an internal source

Exact solutions of nonstationary problems of heat conduction have been obtained for an unbounded rectangular region when the opening angle is equal to π/(2n + 1), where n is any natural number. By passage to the limit it has been shown that no stationary regime is possible for the rectangular region in the case of action of a constant internal source. The exact solution of the stationary problem for an angular region with an arbitrary opening angle κ0 has been given. It has been proved that in the presence of a constant heat source the stationary regime is possible just for the acute angle κ0 ≤ π/2, while for the right or obtuse angles κ0 ≥ π/2 the stationary regime is impossible, since the temperature increases without bound at internal points.