Rigid Line Research Articles

SPILL PREVENTION AT INLAND MARINAS: A SHASTA LAKE, CALIFORNIA, CASE STUDY

ABSTRACT Since the enactment of the Oil Pollution Act of 1990 (OPA 90), there has been a greater focus on spill prevention and response preparedness at large marine transfer facilities. Little attention, however, has been paid to facilities that fall short of 42,000 gallons. Many of these smaller facilities, which are located on the nation's inland waterways, are marinas that fuel recreational boats. Spill prevention at facilities on inland waterways is complicated by factors such as location, hydrologic conditions, regulation under multiple jurisdictions, and lack of available technology. This paper discusses the various types of petroleum product storage, transfer, and delivery systems, as well as spill prevention measures employed by marinas on Shasta Lake, California. Shasta Lake is a mecca of recreational boating, having almost a dozen marinas along its shores. Like many inland waterways, Shasta Lake is affected by precipitation and dam control, which drastically change the surface area of the lake. To stay afloat and operational, marinas, including their fuel transfer capabilities, must be mobile. This presents complex technical and environmental issues for the marinas, which use different combinations of equipment for storing and transferring fuel. Storage systems include fixed or mobile, aboveground or underground storage tanks and floating fuel systems. The piping used to deliver fuel to dispensers located on the marina dock is usually a combination of rigid and flexible lines. Each system is subject to a variety of laws and regulations, with every facility varying in compliance levels. By evaluating the precarious situations and spill events at Shasta Lake and other marinas, we can better assist in compliance efforts and more effectively protect our nation's waterways from oil spills.

Instabilities in the flux-line lattice of anisotropic superconductors

The stability of the flux-line lattice has been investigated within anisotropic London theory. This is a full-scale investigation of instabilities in the ``chain'' state, the equilibrium lattice that is similar to the Abrikosov lattice at large fields but crosses over smoothly to a pinstripe structure at low fields. By calculating the normal modes of the elasticity matrix, it has been found the lattice is stable at large fields, but that instabilities occur as the field is reduced. The field at which these instabilities first arise, ${\mathrm{b}}^{\mathrm{*}}$(\ensuremath{\epsilon},\ensuremath{\theta}), depends on the anisotropy \ensuremath{\epsilon} and the angle \ensuremath{\theta} at which the lattice is tilted away from the c axis. These instabilities initially occur at wave vector ${\mathbf{k}}^{\mathrm{*}}$(\ensuremath{\epsilon},\ensuremath{\theta}). The dependence of ${\mathbf{k}}^{\mathrm{*}}$ on \ensuremath{\epsilon} and \ensuremath{\theta} is complicated, but the component of ${\mathbf{k}}^{\mathrm{*}}$ along the average direction of the flux lines, ${\mathrm{k}}_{\mathrm{z}}$, is always finite. For rigid straight flux lines, the cutoff necessary for London theory has been ``derived'' from Landau-Ginzburg theory, where the shape of the vortex core is known. However, for investigating instability at finite ${\mathrm{k}}_{\mathrm{z}}$ it is necessary to know the dependence of the cutoff on ${\mathrm{k}}_{\mathrm{z}}$, and we have used a cutoff suggested by Sudb\o{} and Brandt. The instabilities only occur for values of the anisotropy \ensuremath{\epsilon} appropriate to a material like BSCCO, and not for anisotropies more appropriate to YBCO. The lower critical field ${\mathrm{H}}_{\mathrm{c}1}$(\ensuremath{\varphi}) is calculated as a function of the angle \ensuremath{\varphi} at which the applied field is tilted away from the crystal axis. The presence of kinks in ${\mathrm{H}}_{\mathrm{c}1}$(\ensuremath{\varphi}) is seen to be related to instabilities in the equilibrium flux-line structure.

Rigid line inclusions under anti-plane deformation and in-plane electric field in piezoelectric materials

The problems of the rigid line inclusions under anti-plane deformation and in-plane electric field in piezoelectric materials are studied by using the complex variable method of Muskhelishvili. The rigid line inclusions are considered, respectively, as a dielectric and conductor. A square-root singularity of the field variables is identified. The singularity exists only if the shear loading is acting perpendicular to the rigid lines and the electric loading is parallel to them. For the rigid dielectric line inclusion, the singularity coefficients of both stress and electric field depend on the material properties, and the mechanical and electrical loads applied at infinity, whereas the electric displacement is a constant on the entire plane. The values of the J-integral are always negative. For the rigid conductor line inclusion, the field singularity coefficients corresponding to the field variables applied at infinity become independent of the material properties and other respective loading parameters. The values of the J-integral can be either positive or negative.

Anisotropic Elasticity: Theory and Applications

1. Matrix Algebra 2. Linear Anisotropic Elastic Materials 3. Antiplane Deformations 4. The Lekhnitskii Formalism 5. The Stroh Formalism 6. The Structures and Identities of the Elasticity Matrices 7. Transformation of the Elasticity Matrices and Dual Coordinate Systems 8. Green's Functions for Infinite Space, Half-space, and Composite Space 9. Particular Solutions, Stress Singularities, and Stress Decay 10. Anisotropic Matrials with an Elliptic Boundary 11. Anisotropic Media with a Crack or a Rigid Line Inclusion 12. Steady State Motion and Surface Waves 13. Degenerate and Near Degenerate Materials 14. Generalization of the Stroh Formulism 15. Three-Dimensionsal Deformations

Programmable dynamic line phantom control

The dynamic line phantom (DLP) produces various test patterns for the qualitative assessment of gamma camera performance, by stepper motor control of the translatory movement of a radioactive rigid line source. The addition of a V24 serial interface port has allowed external control via an RS-232 connection to a personal computer. Programmability has enabled the DLP to be used as a quantitative test tool. One such program produces a variable contrast 'hot' and 'cold' bar pattern. The addition of a Quick Basic computer program modifies the line source movement to compensate for variation in line source activity. This maintains a test pattern with fixed, absolute contrast levels, giving the potential for the measurement of variations in long-term imaging performance. A modulation transfer function (MTF) pattern has been designed which encompasses a sinusoidally varying intensifying function with a changing spatial frequency component. Repeated measurements on two gamma cameras demonstrated poor reproducibility (CV of up to 50% dependent upon spatial frequency) and significant differences between the MTF obtained from line spread function measurements (percentage deviation of up to 23%, dependent upon spatial frequency). Neither test pattern has been adopted for routine quantitative assessment of gamma camera imaging characteristics. The reproducibility of results is poor (dominated by counting statistic limitations), making the techniques insensitive to small changes in camera performance.

A general duality principle in elasticity

Abstract Anisotropic elasticity problems are considered, where the field variables depend on only two spatial coordinate variables, say, the rectangular Cartesian coordinates, x1 and x1. The equilibrium equations are then identically satisfied (no body forces), if the stress components, σij, are such that σj1 = ∂Φj/∂x2 and σj2 = −∂Φj/∂x1, j = 1, 2, 3, where Φ with the component Φj is the stress vector potential. In terms of the six-dimensional vector field η = [u, Φ], the basic elasticity equations reduce to {∂/∂x2}[u, Φ]T = N{∂/∂x1}[u, Φ]T, where u is the displacement field and N is called the fundamental elasticity matrix, given by the elastic moduli of the solid. This formulation and the corresponding duality remove the distinction between the displacement vector field u, and the stress vector-potential field Φ. Indeed, these two vector fields are, in many respects, each other's dual, in the sense that, for a given solid with given geometry and elasticity, the solution to a class of prescribed mixed displacement-traction boundary-value problems also provides the solution of the corresponding dual mixed traction-displacement boundary-value problems, without a change in geometry or elasticity of the solid. This duality principle is first proved rigorously. Then the results are applied to a general mixed boundary-value problem of a multiply connected heterogeneous finite solid with arbitrary piecewise constant anisotropic elasticity. A number of interesting illustrations involving dislocations and concentrated forces, cracks and anticracks (rigid line inclusions), interface problems, and the half-space Green functions, are also presented as special cases of the general duality principle. In addition to the general duality principle which provides a two-way relation between u and Φ, a number of other one-way relations between the displacement field u and the stress vector potential Φ of the same problem, as well as u of one problem and u of its dual, and Φ of one problem and Φ of s dual, are also presented.

Like Sustenance for the Masses: Genre Resistance, Cultural Identity, and the Achievement of Like Water for Chocolate

Laura Esquivel's 1989 Mexican novel Like Water for Chocolate, neither translated into English nor published in the United States until 1992, was both an American bestseller and the basis for an acclaimed motion picture. Interestingly, though, Esquivel's work also seems to be receiving glimmers of the type of critical attention generally reserved for less “popular” works. Two particular critical studies composed in English, one by Kathleen Glenn and the other by Cecelia Lawless, have been devoted entirely to Chocolate, and both of the scholar/authors grace the faculties of reputable American institutions of higher learning. As a student whose academic experience has been replete with elitist attitudes and expressions of disdain for anything that smacks of an appeal to the masses, I was intrigued by Chocolate for this very reason; in a world where scholarly boundaries seem unalterably fixed, a work that appears capable of crossing these rigid lines is, in my opinion, both rare and admirably refreshing. In my studies, I have often hoped for more communication between “popular” and “scholarly” literature; Esquivel's novel provides not only opportunities for this dialogue but for other cross-genre discussions as well.

Microcrack initiation at tip of a rigid line inhomogeneity

A dislocation emission mechanism for microcrack initiation at tip of a rigid line inhomogeneity is proposed in the present paper. For a rigid line inhomogeneity embedded in a ductile matrix, it has been observed that dislocations of one sign are driven away from the tip due to high stress level; while the stationary dislocations of the opposite sign are left behind near the tip of the line inhomogeneity. As the result, a Zener-Stroh crack is initiated at the tip of the inhomogeneity. A very interesting and important result that emerged from the analysis is that the critical stress intensity factor for a line inhomogeneity can be related to the fracture toughness of a crack in the same material.

Properties of eigenfunction expansion form for the rigid line problem in dissimilar media

In this paper, the eigenfunction expansion form (abbreviated as EEF) in the rigid line problem in dissimilar media is derived. The properties of the EEF are discussed in detail. After using Betti’s reciprocal theorem for a particular contour, several path independent integrals are obtained. All the coefficients in the EEF, including the K1R and K2R values can be related to the corresponding path independent integrals. It is found that the J-integral takes a definitely negative value in the present case. A possibility for formulating the weight function is also suggested. Finally, a boundary value problem for a single rigid line embedded in dissimilar media is studied and solved.

Wave Propagation Characteristics of Fluid Contained in a Finite-Length Hydraulic High-Pressure Flexible Hose. (1st Report. Mathematical Model Considering Anisotropic Viscoelasticity of Hose Wall and Boundary Conditions at Hose Fittings).

With the increasing use of high-pressure flexible hose in hydraulic equipment, the accurate knowledge of its dynamic response is required over a wide frequency range. We derive an analytical model for the wave propagation characteristics in a flexible hose with finite length by considering the coupled vibration of the hose wall and fluid in the hose, as well as the effect of the possible longitudinal resonance of the hose wall, where the hose wall is assumed to be linear, compressible and anisotropic viscoelastic with respect to the longitudinal and circumferential directions, while the fluid is assumed to be compressible and viscous and its motion to be laminar and axisymmetric. The membrane shell theory neglecting the radial inertial force is applied to the motion of the hose wall while taking into consideration the fluid pressure, and the Navier-Stokes equations and continuity equation which are simplified for an incompressible fluid are applied to the motion of the fluid after the fluid compressibility is equivalently converted into the compliance of the hose wall. A model is obtained in a transfer matrix representation which relates the pressure and flow ripples at two crosssections of a straight hose with fixed end support under constant fluid temperature and average pressure. In addition, the existing models for flexible, elastic and rigid lines may be considered as special cases of the model developed here.

Stress and Displacement Analysis of Viscoelastic Medium with Crack or Rigid Line Inclusion under In-Plane and Out-of-Plane Loadings.

Stress and Displacement Analysis of Viscoelastic Medium with Crack or Rigid Line Inclusion under In-Plane and Out-of-Plane Loadings.

Antiplane problems of collinear rigid line inclusions in dissimilar media

Antiplane problems of two dissimilar materials with rigid line inclusions along their common straight interface are dealt with. A method is proposed for solving such problems by the application of the Riemann-Schwarz symmetry principle which is integrated with the analysis of singularity of complex functions. The formulation of the general problem and the closed form solutions for some of the problems of practical importance are presented. The stress distribution in the immediate vicinity of the rigid line end is examined, and a comparison is made with that near the crack lip. The formulation and solutions for corresponding homogeneous materials are only special cases when the shear moduli of the two media are the same, and as a consequence some classical formulation and results can again be rederived.

Out-of-plane transverse resistivity in high-Tc superconductors as a signature of flow of rigid vortex lines.

Out-of-plane transverse resistivity in high-Tc superconductors as a signature of flow of rigid vortex lines.

PLAYING THE TRANSPARENCY GAME: CONSULTATION AND POLICY‐MAKING IN THE EUROPEAN COMMISSION

The recent unveiling of a package of measures designed to make the work of the European Commission more‘transparent’is part of a wider effort to make EU decision‐making more open and accessible. Yet, the Commission's transparency package was designed above all to cope with its chronic management problems. These include rigid lines of division between different spheres of the Commission, the strong loyalties of policy‐concerned Directorates‐General (dgs) to their specific‘clientele’, unclear rules governing access to information, and intense rivalries betweendgs and the private offices of individual Commissioners. This article dissects the transparency package and uses case study material to highlight ways in which the transparency initiative seeks to provide antidotes to the Commission's management problems. It offers an early assessment of the transparency package's impact and examines the prospects for reform of the Commission under Jacques Santer.

Singularities and stress intensities at the corner point of a polygonal hole and rigid polygonal inclusion under antiplane shear

A new method is developed to calculate the orders of stress singularity and the stress intensities for the corner of a polygonal hole and a rigid polygonal inclusion under antiplane shear by conformal mapping. The order of stress singularity and the stress intensities are derived explicitly for the corner of a polygonal hole and a rigid polygonal inclusion. Types of polygon used are the regular polygon, lozenge and rectangle. We confirmed that the order of stress singularity and the singular stress fields near the corner coincide with the exact solutions by the method of eigenfunction expansion. Moreover, the order of stress singularity and the stress intensities coincide with the exact solution of a crack and a rigid line inclusion problems when an interior angle of the corner of a lozenge becomes zero.

Nature of the Irreversibility Line in High-Temperature Superconductors

We have performed molecular dynamic simulations of an ensemble of rigid flux lines interacting according to the London model for different pinning strengths. We have studied the equilibrium state and calculated $E\left(J\right)$ curves over a range of temperatures and fields. Analysis of the resulting data shows that the unpinned lattice undergoes a genuine melting transition at the irreversibility line, while weak pins turn the low-temperature phase into a glass. In the case of strong pins, collective effects cease to be important and the irreversibility line simply marks the onset of observable thermally activated depinning.

Rigid inclusions on the interface between dissimilar anisotropic media

Interfacial inclusions greatly affect the load-carrying capacity of a laminated composite. In this paper, the elastic problem of a rigid line inclusion on the interface of dissimilar anisotropic media is studied. By using the analytic function approach, the field potential and the singularity coefficients for both non-oscillatory field and oscillatory field are obtained explicitly. The unknown rigid rotation vector in the field potentials is calculated by considering the equilibrium of the inclusion. The method and results developed in this paper can also be extended to study the corresponding problem of a set of collinear rigid inclusions.

Rigid and abnormal line subdistributions of 2-distributions

A line subdistributionL of the distributionE on then-manifoldM is said to be rigid (abnormal) if anyL-curve is rigid (abnormal), i.e., is an isolated (singular) point of the set of allE-curves joining two fixed points ofM. This paper contains the necessary and sufficient conditions for a line subdistribution to be rigid (abnormal), formulated in geometrical and algebraic terms, the existence theorems, and the analysis of the structure of rigid (abnormal), line subdistributions of generic 2-disrtibutions.

Circular-arc inclusion at isotropic bimaterial interface

A general solution to the circular-arc inclusion problem in bonded dissimilar media is provided. The proposed analysis is based on the use of Hilbert problem formulation, and a special technique of analytical continuation. The general expressions of the complex potentials are derived explicitly in both the circular inhomogeneity and the surrounding matrix. Several specific solutions are provided in closed form which are verified by comparison with existing ones. Numerical examples of composite materials under uniform remote load or a point force acting on the inclusion surface are examined and detailed results are presented. The oscillatory behavior in tractions along the interface is also discussed. HE characteristics of the stress field near the tip of a line inclusion have been extensively studied. A review on the related subject was given by Mura.1 Based on the equivalent inclusion approach of Eshelby 2 and the complex variable method of Muskhelishvil i,3 Wang et al. 4 have considered the problem of a rigid line inhomogeneity in an isotropic elastic body under remote loading. They found analytical expressions of the corresponding elastic field and examined the characteristics of the resulting stress singularity. The same problem has also been considered by Erdogan and Gupta,5 Atkinson,6 and Ballarini,7 among others. Based on Stroh 8 formalism for anisotropic elasticity, a line inclusion in an anisotropic elastic solid has been treated by Li and Ting.9 Wu 10 studied a line inclusion at the interface of an anisotropic bimaterial and found that the neartip stress field exhibits oscillatory singularities of the type r~2±y* with r being the distance measured from the tips of the line inclusion and y* a bimaterial constant. In Wu's paper,10 the strain intensity factors are introduced to characterize the near-tip fields instead of using the stress singularity coefficients proposed by Wang et al. 4 All of the aforementioned investigators have concentrated on the plane problem of a line inclusion in an infinite medium. The corresponding problem associated with curvilinear inclusions has been rather limited. Recently, Chao and Shen11 gave exact solutions of the elastic and thermoelastic problem with a rigid circular-arc inclusion. They showed that near-tip stress field exhibits a square-root singularity similar to the case of a traction-free crack. In this paper, a circular-arc inclusion at an isotropic bimaterial interface is investigated. The Hilbert problem formulation and a special technique of analaytic continuation are employed to derive the stress and displacement fields in an explicit form. The general solution of the present problem is provided in Sec. II. The external loads considered in this study consist of a remote uniform load and concentrated force acting on the inclusion surface which are discussed separately in Sec. Ill and Sec. IV, respectively. In Sec. V, numerical examples for commonly used fiber reinforced composite such as carbon/alumin um and tungsten/aluminum systems are given to illustrate the use of the present approach. Finally, Sec. VI concludes the article. II. Formulation and Solution of the Problem Consider two homogeneous, isotropic elastic materials. Let one occupy the region S+, interior to the unit circle, r = 1, whereas the other occupies the infinite region S~, exterior to the unit circle, Fig. 1. The elastic properties of the material in S+ can be specified by the constants IJL and K and those of the material S~ by ^ and K2 where p,j are the shear modulus, and K]-, = (3 - v/)/U + v/) for generalized plane stress and KJ = (3 - 4v;) for plane strain with

Three-dimensional analysis of stress and strain transmission through line joints of spatial linkage of plates

The examined model consists of two substructures linked by a right angle rigid line joint. One element is a wall loaded externally along its upper edge by an uneven vertical load. The other element, defined as a plate, is not loaded. Stresses and displacements in the vicinity of the joint are analysed, considering the lateral distribution which leads to three-dimensional effects. The proposed solution combines classical approach with numerical means, using appropriate stress distribution polynomial functions along the joint. Space structure constructions supply cases of interest.