Radial Tension Research Articles

Design of radial reinforcement for prestressed concrete containments

Nuclear containments are critical components for safety of nuclear power plants. Failure can result in catastrophic safety consequences as a result of leakage of radiation. Prestressed concrete containments have been used in large nuclear power plants with significant design internal pressure. These containments are generally reinforced with prestressing tendons in the circumferential (hoop) and meridional (vertical) directions. The curvature effect of the tendons introduces radial tensile stresses in the concrete shell which are generally neglected in the design of such structures. It is assumed that such tensile radial stresses are small as such no radial reinforcement is provided for this purpose. But recent instances of significant delaminations in Crystal River Unit 3 in Florida have elevated the need for reevaluation of the radial tension issue in prestressed containment. Note that currently there are no well accepted industry standards for design and detailing of radial reinforcement. This paper discusses the issue of radial tension in prestressed cylindrical and dome shaped structures and proposes formulae to calculate radial stresses. A practical example is presented to illustrate the use of the proposed method which is then verified by using state of art finite element analysis. This paper also provides some practical design consideration for detailing of radial reinforcement in prestressed containments.

Laser-Induced Plasma Exposure on Extreme Ultraviolet Lithography Masks: Damage Analysis

Extreme ultraviolet lithography (EUVL) is considered as a possible next-generation lithography technology for sub-22-nm feature fabrication. Fabrication of zero printing defect mask blanks is one of the key challenges identified for EUVL under 16 nm. One proposed cleaning mechanism is based on laser-induced plasma (LIP) shock waves in which selective nanoparticle removal is possible. However, due to both shockwave thermomechanical loading and radiation intensity heating from the LIP core during cleaning, there have been concerns over substrate damage. In this paper, computational and experimental damage studies are conducted for assessing damage risk of LIP exposure to EUVL blank samples. Based on a finite element analysis, it is found that the level of radial stress on the surface of nanofilm and nanofilm layers is the critical parameter identified in both excitation mechanisms leading to mechanical material failure. Experimentally, it is determined that above a critical LIP clearance distance, no substrate damage is observed for the EUVL blank during cleaning regardless of the number of laser shots. It is concluded that pressure amplification methods and creation of residual radial tension in nanofilms could be employed to extend EUVL mask damage threshold for LIP exposure during cleaning.

A general method for constructing curved traversable wormholes in (2+1)-dimensional spacetime

We develop a general method for constructing curved traversable wormholes in (2+1)-dimensional spacetime, by generating surfaces of revolution around smooth curves. Application of this method to a straight line gives the usual spherically symmetric wormholes. The physics behind (2+1)-d curved traversable wormholes is discussed based on solutions to the Einstein field equations when the tidal force is zero. The Einstein field equations are found to reduce to one equation whereby the mass-energy density varies linearly with the Ricci scalar, which signifies that our (2+1)-d curved traversable wormholes are supported by dust of ordinary and exotic matter without radial tension nor lateral pressure. With this, two examples of (2+1)-d curved traversable wormholes: the helical wormhole and the catenary wormhole, are constructed and we show that there exist geodesics through them supported by non-exotic matter. This general method is applicable to our (3+1)-d spacetime.

Free vibration of membrane/bounded incompressible fluid

Vibration of a circular membrane in contact with a fluid has extensive applications in industry. The natural vibration frequencies for the asymmetric free vibration of a circular membrane in contact with a bounded incompressible fluid are derived in this paper. Considering small oscillations induced by the membrane vibration in an incompressible and inviscid fluid, the velocity potential function is used to describe the fluid field. Two approaches are used to derive the free vibration frequencies of the system, which include a variational formulation and an approximate solution employing the Rayleigh quotient method. A good correlation is found between free vibration frequencies evaluated by these methods. Finally, the effects of the fluid depth, the mass density, and the radial tension on the free vibration frequencies of the coupled system are investigated.

Plastic instabilities in porous cylinders under remote triaxial loading

Abstract Plastic instabilities under remote triaxial loading, including cylindrical cavity expansion, are studied in context of large strain plasticity and constrained plane-strain. Material hardening is taken into consideration and porosity is incorporated using the Gurson (1977) plasticity model. Spontaneous growth of central cavity due to constant applied triaxial remote load (cavitation instability) is examined in an infinite cylindrical medium. It is found that the remote field exhibits instability at a definite value of applied radial tension which may occur before onset of cavitation. That maximum is proposed as an approximation for field stability limit while, as shown, cavitation in the porous solid can occur only for relatively low values of initial porosity and within a limited range of remote loading triaxiality. Analysis is facilitated upon choice of effective stress as independent time-like parameter.

Fatigue analysis of liquid-storage tank shell-to-base connections under multi-axial loading

During severe seismic events the base of unanchored steel liquid-storage tanks can uplift, causing large inelastic rotation demands at the shell-to-base connections and large multi-axial stresses (radial tension and circumferential compression) in the tank base-plate. With repeated cycles of uplift, these shell-to-base connections are susceptible to low-cycle fatigue failure. Limited research exists on the rotation capacity of shell-to-base connections, and the studies that have been conducted have neglected the multi-axial stress states in the tank base-plate. In this paper, an analytical study is conducted to determine the effects of these multi-axial base-plate stresses on the rotation capacity of tank shell-to-base connections. Modeling methods and a low-cycle fatigue failure criterion are validated using experimental results, and then 23 models with varying multi-axial stress states are analyzed under various ranges of cyclic rotation. Results indicate that moderate levels of base-plate radial tension and circumferential compression (between 10 and 20%σy) can significantly reduce connection rotation capacity (between 28% and 48%). Additionally, due to increased yielding from circumferential stresses at low rotations, smaller uplift cycles may contribute more to failure than previously reported in studies neglecting base-plate multi-axial stress-states. Indicated rotation capacities are larger than current code limits.

A new acoustic transducer with a pressure-deformed piezoelectric diaphragm

A new design for wide-band acoustic transducers is described. Radial tension is applied to a thin piezoelectric diaphragm with conductive electrodes on the upper and lower surface. One side of the diaphragm is pressurized, elastically deforming the diaphragm into a slightly curved shape. The in-plane static tension is modulated by applying a time-dependent voltage across the electrodes of the piezoelectric diaphragm. The tension modulation causes transverse displacement oscillations of the diaphragm. This actuation takes place in spite of the fact that the piezoelectric diaphragm does not contain a passive elastic layer, which is necessary for actuation by flexure in planar diaphragms. A theoretical quasi-static model using hexagonal symmetry for the piezoelectric material was developed to predict the electromechanical actuation mechanism, and the mode for optimal operation in non-resonant conditions. Piezoelectric diaphragms were fabricated from PVDF film of nominal thickness 40μm into circular diaphragms 1cm in diameter. For the pressure-deformed transducers fabricated from PVDF film, displacement amplitudes of 9–14.5nm/V were observed, and the maximum displacement amplitude took place at the applied tension and static pressure predicted by the model. Additional measurements with conventional flexure-type transducers containing a diaphragm consisting of a layer of PZT and a passive elastic material fabricated using MEMS processes were performed to compare with the transducers fabricated from PVDF film. The displacement amplitude per unit electric field measured for the transducers fabricated from PVDF film was comparable to those measured from conventional PZT flexure-type transducers, despite the fact that the piezoelectric coupling coefficient for PVDF was approximately 100 times smaller than that for PZT.

Linear Elastic Solutions for Slotted Plates

Two-dimensional problems of finite-length blunted cracks cut into infinite plates subject to remote tractions are solved using complex variable theory. The slot geometry is composed of two flat surfaces connected by rounded ends. This special geometrical shape was derived by Riabouchinsky in the study of two-dimensional ideal fluid flow around parallel plates. The simpler antiplane slotted plate problem is addressed initially for this geometry. From this exact solution, the equivalent of a Westergaard stress potential is found and applied to the two other principal modes of fracture, which are plane elasticity problems. For a plate subject to uniform radial tension at infinity, an analytical solution is obtained that will reduce to the familiar mode I singular crack solution as the separation between the parallel faces of the slot becomes zero. For finite-width mode I slots, the rounded ends have tensile tractions which terminate at the adjoining flat surfaces of the slot, which remain traction-free. In this respect, the finite-width mode I slot problem resembles a Barenblatt cohesive zone model of a plane crack or a Dugdale plastic strip model of a plane crack, although the tractions will vary in magnitude along the slot ends rather than remaining uniform as in the former type of crack problems. Similarly, in the case of the finite-width mode II slot problem, the rounded ends of the slot have shear tractions, while the flat surfaces remain load-free. A distinguishing feature of the mode II slot solution over the mode I slot problem is that the maximum in-plane shear stress is constant along the rounded ends of the slot. Because of this, those particular regions of the boundary can represent incipient plastic yield based on either the Mises or Tresca yield condition under plane strain loading conditions. In this way, the problem resembles the plastic strip models of Dugdale, Cherepanov, Bilby-Cottrell-Swinden, and others. Notably, the mode III slot problem also has a constant maximum shear stress along the curved portions of the slot, while the entire slot boundary remains traction-free, unlike the mode II slot problem. Consequently, the mode III slot problem represents both a generalization of the standard mode III crack problem geometry, while simultaneously satisfying the boundary conditions of a plastic strip model.

Longevity enhancement of bolted joints for aircrafts

New designs of bolted joints with bolt countersunk heads having high longevity in comparison with the used ones were proposed. One type of joint has the bolt heads with the reduced surface taper of the bolt head and in a joined part. Two other types have a spherical head surface, which is in contact with a tapered countersink surface. The rise in the fatigue life is achieved owing to the balance of the radial tension along the contact surfaces of the head and the countersink. Designs of a washer from the direction of a nut are proposed. These washers have ring bulges of wedge-shaped cross section that form areas of plastic deformations around a bolt body during the bolt tightening and reduce the concentration of contact stresses close to an edge of the contact surfaces of the bolt and joined parts. Procedures of fatigue tests were developed. Results of tests of the proposed bolted joints supporting their high longevity are presented. Findings of experimental investigations verify the efficiency of the application of proposed types of bolted joints in the designs of aircrafts.

Estimation of width of fracture process zone in spruce wood by radial tensile test

Fracture behavior of spruce wood under radial tension was analyzed using nonlinear fracture mechanics as wood is classified as a quasi-brittle material. Stress–strain relationship with a strain-softening branch was obtained by digital image analysis and stress redistribution process, and the energy release rate of serial end-matched specimens was measured by performing a single-edge-notched tension test. The width of the fracture process zone (FPZ) was estimated by comparing two kinds of fracture energies. One was the dispersion energy per unit area to model strain localizations using a discontinuum model of damage theory, by integrating the stress–strain function with the strain-softening branch. The other was the energy release rate to determine crack growth. From this analysis, we determined that the width of the FPZ ranged from 0.3 mm to 0.5 mm in the radial direction. However, for a few specimens, the approximate stress–strain function could not be fitted into the stress–strain relationship obtained by the image analysis; it was observed that the fracture planes of these specimens tended to be more or less inclined.

On the bifurcations of the Lamé solutions in plane-strain elasticity

We consider the in-plane bifurcations experienced by the Lamé solutions corresponding to an elastic annulus subjected to radial tension on the curved boundaries. Numerical investigations of the relevant incremental problem reveal two main bifurcation modes: a long-wave local deformation around the central hole of the domain, or a material wrinkling-type instability along the same boundary. Strictly speaking, the latter scenario is related to the violation of the Shapiro–Lopatinskij condition in an appropriate traction boundary-value problem. It is further shown that the main features of this material instability mode can be found by using a singular-perturbation strategy.

Dynamic cavitations in incompressible hyperelastic pre-strained circular sheets

A class of dynamic cavitations is examined for an isotropic incompressible hyperelastic circular sheet under a pre-strained state caused by an initially applied finite radial tension. The solutions that describe the radially symmetric motion of the pre-strained sheet are obtained. The conditions of cavitated bifurcation that describe cavity formation and motion with time at the axial line of the pre-strained sheet are proposed, that is to say, a circular cavity will form if the suddenly applied radial tensile load exceeds a certain critical value; dynamically, it is proved that the formed cavity will present a nonlinearly periodic oscillation, which is essentially different from the singular periodic oscillation of the formed cavity in an incompressible hyperelastic solid sphere. Numerical simulations show the effects of prescribed radial tension, material parameter and tensile load on critical tensile load describing cavity formation and periodic oscillation of the pre-strained circular sheet.

Detailing and Construction of the Pantadome Roof Structure for a Bullring in Xàtiva (Spain)

This paper describes the detailing and construction of a roof structure for a bullring in Xátiva (Spain). The roof has been built by means of a new version of the Pantadome system. The roof dome is spherical shaped with a 42 m diameter central opening and an exterior diameter of 101,6 m. It is supported on 44 columns distributed along a 86,4 m diameter circumference. The structural system is formed by radial truss lattices pinned to the columns and to the inner ring and supported by the action of an outer tension ring, radial tension members and tension (upper chord) and compression (lower chord) in the inner ring. The structure was built near the ground and lifted by shortening 44 radial strands with jacks attached to the inner ring. Strand forces have been transferred to permanent tension members at the end of the process. The kinematics of the deployment has been analyzed. Forces in the jacks have been obtained theoretically from the kinematics and compared with the measured values. Special details, developed for the attachment of the jacks and the force transfer are described. The development of the lifting process together with the results of the geometrical survey show that the new erection system allowed the construction of the dome in a quick and safe way.

Temporal and spatial variation of the stress state of Popocatépetl Volcano, Mexico

The fault plane solutions (FPS) of volcano-tectonic events (VTs), can help in the determination of the stress state of a volcano, before, during and after an eruptive period. Hence, for Popocatépetl, we have calculated the FPS from 1996 to 2003, and we have compared the results with its volcanic activity. For Popocatépetl, there are two main areas of VTs, one below the crater and another in the southeastern zone. For the below crater we have 398 solutions and for the southeastern zone 64. The FPS below the crater have pressure axes (P) with a preferential orientation of S70°W–N70°E, which is consistent with the regional stress state. For the tension axes (T) a radial tension is observed, although a great amount of axes exists with a direction of NW–SE. Most of the FPS are normal solutions and these are present at depths mainly between 0 and 3 km asl, although we have periods where an increase is observed in the number of reverse events, approximately between −3 and 0 km asl. The variability of the solutions with depth is probably associated with the intrusion of magma inside the volcano. The group of events located in the southeastern part of the volcano have pressure axes (P) with directions of S–N and W–E, and the same orientations are observed for the tension axes (T). Most of the mechanisms in this area are strike–slip solutions, which follow two possible faults, which were activated during the early magma intrusions inside of the volcano.

Differential Diagnosis and Physical Therapy Management of a Patient With Radial Wrist Pain of 6 Months' Duration: A Case Report

Case report. Differential diagnosis for patients with radial wrist pain requires consideration of systemic disease, referred pain to the radial aspect of the wrist, and local dysfunction. The list of possible local dysfunctions should include De Quervain syndrome, as well as entrapment neuropathy of the superficial radial nerve. The patient was a 57-year-old man with right radial wrist pain of 6 months' duration. The referral diagnosis was De Quervain syndrome, but a previous course of electrophysical agents-based physical therapy management had been unsuccessful. The physical examination ruled out the cervical, shoulder, elbow, and wrist joints as possible sources of pain. In this case, the diagnosis of entrapment neuropathy of the superficial radial nerve, rather than De Quervain syndrome, was primarily based on the symptom provocation resulting from a modified radial bias upper limb nerve tension test. Based on this diagnosis, treatment consisted of active and passive exercises using neurodynamic techniques. After 1 treatment session, the patient noted changes with regard to current pain intensity and function that exceeded the minimal clinically important difference and the minimal detectable change, respectively. After only 2 treatment sessions, the patient reported a complete resolution of symptoms and a full return to work. This case report critically evaluates the diagnostic process for patients with radial wrist pain and suggests neuropathy of the superficial sensory branch of the radial nerve as a differential diagnostic option. Therapy, level 4.J Orthop Sports Phys Ther 2010;40(6):361-368, Epub 22 April 2010. doi:10.2519/jospt.2010.3210.

Constitutive analysis of thin biological membranes with application to radial stretching of a hollow circular membrane

The constitutive analysis of the mechanical response of thin elastic membranes under inplane deformation is presented by using the multiplicative decomposition of the deformation gradient into its areal and distortional parts. Specific results are obtained for the Evans–Skalak form of the strain energy function. The solution to the problem of radial stretching of a hollow circular membrane obeying this constitutive model is then derived. The stress concentration factor is determined as a function of the relative hole size and the magnitude of the applied tension. The tension boundary is identified above which no compressive stress appears in the membrane. The limit boundary is introduced below which the membrane cannot support the applied loading without unstable wrinkling. For the loading between the tension and the limit boundary, nonuniformly distributed infinitesimal wrinkles appear within the inner portion of the membrane, carrying radial tension but no circumferential stress (tension field). The specific form of the strain energy function is used to describe this behavior, and to calculate the amount of the membrane area absorbed by infinitesimal wrinkles. The wrinkled portion is surrounded by the outer portion of the membrane carrying both radial and circumferential stresses. The limit boundary is reached when wrinkles spread throughout the membrane. It is shown that for a sufficiently large tension at the outer boundary, the wrinkling does not spread throughout the membrane no matter how large the applied tension at the inner boundary of the membrane is, provided that no rupture takes place. The limiting extent of the tension field in such cases is calculated. The linearized version of the analysis is characterized by a closed form solution.

Characteristic of hybrid single electron transistor and metal oxide semiconductor structure in Chua’s circuit

The negative differential resistance (NDR) characteristic equation of single electron transistor and metal oxide semiconductor (SETMOS) hybrid structure is simplified by a fitting method. And a new approach to designing multi-scroll chaotic circuit with SETMOS is proposed. The effect of NDR characteristic on the equilibrium point of multi-scroll Chua’s circuit is analyzed both qualitatively and quantitatively. The results show that the unidirectional motions of radial contract and axial tension occur in the negative sections of multi-scroll Chua’s circuit, whereas in the positive sections appear the scroll motions of radial tension and axial contract. The result provides theoretical basis for the construction of multi-scroll chaotic circuits and the further study of their complex dynamical behaviors.

The influence of die geometry on stress distribution by experimental and FEM simulation on electrolytic copper wiredrawing

The study of die geometry is vital in determining the surface and mechanical properties of drawn wires, and consequently, their application. In this work, annealed electrolytic copper wire (ETP), with 0.5 mm original diameter was reduced by 19% in dies with 2β = 10º and 18º and Hc = 35 and 50%. The best experimental results were then studied by the Finite Element Method to simulate residual stress distribution. The experimental results show that the friction coefficient decreases as the wire drawing speed increases, and that low 2β and Hc values bring about the most favorable wiredrawing conditions. The simulation shows a variation in the axial and radial tensions, both for the compression and traction stresses on all regions during the wire drawing process. In conclusion, the influence of the internal die geometry on the drawn wire is clarified.

Evolving Lorentzian wormholes supported by phantom matter and cosmological constant

In this paper we study the possibility of sustaining an evolving wormhole via exotic matter made of phantom energy in the presence of a cosmological constant. We derive analytical evolving wormhole geometries by supposing that the radial tension of the phantom matter, which is negative to the radial pressure, and the pressure measured in the tangential directions have barotropic equations of state with constant state parameters. In this case the presence of a cosmological constant ensures accelerated expansion of the wormhole configurations. More specifically, for positive cosmological constant we have wormholes which expand forever and, for negative cosmological constant we have wormholes which expand to a maximum value and then recollapse. At spatial infinity the energy density and the pressures of the anisotropic phantom matter threading the wormholes vanish; thus these evolving wormholes are asymptotically vacuum {lambda}-Friedmann models with either open or closed or flat topologies.

Simulation and Analysis of Residual Stress in the Graded Interlayer of MoSi2 Composite/316L Stainless Steel Joint

We reported the simulation and the analysis of the residual stress within the graded interlayered joints of MoSi2 to 316L stainless steel fabricated by spark plasma-sintering (SPS) technique. The residual stress in the joints was analyzed by the finite element ANSYS code. The results show that the maximum radial and axial residual tension stresses first decrease and then increase with the increase of the compositional distribution exponent (P), and consistently decrease with the increase of the number (n) and the thickness (d) of graded layer, respectively. The optimal values of compositional distribution exponent, the thickness, and the number of graded interlayered joints of the MoSi2 composite/316L are P = 0.8, d = 1.0 mm, and n = 9, respectively. The residual tension stresses in the samples treated by nine graded interlayers are reduced to 24% and 25% of those in the joints without the interlayer, respectively.