Elastic Configuration Research Articles

NUMERICAL AND ULTRASONIC EXPERIMENTAL SIMULATIONS OF ELASTIC WAVE PROPAGATION AROUND HOLLOW CYLINDER

A laser-ultrasonic experimental setup was used to study, at a reduced scale, the wave propagation inside and around fluid-filled wells. Simulations tools were also developed and calibrated from comparisons with experimental signals. These tools serve as a connection to realistic scale. A semi-analytical approach, the discrete wave number method was first used to compute signals in a simplified geometrical configuration. This method is fast enough to be used in the identification of the main parameters that describe at best the experimental signals. Then a finite difference scheme was implemented in order to describe accurately the actual well. The two methods describe the attenuation mechanisms by using the Kelvin–Voigt model for the solid and the Maxwell model for the fluid. Comparisons between numerical and experimental waveforms, obtained in the two fundamental elastic configurations: the fast and the slow formations, show very good agreement in arrival times, waveforms and relative amplitudes. This satisfactory result provides insights useful for the recognition and interpretation of wave propagation in complex media. Such is the case of modern sonic-logging technology.

STABILITY OF SPATIAL ELASTICA IN A GRAVITATIONAL FIELD

This paper considers the behavior of a spatial elastica in a gravitational field. The slenderness of the system considered is such that the weight becomes an important consideration in determining elastic equilibrium configurations. Both ends of the elastica are clamped in an initially (planar) horizontal orientation at a fixed distance apart. However, one of the ends allows an increase in arc-length, that is, it is a sleeve joint. Thus, the total arc-length is the primary control parameter. This kind of elastica typically loses stability, resulting in out-of-plane deflections, when the total arc-length is increased beyond a critical value. A small mid-length torque can used to perturb a planar equilibrium configuration in order to test for stability. The aim of this study is to assess the effect of self-weight of the elastica (which is typically ignored) on promoting or delaying the loss of stability. To this end, it is useful to compare and contrast the results of orientation, that is, the system is configured in both an initial "upright" orientation and then in an "upside-down" orientation to highlight the influence of gravity. The results of the weightless elastica are used as a reference. Analysis is based on Kirchhoff's rod theory and Euler parameters, and the resulting set of governing differential equations are solved using a shooting method. The results from an experimental system using a slender superelastic wire made from Nitinol (Nickel Titanium Naval Ordnance Laboratory) exhibit close agreement with the analytical results.

The Einstein field equations for cylindrically symmetric elastic configurations

In the context of relativistic elasticity it is interesting to study axially symmetric space-times due to their significance in modeling neutron stars and other astrophysical systems of interest. To approach this problem, here, a particular class of these space-times is considered. A cylindrically symmetric elastic space-time configuration is studied, where the material metric is taken to be flat. The components of the energy-momentum tensor for elastic matter are written in terms of the invariants of the strain tensor, here chosen to be the eigenvalues of the pulled-back material metric. The Einstein field equations are presented and a condition confirming the existence of a constitutive function is obtained. This condition leads to special cases, in one of which a new system for the metric functions and an expression for the constitutive function are deduced. The new system depends on a particular function, which builds up the constitutive equation.

On the plane strain in a theory for self-gravitating elastic configuration with initial static stress field

This paper is concerned with the plane strain in a theory for an arbitrary, uniformly rotating, self-gravitating, perfectly elastic Earth model with a hydrostatic initial stress field. Using the associated matrices method, a representation of Galerkin type is given. This representation enables us to derive the solution of the vibration problem corresponding to concentrated body forces.

A preliminary study of the load bearing capacity of a new foil thrust gas bearing

With the rapid development of high-speed, oil-free turbomachinery, more and more attention is concentrated on compliant aerodynamic foil bearings. However, the common corrugated bump foil forming the compliant structure is so complicated that manufacturing it is time-consuming and troublesome. In this article, a simple type of aerodynamic foil thrust gas bearing with an elastic hemispherical convex dot support configuration is first proposed. Then experimental investigations on stability and its load capacity characteristic for this foil thrust bearing were conducted on a multi-functional thrust bearing test rig. The preliminary measurement and analysis are presented through the wave and spectrum of axial displacement response in the time and frequency domain. It is demonstrated that the proposed bearing can operate well and has good stability in tests, and experimental results show that the axial load can reach 25 N when the rotational speed is about 114 200 r/min.

Elastic cooperative caching

Next generation tiled microarchitectures are going to be limited by off-chip misses and by on-chip network usage. Furthermore, these platforms will run an heterogeneous mix of applications with very different memory needs, leading to significant optimization opportunities. Existing adaptive memory hierarchies use either centralized structures that limit the scalability or software based resource allocation that increases programming complexity. We propose Elastic Cooperative Caching, a dynamic and scalable memory hierarchy that adapts automatically and autonomously to application behavior for each node. Our configuration uses elastic shared/private caches with fully autonomous and distributed repartitioning units for better scalability. Furthermore, we have extended our elastic configuration with an Adaptive Spilling mechanism to use the shared cache space only when it can produce a performance improvement. Elastic caches allow both the creation of big local private caches for threads with high reuse of private data and the creation of big shared spaces from unused caches. Local data allocation in private regions allows to reduce network usage and efficient cache partitioning allows to reduce off-chip misses. The proposed scheme outperforms previous proposals by a minimum of 12% (on average across the benchmarks) and reduces the number of offchip misses by 16%. Plus, the dynamic and autonomous management of cache resources avoids the reallocation of cache blocks without reuse which results in an increase in energy efficiency of 24%.

Whole analogy between Daniel Bernoulli solution and direct kinematics solution

In this paper, the relationship between the original Euler-Bernoulli's rod equation and contemporary knowledge is established. The solution which Daniel Bernoulli defined for the simplest conditions is essentially the solution of 'direct kinematics'. For this reason, special attention is devoted to dynamics and kinematics of elastic mechanisms configuration. The Euler-Bernoulli equation and its solution (used in literature for a long time) should be expanded according to the requirements of the mechanisms motion complexity. The elastic deformation is a dynamic value that depends on the total mechanism movements dynamics. Mathematical model of the actuators comprises also elasticity forces.

Research and Simulation of Inverse Dynamics of a Wheeled Mobile Single Link Flexible Manipulator

The inverse dynamics modeling of a wheeled mobile single link flexible planar manipulator(WMSLFPM) is presented. Based on Bernoulli-Euler beam theory and under pin-free boundary conditions,the single link flexible manipulator is discretized. The system inverse dynamic model of the WMSLFPM,which is derived by using finite elements by virtue of Hermit interpolation function and Newton-Ouler equations and virtual principle,is concisely described in terms of matrices and vectors measured with respect to a body frame of reference. The numeric simulations are carried out to the inverse dynamic model of a WSMSLFPM in the frequency domain to get the driving torque/force and elastic configuration variables. This technique is suitable for the study on the inverse dynamics of mobile flexible manipulators under the conditions of high precision at the tip of light flexible arms and for building up both open-loop control and closed-loop control strategies.

Structural Abnormalities of the Pulmonary Trunk in Tetralogy of Fallot and Potential Clinical Implications: A Morphological Study

The purpose of this study was to determine whether intrinsic histological abnormalities of the pulmonary trunk (PT) are present from birth and interact with palliative surgery and/or repair. Little is known about PT histology in patients with tetralogy of Fallot (TOF), especially in the era of surgical intervention in childhood. We studied 39 formalin-fixed necropsy heart specimens with TOF and compared them with 17 normal control heart specimens. Sections of the PT and aorta were studied by light microscopy using various stains; histological findings were graded according to severity. Among the TOF group (1 fetus, 11 infants, 14 children, and 13 adults), 11 patients had undergone palliative and 10 patients had undergone reparative surgery at a median age of 8 years (range 2.5 to 18 years). Histological changes of grade 2 or higher were present in 59% (medionecrosis), 36% (fibrosis), 56% (cystlike formation), and 56% (abnormal elastic tissue configuration) of TOF patients. Total histology grading scores were higher in TOF hearts (median 6, range 1 to 9) compared with controls (median 1, range 0 to 6; p < 0.0001). Histological abnormalities were present among infants (median score 3.5, range 1 to 9) and after palliative surgery (median score 5, range 2 to 9) or repair (median score 7.5, range 4 to 9). Marked histological abnormalities in the PT of hearts with TOF exist compared with controls. These changes were present from infancy and among patients who had undergone palliative or reparative surgery, although operations in this cohort were performed late. Our data suggest that structural abnormalities of the PT, similar to these recently shown in the aorta, are intrinsic.

Stressed Fibonacci spiral patterns of definite chirality

Fibonacci spirals are ubiquitous in nature, but the spontaneous assembly of such patterns has rarely been realized in laboratory. By manipulating the stress on Ag core/SiO2 shell microstructures, the authors obtained a series of Fibonacci spirals (3×5to13×21) of definite chirality as a least elastic energy configuration. The Fibonacci spirals occur uniquely on conical supports-spherical receptacles result in triangular tessellations, and slanted receptacles introduce irregularities. These results demonstrate an effective path for the mass fabrication of patterned structures on curved surfaces; they may also provide a complementary mechanism for the formation of phyllotactic patterns.

The structure of reactive grain-boundaries under stress containing confined fluids

We present numerical experiments on structure development in grain-boundaries during dissolution–precipitation creep. Two solids that are represented by an elastic spring configuration are pressed together with a compressible fluid in the grain-boundary. The solid can dissolve or precipitate depending on elastic and surface energy as well as fluid pressure and concentration of dissolved material in the fluid. We perform a number of numerical experiments with different starting configurations that represent a large-scale island-channel interface with solid–solid contacts across the islands, a rough grain-boundary interface with a fluid along the whole interface and a smooth thin-film interface. The simulations suggest that the solid–solid islands become unstable by necking and anti-cracking so that the island-channel interface will develop into a grain-boundary interface. The rough interface of the grain-boundary will coarsen with time so that in the extreme case a smooth thin-film interface will emerge. However the thin-film interface is also not necessarily stable but may develop into a rough grain-boundary where the roughness is initiated by heterogeneous dissolution of the solid. Our numerical experiments suggest that interface structures during dissolution–precipitation creep are transient and that the dominance of one interface structure depends on material properties, the displacement rate, purity of the reacting solid and the scale of observation.

Patient-Tailored Cerebral Arterial Model for Simulating Neurovascular Intervention (2nd Report, In Vitro Reproduction of Membranous Vascular Structure Accompanied with Elastic Deformation)

In this paper, we propose an in vitro patient-specific anatomical model of human cerebral artery, a hardware platform for simulating endovascular intervention for making diagnosis and surgical trainings. Proposed vessel model hollowly reproduces 3-dimensional configuration of vascular lumens with elastic membranous configuration as a transparent silicone structure, using fluoroscopic information, which is obtained with CT (Computed Tomography), MRI (Magnetic Resonance Imaging) and other imaging modalities. This vessel model also reproduces the physical characteristics of artery tissue, such as elastic modulus, Poisson's ratio and friction coefficient, within respectively 10% of errors. Consequently, it allows practically simulating procedures, which is accompanied by realistic vascular deformation, realistic feel of operating catheters and realistic behavior of surgical instruments (e.g. slip/stick motion and unwinding motion). Presented vasculature model should provide a helpful platform for interventionalists to make preliminary simulation, for young trainees to practice surgical procedures and for developers to evaluate surgical robots, device and other various medical instruments.

Single edge-crack stress intensity factor solutions

Weight function arguments and a boundary collocation technique are used to re-examine the stress intensity factor solutions to several classic two-dimensional linear elastic single edge-crack configurations. Limits to applicability and the solutions to the three and four-point bend, pure bending, eccentrically loaded tension, and other boundary condition problems are extracted from the solution to the uniformly loaded single edge-cracked configuration. A simple representation of the asymptotic behavior is proposed and a common expression that captures the full range of crack length to specimen width ratio is presented.

Off-diagonal elastic constant and sp2-bonded graphitic grain boundary in nanocrystalline-diamond thin films

This letter studies the relationship between the off-diagonal elastic constant C12 and bond configuration in nanocrystalline-diamond (NCD) thin films deposited by the nitrogen-doped chemical vapor deposition method. The film thickness was varied between 2.4 and 11.3μm. The elastic constants were measured by resonant-ultrasound spectroscopy coupled with laser-Doppler interferometry. The diagonal elastic constants C11 and C44, and Young’s modulus in NCD films are smaller than those of the bulk polycrystalline diamond and microcrystalline-diamond (MCD) thin films, and they decrease as the film thickness decreases. However, the off-diagonal elastic constant of the NCD films is significantly larger than that of the bulk diamond, while that of the MCD films is smaller. Micromechanics calculations revealed that this exceptional enhancement of C12 occurs when the material includes randomly distributed thin graphitic plates in the isotropic diamond matrix. Thus, this result indicates that the NCD films consist of sp3-bonded diamond grains and sp2-bonded grain boundaries.

Theory of self-contact in Kirchhoff rods with applications to supercoiling of knotted and unknotted DNA plasmids.

There are circumstances under which it is useful to model a molecule of duplex DNA as a homogeneous, inextensible, intrinsically straight, impenetrable elastic rod of circular cross-section obeying the theory of Kirchhoff. For such rods recent research has yielded exact analytical solutions of Kirchhoff's equations of mechanical equilibrium with the effects of impenetrability taken into account, and criteria have been derived for determining whether an equilibrium configuration is stable in the sense that it gives a strict local minimum to the elastic energy. This paper contains a summary of published results on equilibrium configurations for the case in which a rod has been pre-twisted and closed to form a knot-free ring. Emphasis is placed on the way the writhe Wr of the ring, the number of its discrete points of self-contact, and the presence or absence of lines of contact, depend on the excess link, Delta Lk, which is a measure of the amount the rod was twisted before its ends were joined. Bifurcation diagrams are presented and a summary is given of the properties of the primary, secondary and tertiary branches that arise by successive bifurcations from the 'trivial branch' comprised of configurations for which the axial curve is a circle. New results are presented in the theory of equilibrium configurations of closed rods with the topology of torus knots. It is remarked that examples of equilibrium configurations of closed rods of one knot type can be obtained from examples of other knot types using methods previously employed to calculate isolas of equilibrium configurations of knot-free rings. Bifurcation diagrams are shown for supercoiled (2,3) torus knots (trefoil knots). It is observed that for sufficiently large and sufficiently small Delta Lk the minimum elastic energy configuration of a trefoil knot contains plectonemic loops with straight contact lines, although the configuration that minimizes the elastic energy of a general (2,q) torus knot over the entire range of Delta Lk has self-contact along a closed curve. As the ratio of the diameter of the rod to its length approaches zero, that contact curve becomes a circle, and there is an open interval of values of Delta Lk for which stable equilibrium configurations with such circular contact curves exist. Examples of minimum energy configurations are presented for both torus knots and catenates formed by linking two unknots.

Dynamic load-carrying capacity of mobile-base flexible joint manipulators

A computational technique for obtaining the maximum load-carrying capacity of robotic manipulators with joint elasticity is described while different base positions are considered. The maximum load-carrying capacity which can be achieved by a robotic manipulator during a given trajectory is limited by a number of factors. Probably the most important factors are the actuator limitations, joint elasticity (transmissions, reducers and servo drive system) and relative configuration of the robot with respect to its base. Therefore, both actuator torque capacity constraint considering typical torque-speed characteristics of DC motors and trajectory accuracy constraints considering a series of spherical bounds centred at each desired trajectory are applied as the main constraints. For the desired trajectory of load, different base locations are considered. It is seen that the load-carrying capacity at different base positions is different due to distinct dynamic effects of links and load motions on joint actuators. Then, a general computational algorithm for a multi-link case on a given trajectory and different base location is laid out in detail. Finally, two numerical examples involving a two-link manipulator and a PUMA robot using the method are presented. The obtained results illustrate the effect of base location, dual actuator torque and end effector precision constraints on load-carrying capacity on a given trajectory .

Line defect dynamics around a colloidal particle

We study experimentally the dynamics of a topological defect located around a colloidal particle suspended in a thermotropic nematic liquid crystal. The considered defect consists of a disclination loop encircling the particle at the equator. Under specific conditions, it is shown that this disclination continuously shrinks to a hedgehog defect located in the immediate vicinity of the particle. This phenomenon corresponds to a transition between an elastic quadrupolar configuration and an elastic dipolar configuration. We performed a basic numerical calculation to get an estimate of the dissipated energy during the transition; we compare the results with theoretical predictions that describe the elastic energy of particles surrounded by defects.

On the Conversion of K - to J -Characterization in Linear Elastic 3D Configurations

An equation for converting characterization of 3D fields in cracked plates in terms of the stress intensity factor to the one in terms of J-integral is developed. It can be used in applications such as finite element codes and identification of the adequate “effective” elastic modulus in the ASTM E1921 standard. We consider standard specimens — plates that can be thin or thick as compared to the in-plane dimension. It is found that the actual specimen compliance lies in-between the ones corresponding to the 2D plane stress and 2D plane strain approximations. However, the near tip field that governs the K to J conversion is predominantly plane strain for the studied cases. Another finding is that the geometrical factor in 2D, f(a/W), for standard specimens is different from the one obtained on the basis of a 3D analysis.

Application of an electric field to colloidal particles suspended in a liquid-crystal solvent.

We study the behavior of colloidal particles suspended in a thermotropic nematic solvent in the presence of an electric field. For normal boundary conditions of the nematic director at the particles' surface, we show experimentally that an electric field applied along the dipolar axis of an elastic dipole induces a transition to an elastic quadrupolar configuration. Turning the field off makes the system go back to the initial state. We also show that it is possible to directly evidence an elastic quadrupolar repulsion between droplets.

Far-infrared properties of resonant modes and tunnelling statesin rare-earth-doped calcium fluoride

The low-temperature observation of a broad distribution of two-level systemsin chemically disordered fluorite mixed crystals has heightened interest inthe spectroscopic properties of the corresponding lightly doped crystals. Thelow-temperature far-ir absorption of calcium fluoride crystals doped withY3+, La3+ or Lu3+ in the range less than 1 mol% shows threecompletely different types of defect-induced spectra and the temperature andconcentration dependence are found to vary widely. In addition, the far-irproperties of CaF2 doped with Y3+ or Lu3+ can be dramaticallyaltered by heat treatment, indicating that clustering plays an important role.By comparing the spectroscopic signatures with those previously observed forother defect systems, the lowest-lying excitations for these doped CaF2crystals have been assigned as follows: tunnelling transitions in twodifferent elastic configurations for Y3+, a variety of ground statetunnelling transitions for the La3+ doping and an anharmonic resonantmode for the Lu3+ doped system. The surprising result is that a broaddistribution of two-level systems is clearly evident in two of the threesystems and the optical activity of this distribution appears to be controlledby the optical activity of the dominant defect dynamics.