Elastic Line Research Articles

Relaxed elastic lines of second kind on oriented surface in Minkowski space

The relaxed elastic line of second kind on an oriented surface in the Minkowski space was defined and for the relaxed elastic line of second kind which is lying on an oriented surface the Euler-Lagrange equations were derived. Furthermore, whether these curves lie on a curvature line or not was investigated and some applications were given.

Dynamics below the Depinning Threshold in Disordered Elastic Systems

We study the steady-state low-temperature dynamics of an elastic line in a disordered medium below the depinning threshold. Analogously to the equilibrium dynamics, in the limit T-->0, the steady state is dominated by a single configuration which is occupied with probability 1. We develop an exact algorithm to target this dominant configuration and to analyze its geometrical properties as a function of the driving force. The roughness exponent of the line at large scales is identical to the one at depinning. No length scale diverges in the steady-state regime as the depinning threshold is approached from below. We do find a divergent length, but it is associated only with the transient relaxation between metastable states.

Prediction of workpiece elastic deflections under cutting forces in turning

One of the problems faced in turning processes is the elastic deformation of the workpiece due to the cutting forces resulting in the actual depth of cut being different than the desirable one. In this paper, a cutting mechanism is described suggesting that the above problem results in an over-dimensioned part. Consequently, the problem of determining the workpiece elastic deflection is addressed from two different points of view. The first approach is based on solving the analytical equations of the elastic line, in discretized segments of the workpiece, by considering a stored modal energy formulation due to the cutting forces. Given the mechanical properties of the workpiece material, the geometry of the final part and the cutting force values, this numerical method can predict the elastic deflection. The whole approach is implemented through a Microsoft Excel © workbook. The second approach involves the use of artificial neural networks (ANNs) in order to develop a model that can predict the dimensional deviation of the final part by correlating the cutting parameters and certain workpiece geometrical characteristics with the deviations of the depth of cut. These deviations are calculated with reference to final diameter values measured with precision micrometers or on a CMM. The verification of the numerical method and the development of the ANN model were based on data gathered from turning experiments conducted on a CNC lathe. The results support the proposed cutting mechanism. The numerical method qualitatively agrees with the experimental data while the ANN model is accurate and consistent in its predictions.

The bending equations of sandwich plates with a prestressed filling

An approximate model of the linear bending of an orthotropic sandwich plate is proposed, taking into account the excess pressure in the space of the filling and the difference in the areas of the surfaces of the elastically curved supporting layers, and the dependence of the shear modulus of the filling on the pressure is postulated. The bending equations of the plate are also given, taking into account the external excess pressure. The value of the transverse distributed force acting on the plate due to the excess pressure in the space of the middle layer and the curvature of the elastic line is obtained. It is shown that this pressure leads to an increase in the bending. If the space of the filling is closed, so that stretching forces due to the pressure act on the boundary sections, the bending is independent of the pressure drop. The dependence of the distributed transverse force on the external pressure is derived. The change in the shear modulus of the filling as a function of the external pressure drop is also considered.

Collective acoustic modes as renormalized damped oscillators: Unified description of neutron and x-ray scattering data from classical fluids

In the Q range where inelastic x-ray and neutron scattering are applied to the study of acoustic collective excitations in fluids, various models of the dynamic structure factor S(Q, omega) generalize in different ways the results obtained from linearized-hydrodynamics theory in the Q-->0 limit. Here we show that the models most commonly fitted to experimental S(Q, omega) spectra can be given a unified formulation. In this way, direct comparisons among the results obtained by fitting different models become now possible to a much larger extent than ever. We also show that a consistent determination of the dispersion curve and of the propagation Q range of the excitations is possible, whichever model is used. We derive an exact formula which describes in all cases the dispersion curve and allows for the first quantitative understanding of its shape, by assigning specific and distinct roles to the various structural, thermal, and damping effects that determine the Q dependence of the mode frequencies. The emerging picture describes the acoustic modes as Q-dependent harmonic oscillators whose characteristic frequency is explicitly renormalized in an exact way by the relaxation processes, which also determine, through the widths of both the inelastic and the elastic lines, the whole shape of collective-excitation spectra.

Intrinsic formulation for elastic line deformed on a surface by external field in the Minkowski 3-space [formula omitted

In this work, we developed intrinsic formulation for elastic line deformed on a surface by an external field in the Minkowski 3-space.

RC large displacements: Optimization applied to experimental results

A large number of towers for telecommunication were installed during the implantation of cellular telephony services in Brazil. Some of those towers presented problems as excessive displacements, residual displacements, cracking and some accidents happened. On the other hand, the computation of large displacements in slender reinforced concrete structures is a very difficult task as the flexural stiffness of the sections changes continuously as the bending moment increases, due to the very non-linear material behavior of concrete, involving such phenomena as formation of cracks and plastification. The goal of this paper is to present some initial results of the application of optimization techniques to experimental data relative to the determination of the effective bending stiffness of transverse sections of reinforced concrete structures. The objective is to determine parameters of reduction of the stiffness of unstressed sections for the correct calculation of the displacements of those structures. The results of a test with a reinforced concrete tower for telecommunications of 30m of length, circular ring cross-section with 50cm diameter, were used. For several cross-sections along the axis of this structure the effective stiffness was computed. For analysis purposes, the structure was discretized and the differential equation of the elastic line integrated to obtain the rotations and displacements. The values of the effective stiffness of the cross-sections were obtained using optimization techniques. The effective stiffness is presented in graphs as function of the solicitation level (the ratio between the characteristic bending moment and the ultimate moment of the cross-section). The section where the largest stiffness loss happened is the section that indeed collapsed in a real similar structure. Directions for future researches are presented.

Identification of multiple cracks in beams under bending

The identification of a transverse crack on a beam is the subject of many investigators. Identifying the crack means to find its position and depth. In many cases there are more than one cracks on a beam. Then the solutions, or the combinations of parameters characterising the cracks are more and the problem becomes more complicated particularly when the crack must be identified using one more parameter, the relative each other angular position. In the present paper the dynamic behaviour of a cracked beam with two transverse surface cracks is studied. Each crack is characterised by its depth, position and relative angle. Both cracks are considered to lie in arbitrary angular positions with respect to the longitudinal axis of the beam and at any distance from the left end. A local compliance matrix of two degrees of freedom, bending in the horizontal and the vertical planes is used to model the rotating transverse crack in the shaft and is calculated based on the available expressions of the stress intensity factors and the associated expressions for the strain energy release rates. The compliance matrix is calculated for the first time at any angle of rotation. Thus, the compliance is given as a function of both the crack depth and the angular location. These expressions are usable, due to the stress intensity function limitations, only for limited regions around the zero angular position of the crack and not for every crack angle. For these cases, B-spline curves are used to interpolate the known points and a function in analytical form is given for every crack depth and angle. It is well known that when a crack exists in a structure, such as a beam, then the natural frequency of vibration decreases. This reduction is studied here for six independent parameters namely the depth, the location, and the rotational angle of each crack. By keeping these six parameters constant, the first three flexural eigenmodes can be computed and plotted. Due to its sensitivity in slope or displacement changes the theory of wavelets is used here to identify the locations of the cracks reducing thus the number of independent parameters. As it is well known the existence of a crack on a beam in bending, creates in the elastic line of the beam a slope discontinuity analog generally to the crack depth and additionally here to the angular position. The wavelet transformation of a vibration mode or of the vibration response of the structure under some circumstances could be used to locate the cracks. If the positions are known, then the depths and the respective angles can be determined. Here the diagrams of the first three eigenvalues versus both the crack depth and the rotational angle, are used to identify the remaining unknown parameters for both cracks.

Transit passenger origin-destination estimation in congested transit networks with elastic line frequencies

This paper deals with the transit passenger origin-destination (O-D) estimation problem by using updated passenger counts in congested transit networks and outdated prior O-D matrix. A bilevel programming approach is extended for the transit passenger O-D updating problem where the upper-level problem seeks to minimize the sum of error measurements in passenger counts and O-D matrices, while the lower level is the stochastic user equilibrium assignment problem for congested transit networks. The transit assignment framework is based on a frequency-adaptive transit network model in this paper, which can help determine transit line frequencies and the network flow pattern simultaneously in congested transit networks. A heuristic solution algorithm is adapted for solving the transit passenger O-D estimation problem. Finally, a numerical example is used to illustrate the applications of the proposed model and solution algorithm.

Elastic lines on splayed columnar defects studied numerically

We investigate by exact optimization method properties of two- and three-dimensional systems of elastic lines in presence of splayed columnar disorder. The ground state of many lines is separable both in two (2D) and three dimensions (3D), leading to a random walk-like roughening in 2D and ballistic behavior in 3D. Furthermore, we find that in the case of pure splayed columnar disorder, in contrast to point disorder, there is no entanglement transition in 3D. Entanglement can be triggered by perturbing the pure splay system with point defects.

The origin of an elastic line in the L 3 x-ray emission spectrum of metallic manganese

A strong elastic line has been found in the L3 x-ray emission spectrum of metallic Mn. To unravel its physical nature, the ground-state properties of α-Mn were studied in comparison with those of 3d metals (Cr and Fe in bcc structure), as well as the properties of the L3 absorption final states of these three transition metals. To model the electronic structure, LSDA band-structure calculations of Cr, Mn, and Fe were carried out, and L3 absorption spectra of these metals were computed in the atomic approximation. A joint analysis of the properties of the ground state and of the final absorption state excited by an x-ray-produced core hole suggests that the elastic line in the α-Mn spectra should be assigned to the specific character of the absorption final-state multiplet.

Metadislocation arrangements in the complex metallic alloy ξ′-Al–Pd–Mn

In the present work different types of metadislocation arrangements are studied. It is shown that metadislocations can form dipoles or dissociate into partials, which leads to a decrease of the elastic line energy. Connected groups of metadislocations can assume large and complex network structures. Although the local elastic strain at the individual metadislocation cores remains small, they posses large total Burgers vectors and are highly effective means of plastic deformation. Furthermore, we present a characterization of phase boundaries built up by regular metadislocation arrays and show that these metadislocations almost fully compensate the lattice mismatch.

Out-of-Equilibrium Dynamics of the Vortex Glass in Superconductors

We study the relaxational dynamics of flux lines in high-temperature superconductors with random pinning using Langevin dynamics. At high temperatures the dynamics is stationary and the fluctuation dissipation theorem (FDT) holds. At low temperatures the system does not equilibrate with its thermal bath: a simple multiplicative aging is found, the FDT is violated, and we find that an effective temperature characterizes the slow modes of the system. The generic features of the evolution--scaling laws--are dictated by those of the single elastic line in a random environment.

Probit-Type Reliability-Based Transit Network Assignment

This paper proposes a new probit-type reliability-based transit assignment model in a congested network with unreliable transit services. A new disutility function is developed to model the passenger route choice behavior under unreliable conditions; passengers will make a trade-off between the transit service reliability and the expected travel time for their route choice. In the proposed model, the total transit passenger demand is fixed, but the in-vehicle travel times by transit routes are formulated stochastically because of unreliable traffic conditions, particularly for buses on the road network. The effects of congestion on transit networks, such as elastic transit line frequencies and passenger overload delays, are also considered in the proposed model. A numerical example is provided to illustrate the applications of the proposed model and solution algorithm. It is shown that the traditional probit-type stochastic user equilibrium transit assignment is a special case of the proposed model. The findings also reveal the distribution of passenger waiting times and their overload delays at congested transit stations.

Probit-Type Reliability-Based Transit Network Assignment

This paper proposes a new probit-type reliability-based transit assignment model in a congested network with unreliable transit services. A new disutility function is developed to model the passenger route choice behavior under unreliable conditions; passengers will make a trade-off between the transit service reliability and the expected travel time for their route choice. In the proposed model, the total transit passenger demand is fixed, but the in-vehicle travel times by transit routes are formulated stochastically because of unreliable traffic conditions, particularly for buses on the road network. The effects of congestion on transit networks, such as elastic transit line frequencies and passenger overload delays, are also considered in the proposed model. A numerical example is provided to illustrate the applications of the proposed model and solution algorithm. It is shown that the traditional probit-type stochastic user equilibrium transit assignment is a special case of the proposed model. The findings also reveal the distribution of passenger waiting times and their overload delays at congested transit stations.

Hydrodynamic interactions and relative motions of two floating platforms with mooring lines in side-by-side offloading operation

The hydrodynamic interaction and mechanical coupling effects of two floating platforms connected by elastic lines are investigated by using a time-domain multi-hull/mooring/riser coupled dynamics analysis program. Particular attention is paid to the contribution of off-diagonal hydrodynamic interaction terms on the relative motions during side-by-side offloading operation. In this regard, the exact method (CMM: combined matrix method) including all the vessel and line dynamics, and the 12×12 hydrodynamic coefficients in a combined matrix is developed. The performance of two typical approximation methods (NHI/No Hydrodynamic Interaction: iteration method between two vessels without considering hydrodynamic interaction effects; SMM/Separated Matrix Method: iteration method between two vessels with partially considering hydrodynamic interaction effects, i.e. ignoring off-diagonal cross-coupling terms in the 12×12 hydrodynamic coefficient matrix) is also tested for the same side-by-side offloading operation in two different environmental conditions. The numerical examples show that there exists significant discrepancy at sway and roll modes between the exact and the approximation methods, which means that the cross-coupling (off-diagonal block) terms of the full hydrodynamic coefficient matrix play an important role in the case of side-by-side offloading operation. Therefore, such approximation methods should be used with care. The fender reaction forces, which exhibit large force with contact but no force without contact, are also numerically modeled in the present time-domain simulation study.

Numerical Analysis of Nanotube Based NEMS Devices — Part II: Role of Finite Kinematics, Stretching and Charge Concentrations

In this paper a nonlinear analysis of nanotube based nano-electromechanical systems is reported. Assuming continuum mechanics, the complete nonlinear equation of the elastic line of the nanotube is derived and then numerically solved. In particular, we study singly and doubly clamped nanotubes under electrostatic actuation. The analysis emphasizes the importance of nonlinear kinematics effects in the prediction of the pull-in voltage of the device, a key design parameter. Moreover, the nonlinear behavior associated with finite kinematics (i.e., large deformations), neglected in previous studies, as well as charge concentrations at the tip of singly clamped nanotubes, are investigated in detail. We show that nonlinear kinematics results in an important increase in the pull-in voltage of doubly clamped nanotube devices, but that it is negligible in the case of singly clamped devices. Likewise, we demonstrate that charge concentration at the tip of singly clamped devices results in a significant reduction in pull-in voltage. By comparing numerical results to analytical predictions, closed form formulas are verified. These formulas provide a guide on the effect of the various geometrical variables and insight into the design of novel devices.

Quasidislocations in anisotropic bicrystals

AbstractWeertman has recently pointed out that an elastic line singularity of dislocation/force line character but of zero Burgers vector and zero line force can move at the Stoneley velocity along the interface in a bicrystal of two different isotropic materials [J. Weertman, Phys. Rev. Lett. 93, 2655 (2004)]. The theory of this quasidislocation is generalized to the case of anisotropic bicrystals. The quasidislocation–Stoneley wave connection remains generally true and is further elucidated. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Relaxed elastic line on a curved pseudo-hypersurface in pseudo-Euclidean spaces

In this work, we derive the Euler–Lagrange equation for an elastic line which is lying on a pseudo-hypersurface in pseudo-Euclidean spaces E ν n . Following this, we check the solutions which depend on the boundary conditions whether they are geodesic on a pseudo-hypersurface or not. The relaxed elastic line on a pseudo-hyperplane, a pseudo-hypersphere, and pseudo-hyperbolic space is a geodesic. However, the relaxed elastic line on a pseudo-hypercylinder, is a space-like geodesic.

Metadislocation reactions and metadislocation networks in the complex metallic alloy ξ′-Al–Pd–Mn

Metadislocations are novel structural defects firstly observed in the complex metallic alloy ξ′-Al–Pd–Mn. We present a transmission electron microscopy study on metadislocation reactions and networks. It is shown that metadislocations can dissociate into partials, which leads to a decrease of the elastic line energy. Connected groups of metadislocations can assume large and complex network structures with large total Burgers vectors. However, the local elastic strain at the individual metadislocation cores as well as the fault-plane energies remain small. By this mechanism, effective large Burgers vectors, contributing massively to plastic strain, can be distributed over a large portion of the material.