Stretch and twist of rotating prismatic beam

A turbine blade is modelled as a uniform isotropic prismatic beam of general cross-section and “setting angle” rotating about one end, and is analysed according to the linear theory of elasticity. A semi-inverse solution is presented which reduces the three-dimensional problem to one of two dimensions, and explicit stress and strain components given for the mathematically amenable elliptic cross-section. As expected, the planar stresses σ_x,σ_y, and τ_xy arising from the two-dimensional problem are found to be small. For the general section, the theory predicts small curvature of the blade centre line, and a twisting moment which tends to reduce the “angle of set”.     

Asymptotic analysis of an end-loaded, transversely isotropic, elastic, semi-infinite strip weak in shear

We use linear elasticity to study a transversely isotropic (or specially orthotropic), semiinfinite slab in plane strain, free of traction on its faces and at infinity and subject to edge loads or displacements that produce stresses and displacements that decay in the axial direction. The governing equations (which are identical to those for a strip in plane stress, free of traction on its long sides and at infinity, and subject to tractions or displacements on its short side) are reduced, in the standard way. to a fourth-order partial differential equation with boundary conditions for a dimensionless Airy stress function ƒ. We study the asymptotic solutions to this equation for four sets of end conditions—traction, mixed (two), displacement—as g3, the ratio of the shear modulus to the geometric mean of the axial and transverse extensional moduli, approaches zero. In all cases, the solutions for ƒ consist of a “wide” boundary layer that decays slowly in the axial direction (over a distance that is long compared to the width of the strip) plus a “narrow” boundary layer that decays rapidly in the axial direction (over a distance that is short compared to the width of the strip). Moreover, we find that the narrow boundary layer has a “sinuous” part that varies rapidly in the transverse direction, but which, to lowest order, does not enter the boundary conditions nor affect the transverse normal stress or the displacements. Because the exact biorthogonality condition for the cigenfunctions associated with ƒ can be replaced by simpler orthogonality conditions in the limit as →b 0, we are able to obtain, to lowest order, explicit formulae for the coeflicients in the eigenfunction expansions of ƒ for the four different end conditions.     

Quasi-isochoric ion beam heating using dynamic confinement in spherical geometry for X-ray scattering experiments in WDM regime

Extreme states of matter such as Warm Dense Matter “WDM” and Dense Strongly Coupled Plasmas “DSCP” play a key role in many high energy density experiments, however, creating WDM and DSCP in a manner that can be quantified is not readily feasible. In this paper, isochoric heating of matter by intense heavy ion beams in spherical symmetry is investigated for WDM and DSCP research: the heating times are long (100 ns), the samples are macroscopically large (millimeter-size) and the symmetry is advantageous for diagnostic purposes. A dynamic confinement scheme in spherical symmetry is proposed which allows even ion beam heating times that are long on the hydrodynamic time scale of the target response. A particular selection of low-Z target tamper and X-ray probe radiation parameters allows to identify the X-ray scattering from the target material and use it for independent charge state measurements Z* of the material under study.     

Energy approach to crack growth in a fiber-reinforced brittle material modeled by an inclusion

Brittle materials randomly reinforced with a low volume fraction of strong, stiff and ductile fibers are considered, with specific reference to fiber-reinforced cements and concrete. Visible cracks in such materials are accompanied by a surrounding damage zone – together these constitute a very complex “crack system”. Enormous effort has been put into trying to understand the micromechanics of such systems. Almost all of these efforts do not deal with the “crack system” propagation behavior as a whole. The propagation process of such a “crack system” includes propagation of the visible crack and the growth of the damage zone. Propagation may take place by lengthening of the visible crack together with the concomitant lengthening of the surrounding damage zone, or simply by broadening of the damage zone while the visible crack length remains unchanged – or simultaneously by growth of both types. A phenomenological completely theoretical model (for an ideal material) is here proposed which can serve to examine the propagation process by means of energy principles, without recourse to the microscopic details of the process. An application of this theoretical approach is presented for the case of a damage zone evolving with a rectangular shape. This shape is chosen because it is expected that it will illustrate the nature of damage evolution and because the computational procedure necessary to follow the growth is the most straightforward.     

Interaction of a One-Dimensional Continuum with an Inertial Object Moving over the Continuum

Free transverse oscillations in a system consisting of an infinite moment continuum, such as the Euler-Bernoulli beam lying on the Winkler foundation, and a rigid body moving along the beam with a constant velocity and having a point contact with the guide are studied. The range of the considered velocities of the concentrated inertial object along the continuum is limited by the requirement of a finite energy of elastic deformation of the infinite continuum, corresponding to cojoint free osillations of an unbounded system. An analytical solution of the corresponding spectral problem in a system with a mixed spectrum is constructed. Limiting situations are analyzed, where the inertial rigid object moving along the beam is devoid of one “oscillatory” degree of freedom for some reasons. In particular, an inertial object devoid of mass but having a nonzero tensor of inertia is considered. Dependences of all characteristics of the discrete spectrum of oscillations and their shapes on the magnitude of object velocity along the moment elastoinertial guide are given.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 4, pp. 88–97, July– August, 2005.     

A “quasi-elastic” affine formulation for the homogenised behaviour of nonlinear viscoelastic polycrystals and composites

The derivation of the overall behaviour of nonlinear viscoelastic (or rate-dependent elastoplastic) heterogeneous materials requires a linearisation of the constitutive equations around uniform per phase stress (or strain) histories. The resulting Linear Comparison Material (LCM) has to be linear thermoviscoelastic to fully retain the viscoelastic nature of phase interactions. Instead of the exact treatment of this LCM (i.e., correspondence principle and inverse Laplace transforms) as proposed by the “classical” affine formulation, an approximate treatment is proposed here. First considering Maxwellian behaviour, comparisons for a single phase as well as for two-phase materials (with “parallel” and disordered morphologies) show that the “direct inversion method” of Laplace transforms, initially proposed by Schapery (1962), has to be adapted to fit correctly exact responses to creep loading while a more general method is proposed for other loading paths. When applied to nonlinear viscoelastic heterogeneous materials, this approximate inversion method gives rise to a new formulation which is consistent with the classical affine one for the steady-state regimes. In the transient regime, it leads to a significantly more efficient numerical resolution, the LCM associated to the step by step procedure being no more thermoviscoelastic but thermoelastic. Various comparisons for nonlinear viscoelastic polycrystals responses to creep as well as relaxation loadings show that this “quasi-elastic” formulation yields results very close to classical affine ones, even for high contrasts.     

Geomechatronics – Interaction between ground and construction machinery and its application to construction robotics

“Geomechatronics” is a technical field in which “Geotechniques” is fused with “Mechatronics” that is the technical field to promote the automatic control of machines by using the electronics. In the field of “Geomechatronics”, a construction machine, which treats geotechnical materials such as soil and rock, automatically evaluates the properties and conditions of the ground and determines the optimum controlling method of itself for the ground with the base of the machine–ground interaction. Some researches for practical use in the field of geomechatronics are introduced, and then the progressing view of this research and technical filed is explained in this paper.     

Development of a surface-cracked specimen

A surface-cracked specimen has been developed that features a web which facilitates fatigue precracking. In addition, when the web is removed, the remaining semi-elliptical surface crack forms a “natural” intersection with the free surface. The specimen, which resembles an elongated compact tension specimen, is quite efficient in its load requirements; relatively low loads are necessary to produce a given level of stress intensity factor.     

Bounds for the effective properties of heterogeneous plates

This paper presents new bounds for heterogeneous plates which are similar to the well-known Hashin–Shtrikman bounds, but take into account plate boundary conditions. The Hashin–Shtrikman variational principle is used with a self-adjoint Green-operator with traction-free boundary conditions proposed by the authors. This variational formulation enables to derive lower and upper bounds for the effective in-plane and out-of-plane elastic properties of the plate. Two applications of the general theory are considered: first, in-plane invariant polarization fields are used to recover the “first-order” bounds proposed by Kolpakov [Kolpakov, A.G., 1999. Variational principles for stiffnesses of a non-homogeneous plate. J. Meth. Phys. Solids 47, 2075–2092] for general heterogeneous plates; next, “second-order bounds” for n-phase plates whose constituents are statistically homogeneous in the in-plane directions are obtained. The results related to a two-phase material made of elastic isotropic materials are shown. The “second-order” bounds for the plate elastic properties are compared with the plate properties of homogeneous plates made of materials having an elasticity tensor computed from “second-order” Hashin–Shtrikman bounds in an infinite domain.     

Passive effects of rare-earth permanent magnets on flexible conductive structures

The paper presents a theoretical and experimental study of vibrating structures where paramagnetic or diamagnetic systems interact with rare-earth passive magnets.The theoretical model of the system is focused on the damping properties of permanent magnets and on their interactions with the dynamic behaviour of an Euler–Bernoulli beam. In particular, the magnetic model is based on the analogy of the equivalent currents method in a quasi-static open-circuit-type configuration and it is used to determine the influence of eddy currents on the dynamic behaviour of conducting material structures. The magnetic effects are characterised by a viscous-type damping and by a stiffening dynamic effect of the structure, called “phantom effect”.The authors present the experimental outcomes for uniform cantilever clamped-free beams of different kinds of paramagnetic or diamagnetic conducting materials. It appears that the system frequency response can be modified by the presence of a pair of concordant or discordant permanent magnets of high residual induction settled at the free end.Through the comparison between theoretical and experimental results, the paper demonstrates the validity of the model, that is able to describe both the above mentioned effect of dynamic stiffening of the structure and the considerable localised damping properties in paramagnetic or diamagnetic materials having low electric resistivity.     

Fatigue crack growth in high and low strength steel under torsional loading

During loading of a crack in mode III the crack surfaces in contact slide against each other giving rise to friction, abrasion and mutual support, thereby reducing the effective stress at the crack tip (“sliding mode crack closure”). This phenomenon was investigated in a high strength steel (AISI 4340) and in a low strength steel (AISI C1018) in circumferentially notched specimens under pure cyclic torsion and combined loading (cyclic torsion plus static axial load). The influence of sliding mode crack closure on fatigue crack propagation is shown and “true” crack growth values (without the sliding mode crack closure influence) are determined on the basis of an extrapolation procedure. Explanations are given for causes of the various fracture modes observed, such as “factory roof” fracture, macroscopically flat mode III fracture and “lamella” fracture. Finally the scientific and technical importance of sliding mode crack closure is demonstrated.     

Dynamic global postbuckling behavior of beams by cell-to-cell mapping

A dynamic approach was applied to study the behavior of an axially loaded buckled inextensible beam. The “cell-to-cell mapping method” was used to define the equilibrium positions of the beam and their domains of attraction. These domains were pictured on a displacement-velocity phase plane and the magnitudes of “safe” deflection and velocity disturbances, under the action of which the structure will resume its pre-interrupted equilibrium position, were thus determined. It was found that material properties do not affect the value of safe deflection, but the safe velocity disturbance is proportional to .     

Free-surface fluctuations in hydraulic jumps: Experimental observations

A hydraulic jump is the rapid and sudden transition from a high-velocity supercritical open channel flow to a subcritical flow. It is characterised by the dynamic interactions of the large-scale eddies with the free-surface. New series of experimental measurements were conducted in hydraulic jumps with Froude numbers between 3.1 and 8.5 to investigate these interactions. The dynamic free surface measurements were performed with a non-intrusive technique while the two-phase flow properties were recorded with a phase-detection probe. The shape of the mean free surface profile was well defined and the turbulent fluctuation profiles highlighted a distinct peak of turbulent intensity in the first part of the jump roller, with free-surface fluctuation levels increasing with increasing Froude number. The dominant free-surface fluctuation frequencies were typically between 1 and 4 Hz. A comparison between the acoustic sensor signals and conductivity probe data suggested that the air–water “free-surface” detected by the acoustic sensor corresponded to about the boundary between the turbulent shear layer and the upper free-surface layer. Simultaneous measurements of free surface and bubbly flow fluctuations for Fr = 5.1 indicated that the frequency ranges of both sensors were similar (F < 5 Hz) whatever the position downstream of the toe. The present results highlighted that the dynamic free-surface measurements can be conducted successfully using acoustic displacement meters, and the time-averaged depth measurements was a physical measure of the free-surface location in hydraulic jumps.     

Mechanics of granular materials: The discrete and the continuum descriptions juxtaposed

In recent years a discussion could be followed where the pros and cons of the applicability of the Cosserat continuum model to granular materials were debated [Bardet, J.P., Vardoulakis, I., 2001. The asymmetry of stress in granular media. Int. J. Solids Struct. 38, 353–367; Kruyt, N.P., 2003. Static and kinematics of discrete Cosserat-type granular materials. Int. J. Solids Struct. 40, 511–534; Bagi, K., 2003. Discussion on “The asymmetry of stress in granular media”. Int. J. Solids Struct. 40, 1329–1331; Bardet, J.P., Vardoulakis, I. 2003a. Reply to discussion by Dr. Katalin Bagi. Int. J. Solids Struct. 40, 1035; Kuhn, M., 2003. Discussion on “The asymmetry of stress in granular media”. Int. J. Solids Struct. 40, 1805–1807; Bardet, J.P., Vardoulakis, I., 2003b. Reply to Dr. Kuhn’s discussion. Int. J. Solids Struct. 40, 1809; Ehlers, W., Ramm, E., Diebels, S., D’Addetta, G.A., 2003. From particle ensembles to Cosserat continua: homogenization of contact forces towards stresses and couple stresses. Int. J. Solids Struct. 40, 6681–6702; Chang, C.S., Kuhn, M.R., 2005. On virtual work and stress in granular media. Int. J. Solids Struct. 42, 3773–3793]. The authors follow closely this debate and try, with this paper, to provide a platform where the various viewpoints could find their position. We consider an ensemble of rigid, arbitrarily shaped grains as a set with structure. We establish a basic mathematical framework which allows to express the balance laws and the action–reaction laws for the discrete system in a “global” form, through the concepts of “part”, “granular surface”, “separately additive function” and “flux”. The independent variable in the balance laws is then the arbitrary part of the assembly rather than the single grain. A parallel framework is constructed for Cosserat continua, by applying the axiomatics established by [Noll, W., 1959. The foundation of classical mechanics in the light of recent advances in continuum mechanics. In: The axiomatic method, with special reference to Geometry and Physics, North-Holland Publishing Co., Amsterdam pp. 266–281, Gurtin, M.E., Williams, W.O., 1967. An axiomatic foundation of continuum thermodynamics. Arch. Rat. Mech. Anal. 26, 83–117, Gurtin, M.E., Martins, L.C., 1976. Cauchy’s theorem in classical physics. Arch. Rat. Mech. Anal. 60, 305–324]. The comparison between the two realisations suggests the microscopic interpretation for some features of Cosserat Mechanics, among which the asymmetry of the Cauchy-stress tensor and the couple-stress.     

ROBUST CONTROL OF VORTEX-INDUCED VIBRATION OF A RIGID CYLINDER SUPPORTED BY AN ELASTIC BEAM USING μ -SYNTHESIS

For lightweight and flexible structures, it is important to suppress the vibrations induced by interactions between fluid and structures. This paper presents the robust control of the vortex-induced vibration of a rigid circular cylinder supported by an elastic cantilever beam in which the fluid force is considered as an external excitation on the structure. For the problems considered here, the excitation frequency is assumed to be equal to the natural frequency of the structure or the “lock-in” frequency. The natural frequencies of this analytical model are calculated by using the modal analysis method and then modal coordinates are introduced to obtain the state equations of the structural system. A pair of piezoelectric devices fixed under the base plate, on which the elastic beam is clamped, were used as actuators. A robust controller satisfying the nominal performance and robust performance is designed using μ -synthesis theory based on the structured singular value. Simulation and experiment were carried out with the designed controller and the effectiveness of the robust control strategy was verified by both experimental and simulation results.     

A new Finite Element Method for magneto-dynamical problems: two-dimensional results

A mixed Lagrange finite element technique is used to solve the Maxwell equations in the magneto-hydrodynamic (MHD) limit in an hybrid domain composed of vacuum and conducting regions. The originality of the approach is that no artificial boundary condition is enforced at the interface between the conducting and the insulating regions and the non-conducting medium is not approximated by a weakly conducting medium as is frequently done in the literature. As a first evaluation of the performance of the method, we study two-dimensional (2D) configurations, where the flow streamlines of the conducting fluid are planar, i.e., invariant in one direction, and either the magnetic field (“magnetic scalar” case) or the electric field (“electric scalar” case) is parallel to the invariant direction. Induction heating, eddy current generation, and magnetic field stretching are investigated showing the usefulness of finite element methods to solve magneto-dynamical problems with complex insulating boundaries.     

L''exactitude du rendement des machines agricoles

Precision of the working height, or depth, of earth-moving equipment and other farm machinery can have a marked effect on the quality of the operation. The main factors affecting a machine's performance in maintaining the correct working height are its geometric parameters and the soil surface upon which it operates. The soil surface profile is defined by the “mean slope”, by the “root-mean-square” (RMS) of the deviations from the mean slope, and by the wavelengths calculated by Fourier analysis. The shortest wavelength with an amplitude above 1 cm was used in this study to find the effect of the soil surface waves on the accuracy of farm machinery operations. The machine's geometric parameters affecting its accuracy are its wheelbase and the lengthwise location of the working point (above or under ground) in relation to the wheels. A computer simulation analysis showed that the minimum deviations from the required height are found at the wheels of the machine. The deviations increased at the middle of the machine's span and rose steeply outside the span. The shorter the wheel-span of the machine relative to the wavelengths, the smaller the deviations will be. Smoothed surfaces have longer wavelengths and smaller deviations and as a result, higher accuracy of the working height, or depth, of the machines working on them.     

Relativistic electron transport and confinement within charge-insulated, mass-limited targets

We present experimental results on the interaction of short-pulse ultra-high-intensity laser beams with small size (“mass-limited”) targets. Several diagnostics (X-ray spectroscopy, K_α and optical imaging of target rear side) have been simultaneously used in order to characterize the laser-generated fast electron transport and energy deposition into the target material. Our results show that fast electrons are effectively confined inside the target by the induced space charge. This electrostatic confinement opens new opportunities to create “Warm Dense Matter” states characterized by solid-state density and temperatures of the order of a few tens of eV.     

Steady shear banding in complex fluids

Shear banding (SB) is manifested by the abrupt “demixing” of the flow into regions of high and low shear rate. In this paper, we first relate analytically the rheological parameters of the fluid with the range of shear rates and stresses of SB occurrence. For this, we accept that the origin of shear banding is constitutive, and adopt a non-linear viscoelastic expression able to accommodate the double-valuedness of the stress with flow intensity, under certain conditions. We then implement the model for the case of pressure driven flow through a cylindrical pipe; we derive approximate expressions for the velocity profile in the two-banded regions (core and outer annular), the overall throughput in the presence or absence of “spurt”, and the radial location limits of the shear rate discontinuity.     

Simply approximate estimation of local failure position of a free-free slender shell

Dynamic plastic failure characteristics of a space free-free slender shell subjected to intense dynamic loading of suddenly applied pressure unsymmetrical triangle distributed along its span was studied. Both rigid perfectly plastic (r-p-p) analytical method and finite element method based elastic perfectly plastic (e-p-p) material idealization and shell element model were adopted to predict the local failure position in the structure. It was shown that both r-p-p and e-p-p model could estimate a plastic “kink” taking place in the slender shell, which reflects the strain localization of deformation. The comparison for the position of “kink” predicted by using r-p-p and e-p-p methods is found to be reasonable good.