Shear Rigidity Research Articles

Particle mobility between two planar elastic membranes: Brownian motion and membrane deformation

We study the motion of a solid particle immersed in a Newtonian fluid and confined between two parallel elastic membranes possessing shear and bending rigidity. The hydrodynamic mobility depends on the frequency of the particle motion due to the elastic energy stored in the membrane. Unlike the single-membrane case, a coupling between shearing and bending exists. The commonly used approximation of superposing two single-membrane contributions is found to give reasonable results only for motions in the parallel direction, but not in the perpendicular direction. We also compute analytically the membrane deformation resulting from the motion of the particle, showing that the presence of the second membrane reduces deformation. Using the fluctuation-dissipation theorem we compute the Brownian motion of the particle, finding a long-lasting subdiffusive regime at intermediate time scales. We finally assess the accuracy of the employed point-particle approximation via boundary-integral simulations for a truly extended particle. They are found to be in excellent agreement with the analytical predictions.

Large deflection and rotation of Timoshenko beams with frictional end supports under three-point bending

Three-point bending of a beam is studied based on the Timoshenko beam theory. Large deflection and large rotation of a beam resting on simple supports with friction are calculated for a concentrated force acting at the midspan. Using the Lagrangian kinematic relations, a system of non-linear differential equations are obtained for a prismatic shear-deformable Timoshenko beam. Exact solutions for the deflection, horizontal displacement, and rotation of cross-section are derived analytically. Two deflections of small and large scale exist under three-point bending. The solutions corresponding to linearized model coincide with the well-known solutions to the classical Timoshenko beams. Numerical calculations are carried out to show the effect of the important parameters such as shear rigidity of the beam and the coefficient of friction at the contact position between the beam and supports on the deflection. The load–deflection curves are graphically presented. A comparison of large deflections and large rotations with their classical counterparts and with experimental data is made. The obtained results are useful in safety design of linear and non-linear beams subject to three-point bending.

Analysis of a two-way tension-shear coupling in woven fabrics under combined loading tests: Global to local transformation of non-orthogonal normalized forces and displacements

Dependence of shear rigidity of woven fabrics on yarn pre-tension has been reported in the recent literature, however some conflict regarding the trend of this effect is observed. Sources of this conflict are discussed and resolved in the present article using a new characterization framework and a custom-design combined loading fixture. It is shown that in order to correctly characterize the tension-shear coupling behavior in woven fabrics, instead of using global measured data, local normalized forces and displacements should be driven via a non-orthogonal transformation procedure, while considering kinematic force coupling in the setup. In addition, the effect of fabric shear on the tensile behavior of yarns has been investigated, suggesting that the coupling under question is in fact two-way. In particular, results revealed that applying yarn pre-tension increases the shear resistance of the fabric reinforcement, while the tensile behavior of the material becomes more compliant when undergoing shear deformation.

Flexural Rigidity and Shear Stiffness of Flagella Estimated from Induced Bends and Counterbends

Motile cilia and flagella are whiplike cellular organelles that bend actively to propel cells or move fluid in passages such as airways, brain ventricles, and the oviduct. Efficient motile function of cilia and flagella depends on coordinated interactions between active forces from an array of motor proteins and passive mechanical resistance from the complex cytoskeletal structure (the axoneme). However, details of this coordination, including axonemal mechanics, remain unclear. We investigated two major mechanical parameters, flexural rigidity and interdoublet shear stiffness, of the flagellar axoneme in the unicellular alga Chlamydomonas reinhardtii. Combining experiment, theory, and finite element models, we demonstrate that the apparent flexural rigidity of the axoneme depends on both the intrinsic flexural rigidity (EI) and the elastic resistance to interdoublet sliding (shear stiffness, ks). We estimated the average intrinsic flexural rigidity and interdoublet shear stiffness of wild-type Chlamydomonas flagella in vivo, rendered immotile by vanadate, to be EI = 840 ± 280 pN⋅μm2 and ks = 79.6 ± 10.5 pN/rad, respectively. The corresponding values for the pf3; cnk11-6 double mutant, which lacks the nexin-dynein regulatory complex (N-DRC), were EI = 1011 ± 183 pN·μm2 and ks = 39.3 ± 6.0 pN/rad under the same conditions. Finally, in the pf13A mutant, which lacks outer dynein arms and inner dynein arm c, the estimates were EI = 777 ± 184 pN·μm2 and ks = 43.3 ± 7.7 pN/rad. In the two mutant strains, the flexural rigidity is not significantly different from wild-type (p > 0.05), but the lack of N-DRC (in pf3; cnk11-6) or dynein arms (in pf13A) significantly reduces interdoublet shear stiffness. These differences may represent the contributions of the N-DRCs (∼40 pN/rad) and residual dynein interactions (∼35 pN/rad) to interdoublet sliding resistance in these immobilized Chlamydomonas flagella.

Buckling of Standing Tapered Timoshenko Columns with Varying Flexural Rigidity Under Combined Loadings

The stability of a nonuniform column subjected to a tip force and axially distributed loading is investigated based on the Timoshenko beam theory. An emphasis is placed on buckling of a standing column with varying cross-section and variable material properties under self-weight and tip force. Four kinds of columns with different taper ratios are analyzed. A new initial value method is suggested to determine critical tip force and axial loading at buckling. The effectiveness of the method is confirmed by comparing our results with those for Euler–Bernoulli columns for the case of sufficiently large shear rigidity. The effects of shear rigidity, taper ratio, and gravity loading on the buckling loads of a heavy standing or hanging column are examined.

Experimental and analytical behavior of sandwich composite beams: Comparison of natural and synthetic materials

In this study, the flexural behavior of sandwich composite beams made of fiber-reinforced polymer (FRP) skins and light-weight cores are studied. The focus is on the comparison of natural and synthetic fiber and core materials. Two types of fiber materials, namely glass and flax fibers, as well as two types of core materials, namely polypropylene honeycomb and cork, are considered. A total of 105 small-scale sandwich beam specimens (50 mm wide) were prepared and tested under four-point bending. Test parameters were fiber types (flax and glass fibers), core materials (cork ad honeycomb), skin layers (0, 1, and 2 layers), core thicknesses (6–25 mm), and beam spans (150 and 300 mm). The load–deflection behavior, peak load, initial stiffness, and failure mode of the specimens are evaluated. Moreover, the flexural stiffness, shear rigidity, and core shear modulus of the sandwich composites are computed based on the test results of the two spans. An analytical model is also implemented to compute the flexural stiffness, core shear strength, and skin normal stress of the sandwich composites. Overall, the natural fiber and cork materials showed a promising and comparable structural performance with their synthetic counterparts.

FINITE ELEMENT ANALYSIS OF CONCRETE FILLER INFLUENCE ON DYNAMIC RIGIDITY OF HEAVY MACHINE TOOL PORTAL

Virtual testing of portal machine tool has been carried out with the help of finite elements method (FEM). Static, modal and harmonic analyses have been made for a heavy planer. The paper reveals influence of concrete filler on machine tool dynamic flexibility. A peculiar feature of the simulation is concrete filling of a high-level transverse beam. Such approach oes look a typical one for machine-tool industry. Concrete has been considered as generalized material in two variants. It has been established that concrete application provides approximately 3-fold increase in machine tool rigidity per each coordinate. In this regard it is necessary to arrange closure of rigidity contour by filling all the cavities inside of the portal. Modal FEA makes it possible to determine that concrete increases comparatively weakly (1.3–1.4-fold) frequencies of resonance modes. Frequency of the lowest mode rises only from 30.25 to 42.86 Hz. The following most active whole-machine eigenmodes have been revealed in the paper: “Portal pecking”, “Parallelogram” and “Traverse pecking”. In order to restrain the last mode it is necessary to carry out concrete filling of the traverse, in particular. Frequency-response characteristics and curves of dynamic rigidity for a spindle have been plotted for 0–150 Hz interval while using harmonic FEM. It has been determined that concrete increases dynamic machine tool rigidity by 2.5–3.5-fold. The effect is obtained even in the case when weakly damping concrete (2 %) is used. This is due to distribution of vibrational energy flow along concrete and along cast iron as well. Thus energy density and vibration amplitudes must decrease. The paper shows acceptability for internal reinforcement of high-level machine tool parts (for example, portal traverses) and fillers are applied for this purpose. Traverse weighting is compensated by additional torsional, shear and bending rigidity. The machine tool obtains the possibility for rough intermittent cutting even at resonance frequencies. Complete concrete filling of portal cavities is definitely a positive action for static and dynamic properties of the machine tool.

Exact solution of Eringen's nonlocal integral model for bending of Euler–Bernoulli and Timoshenko beams

Despite its popularity, differential form of Eringen nonlocal model leads to some inconsistencies that have been demonstrated recently for the cantilever beams by showing the differences between the integral and differential forms of the nonlocal equation, which indicates the importance and necessity of using the original integral model.With this motivation, this paper aims to derive the closed-form analytical solutions of original integral model for static bending of Euler Bernoulli and Timoshenko beams, in a simple manner, for different loading and boundary conditions. For this purpose, the Fredholm type integral governing equations are transformed to Volterra integral equations of the second kind, and Laplace transformation is applied to the corresponding equations.The analytical expressions of the beam deflections which are obtained through the utilization of the proposed solution technique are validated against to those of other studies existing in literature. Furthermore, for all boundary and loading conditions, in contrast to the differential form, it is clearly established that the integral model predicts the softening effect of the nonlocal parameter as expected. In case of Timoshenko beam theory, an additional term that includes the nonlocal parameter is introduced. This extra term is related to the shear rigidity of the beam indicating that the nonlocal effect manifests itself via not only bending, but also shear deformation.

Shear behavior of a shear thickening fluid-impregnated aramid fabrics at high shear rate

Shear-thickening fluid-impregnated aramid (STF-im-AR) fabrics have been manufactured for advanced soft body armor applications for which they provide improved ballistic and stab resistances. It is not yet clear whether or not such improvements can be attributed solely to the STF. In this study, the rate-dependent behavior of an STF-im-AR fabric was investigated at the fabric level, using uniaxial tensile, bias-extension, and picture-frame tests. Rate-dependent behavior of the STF-im-AR fabric was observed during uniaxial tensile testing; however, the effect of the STF treatment was slight and consistent with only the inherent effect of the polymeric nature of its constituent fibers. The shear rigidity of the STF-im-AR fabric increased, due to the presence of the STF and the sensitivity of the fabric's shear stiffness to changes in the shear strain rate also increased slightly. This rate-sensitive shear stiffness of STF-im-AR fabrics may contribute to improved ballistic and stab resistances.

Size-dependent effects on critical flow velocity of fluid-conveying microtubes via nonlocal strain gradient theory

Size-dependent Timoshenko and Euler–Bernoulli models are derived for fluid-conveying microtubes in the framework of the nonlocal strain gradient theory. The equations of motion and boundary conditions are deduced by employing the Hamilton principle. A flow-profile-modification factor, which is related to the flow velocity profile, is introduced to consider the size-dependent effects of flow. The analytical solutions of predicting the critical flow velocity of the microtubes with simply supported ends are derived. By choosing different values of the nonlocal parameter and the material length scale parameter, the critical flow velocity of the nonlocal strain gradient theory can be reduced to that of the nonlocal elasticity theory, the strain gradient theory, or the classical elasticity theory. It is shown that the critical flow velocity can be increased by increasing the flexural rigidity, decreasing the length of tube, decreasing the mass density of internal flow, or increasing the shear rigidity. The critical flow velocity can generally increase with the increasing material length scale parameter or the decreasing nonlocal parameter. The flow-profile-modification factor can decrease the critical flow velocity. The critical flow velocity predicted by classical elasticity theory is generally larger than that of nonlocal strain gradient theory when considering the size-dependent effect of flow.

Theoretical analysis of geometrical and mechanical parameters in plain woven structures

An analytic solution for the estimation of structural parameters and initial tensile modulus of plain woven fabrics under uniaxial tensile loading in their linear elastic domain of deformation is presented. For this purpose, a new approach in straight line geometry with a parallel segment to the fabric plane and an inclined segment at the weave intersection in 3D form is proposed which leads to the theoretical estimation of all the structural parameters of plain woven fabrics with saw-tooth geometry. Defining and applying of JJ2 Ratio in the model enable us to modify the geometrical model and estimate the value of structural parameters considering the history of samples influenced mainly by its manufacturing process. The strain energy method and Castigliano’s theorem are used for the mechanical analysis of the structure. The elasticity, bending, shearing, and compression rigidity of yarns are incorporated into the model. It has been shown that predicting the geometrical and mechanical parameters of woven fabrics before production are possible if and only if the crimp value of the fabrics can be estimated before their production. The proposed theory is validated and compared by applying into some experimental data and a previous model.

Discovery of Superconductivity in Hard Hexagonal ε-NbN.

Since the discovery of superconductivity in boron-doped diamond with a critical temperature (TC) near 4 K, great interest has been attracted in hard superconductors such as transition-metal nitrides and carbides. Here we report the new discovery of superconductivity in polycrystalline hexagonal ε-NbN synthesized at high pressure and high temperature. Direct magnetization and electrical resistivity measurements demonstrate that the superconductivity in bulk polycrystalline hexagonal ε-NbN is below ∼11.6 K, which is significantly higher than that for boron-doped diamond. The nature of superconductivity in hexagonal ε-NbN and the physical mechanism for the relatively lower TC have been addressed by the weaker bonding in the Nb-N network, the co-planarity of Nb-N layer as well as its relatively weaker electron-phonon coupling, as compared with the cubic δ-NbN counterpart. Moreover, the newly discovered ε-NbN superconductor remains stable at pressures up to ∼20 GPa and is significantly harder than cubic δ-NbN; it is as hard as sapphire, ultra-incompressible and has a high shear rigidity of 201 GPa to rival hard/superhard material γ-B (∼227 GPa). This exploration opens a new class of highly desirable materials combining the outstanding mechanical/elastic properties with superconductivity, which may be particularly attractive for its technological and engineering applications in extreme environments.

Modeling, Analysis, and Behavior of Load-Carrying Precast Concrete Sandwich Panels

AbstractThis paper investigates the behavior of precast concrete sandwich panels (PCSPs) made with truss shear connectors, which accounts for partial shear interaction. A theoretical model is developed based on variational principles and equations of equilibrium that account for the axial and bending rigidities of reinforced concrete (RC) layers and their potential cracking, the shear and normal rigidities of the insulation layer, and the elastic flexibility of the diagonal truss connectors. This layered modeling approach is general and can be used to describe the structural behavior under various loading patterns and boundary conditions, with the influence of the partial shear interaction as an automatic outcome of the analysis. As such, it provides a better and a more reliable tool than other existing simplified models in the literature for describing the complex structural behavior of PCSPs. A parametric study is presented, which investigates key parameters in the design of concrete sandwich panels, su...

Surface waves in granular phononic crystals.

The existence of surface elastic waves at a mechanically free surface of granular phononic crystals is studied. The granular phononic crystals are made of spherical particles distributed periodically on a simple cubic lattice. It is assumed that the particles are interacting by means of normal, shear, and bending contact rigidities. First, Rayleigh-type surface acoustic waves, where the displacement of the particles takes place in the sagittal plane while the particles possess one rotational and two translational degrees of freedom, are analyzed. Second, shear-horizontal-type waves, where the displacement of the particles is normal to the sagittal plane while the particles possess one translational and two rotational degrees of freedom are studied. The existence of zero-group-velocity surface acoustic waves of Rayleigh type is theoretically predicted and interpreted. A comparison with surface waves predicted by the reduced Cosserat theory is performed, and some limitations of the latter are established.

Improvement of squeezing ground prediction and monitoring capabilities for Mount Isa Mines Northern 3500 orebody

This paper investigates readily incorporable improvements to the identification of squeezing ground conditions and the determination of the depth of movement for Mount Isa Copper Operations’ Northern 3500 (MICO N3500) orebody. Numerical modelling using the boundary element method (BEM) indicated that the current use of elastic material properties to calculate the rockwall condition factor and predict tunnel squeezing is appropriate, as no apparent benefit was gained by employing elastoplastic material properties or including the tunnel void geometry. Further analysis using the finite element method indicated that complex, large-scale models would be required to make meaningful improvement on the elastic BEM model. However, due to large time and computational overheads such models are not practical within the site’s engineering workflow. In conjunction with numerical modelling, a prototype monitoring device was also developed to address the problem of rigid instrument shear and inspection camera obstruction when determining the depth of movement in a squeezing rockmass. The reverse downhole probe device will allow distance measurement and a live video feed to be returned to the excavation surface by taking advantage of stable ground beyond the excavation zone of influence and using a thin, flexible cable to transmit power and data.

A case study in quantitative interpretation ambiguity, lambda-mu-rho, and rock-physics modeling in the Otway Basin, Australia

A rock-physics study and AVO modeling study have been completed to assist in the interpretation of seismic amplitude and AVO anomalies in the Shipwreck Trough of the offshore Otway Basin of southeastern Australia. Elastic log data, core data (both full and sidewall), and associated thin-section analysis of composition and texture were available on several wells, and these data are important in calibrating proposed rock-physics models that suggest that incorporating cement is critical to understanding anomalies in seismic and measured log data. Lithoprobability volumes based on conventional interpretation paradigms, such as low VP/VS values indicating gas presence, that do not incorporate an understanding of rock physics lead to biased interpretations. Ratios in particular can be misleading because there is ambiguity about whether an anomalous ratio is driven by the numerator or denominator. As a classic gas indicator, low VP/VS values are interpreted to be driven by a decrease in VP associated with gas replacing brine in a rock. Using Lamé impedance terms λρ and μρ, however, provides an alternative interpretation template that does not use ratios and can improve insight into rock properties. As in this recent case study, using lambda-mu-rho (LMR) can be an important tool when shear velocity has increased relative to compressional velocity, irrespective of any pore-fluid change. In the reservoir rocks of the Shipwreck Trough, low VP/VS in both gas-saturated and brine-filled sandstone is caused by quartz cement. This presents a substantial challenge to the use of a standard rock-physics template. In LMR space, however, low VP/VS data points clearly are characterized by high shear rigidity — an important point to recognize and incorporate into AVO interpretation workflows.

Determination of Shear Center of Arbitrary Cross-Section

In structural analysis, it is often necessary to determine the geometrical properties of cross section. The location of the shear center is greater importance for an arbitrary cross section. In this study, the problems of coupled shearing and torsional were analyzed by using the finite element method. Namely, the simultaneous equations with respect to the warping, shear deflection, angle of torsion and Lagrange’s multipliers are derived by finite element approximation. Solving them numerically, the matrix of the shearing rigidity and torsional rigidity is obtained. This matrix indicates the coupled shearing and torsional deflection. The shear center can be obtained determining the coordinate axes so as to eliminate the non-diagonal terms. Several numerical examples are performed and show that the present method gives excellent results for an arbitrary cross section.

PTT/Tencel/Cotton 친환경 MVS 혼방사 편성물의 물성에 관한 연구 (II)

This paper investigated the wearing performance of knitted fabrics made of air vortex yarns using PTT/tencel/cotton fibres in comparison with ring and compact yarns for emotional garment. Wicking property of knitted fabric made of MVS yarns was worse than those by ring and compact yarns, however, drying property of knitted fabric made of MVS yarns was better than those by ring and compact yarns, which was explained as more water vapor transport due to larger openness between fibres in the MVS yarns than those in the ring and compact yarns. Thermal conductivity of knitted fabric made of MVS was lower than those of ring and compact yarns and maximum heat flow(Q_max) at the transient state of MVS knitted fabric was lower than those of ring and compact yarns, which may be attributed to MVS yarn structure that has parallel fibres in the core part of the yarn and fasciated fibre bundles on the sheath part with roughness on the yarn surface. However, pilling of MVS knitted fabric was better than those by ring and compact yarns, which was caused by less and shorter hairy fibres protruded from MVS yarn surface than those of ring and compact yarns. It was observed that tactile hand of MVS yarn knitted fabrics was stiffer than those of ring and compact yarns knitted fabrics. It was explained by low extensibility and compressibility and high bending and shear rigidities of the MVS yarn knitted fabrics, which resulted in bad wearing performance of MVS knitted fabric.

Revealing spatially heterogeneous relaxation in a model nanocomposite.

The detailed nature of spatially heterogeneous dynamics of glycerol-silica nanocomposites is unraveled by combining dielectric spectroscopy with atomistic simulation and statistical mechanical theory. Analysis of the spatial mobility gradient shows no "glassy" layer, but the α-relaxation time near the nanoparticle grows with cooling faster than the α-relaxation time in the bulk and is ∼20 times longer at low temperatures. The interfacial layer thickness increases from ∼1.8 nm at higher temperatures to ∼3.5 nm upon cooling to near bulk Tg. A real space microscopic description of the mobility gradient is constructed by synergistically combining high temperature atomistic simulation with theory. Our analysis suggests that the interfacial slowing down arises mainly due to an increase of the local cage scale barrier for activated hopping induced by enhanced packing and densification near the nanoparticle surface. The theory is employed to predict how local surface densification can be manipulated to control layer dynamics and shear rigidity over a wide temperature range.

Friction and wear behavior of linear standing-wave ultrasonic motors with V-shape transducers

Coulomb friction model is modified with considering the preliminary distance of rigid bristles and shear stiffness of the contact surface. The degeneration in friction drive and wear behavior induced by nonlinear contact (i.e., impact, intermittent, and fretting) is outlined. Wear tests of LUSMs with V-shape transducers are conducted by a homemade reciprocating apparatus. Results show that chemical inertness, thermotolerance, elasticity as well as surface topography are critical for the contact interface of LUSMs A systematic approach involving, for instance, dynamic contact, friction model, and wear behavior provides new perspectives in improving service performances and promoting practical applications.