Prediction Of Shear Stress Research Articles

Interlaminar stress analysis with a new Multiparticle modelization of Multilayered Materials (M4)

We propose a new model for calculating the interlaminar stresses in a multilayered medium. It is well known that the classical analysis methods for multilayered materials do not provide sufficient information about the interlaminar stresses that cause damage. The model we propose describes the multilayered medium as a surface with as many particles in each point of the surface as the number of layers in the medium. For this reason, it is referred to as a Multiparticle Model of Multilayered Materials (M4 in the following text). It permits the direct calculation of the stresses as interactions between particles at the same point of the surface. In a certain sense, the M4 model belongs to the same family as the well known shear-lag model (Garett and Bailey, J. Mater. Sci., 12, 1977; 1 Macquire et al., Composites Polymers, 5, 1992 2) and Pagano's global-local model (Pagano and Soni, Int.J. Solids Structures, 19, 207–228, 1983 3). It is more general than the shear-lag approach and simpler than the Pagano global-local model. In this paper we present the equations of the model and establish an analytical solution for a cylindrical bending multilayered plate problem. Through this example, we show that we may obtain good predictions of displacements and shear stresses and that the M4 model is an appropriate tool for the study of interlaminar stresses.

Eight-noded zig-zag element for deflection and stress analysis of plates with general lay-up

Abstract Based on the kinematics of a third-order zig-zag plate model accounting for the zero transverse shear stress conditions at upper and lower free surfaces irrespective for the lay-up, a eight-noded, 56 d.o.f. curvilinear plate element is formulated and tested. Nodal parameters are membrane displacements, transverse shear rotations, deflections, slopes and curvatures for corner nodes, membrane displacements and transverse shear rotations for mid-side nodes. Suitably defining the parameters appearing in the plate model, some higher-order plate elements, comprising previous zig-zag elements and some smeared-laminate plate elements, are obtained as particular cases. The benchmark problem is the cylindrical bending of simply-supported, symmetric and antisymmetric cross-ply plates under a sinusoidally distributed transverse loading. The body of numerical results is as follows. Closed-form solutions for the present plate model, together with the ones that can be particularized in it, are given that provide analytical comparison results. Finite element results by the present element and by the ones that are particularized in it are compared with closed-form solutions and with the exact three-dimensional elasticity solution, available for this benchmark problem. A great importance of stress-free conditions appears when plates are thick and unsymmetric. This justify development of present element accounting for unsymmetry in the lay-up. The quadratic approximation makes the present element able to accurately predict stresses by integrating local equilibrium equations. Inclusion of the layerwise kinematics of zig-zag models allows for satisfactory predictions of transverse shear stresses via constitutive equations. Use of C 2 approximation for deflections, instead of C 1 approximation required for obtaining conforming elements, appear to little improve accuracy.

A Comparison of General Circulation Model Predictions to Sand Drift and Dune Orientations

The growing concern over climate change and decertification stresses the importance of aeolian process prediction. In this paper the use of a general circulation model to predict current aeolian features is examined. A GCM developed at NASA/Goddard Space Flight Center was used in conjunction with White`s aeolian sand flux model to produce a global potential aeolian transport map. Surface wind shear stress predictions were used from the output of a GCM simulation that was performed as part of the Atmospheric Model Intercomparison Project on 1979 climate conditions. The spatial resolution of this study (as driven by the GCM) is 4{degrees} X 5{degrees}; instantaneous 6-hourly wind stress data were saved by the GCM and used in this report. A global map showing potential sand transport was compared to drift potential directions as inferred from Landsat images from the 1980s for several sand seas and a coastal dune field. Generally, results show a good correlation between the simulated sand drift direction and the drift direction inferred for dune forms. Discrepancies between the drift potential and the drift inferred from images were found in the North American deserts and the Arabian peninsula. An attempt to predict the type of dune that would bemore » formed in specific regions was not successful. The model could probably be further improved by incorporating soil moisture, surface roughness, and vegetation information for a better assessment of sand threshold conditions. The correlation may permit use of a GCM to analyze {open_quotes}fossil{close_quotes} dunes or to forecast aeolian processes. 48 refs., 8 figs.« less

A Statistical Study of Rheological Models for Drilling Fluids

AbstractIn order to determine laminar friction losses of non-Newtonian drilling fluids it is standard practice to utilise a simple rheological model with parameter estimation via explicit solution of the required number of simultaneous equations. This limits the choice of available models and, together with the fitting procedure, frequently results in poor fits. Numerous alternative models have been proposed, but their worth has never been clearly demonstrated. Here we consider the rheological models to form the deterministic part of a stochastic model hence acknowledging that observed data arise from randomness due to the system. Parameter estimates are obtained by nonlinear least squares using data readings from eight standard Fann viscometer settings. Results are presented for 20 rheological models on 414 Fann viscometer data sets that encompass a variety of different drilling fluids. The goodness of fit of the models is assessed by comparing boxplots of the resulting residual mean square values. Several of the alternative models are shown to be consistently capable of excellent shear stress prediction over all of the shear rate range expected during drilling operations. The use of statistical methodology allows us to go beyond mere data relationship estimation: it permits the calculation of confidence intervals and tests of significance of functions of the model parameters, for example equivalent circulating density. The validity of such calculations relies on the extent to which the behaviour of the nonlinear least squares estimates approximates the asymptotic properties of being unbiased, normally distributed and minimum variance estimators. The estimation behaviour of the ‘best’ fitting models is analysed and a reparameterised form of the Sisko model is identified as having reasonable behaviour. Thus, despite the small data size, when using this model form the subsequent estimates, confidence intervals and tests of significance of functions of the model parameters can be confidently reported.

Reynolds stress closure applied to axisymmetric, impinging turbulent jets

A second-order, single-point closure model for calculating the transport of momentum in turbulent flows is extended to cover flows that are close to solid surfaces. In such flows the proximity of a solid boundary directly influences the fluctuating pressure field within the main body of the flow and leads to a dampening of velocity fluctuations normal to the wall. These effects are accommodated through the incorporation of an additional contribution in the modelled form of the redistributive fluctuating pressure term used in the Reynolds stress transport equation. Predictions of the extended closure model are compared with available data in configurations where an air jet impinges orthogonally onto a plane surface. The inclusion of the wall reflection model is shown to result in superior predictions of mean velocities, and normal and shear stresses. In particular, normal-to-wall velocity fluctuations and shear stresses are successfully damped resulting in agreement with observations.

Three-dimensional finite element analysis of thick laminated plates

A displacement-based, three-dimensional finite element scheme is proposed for analyzing thick laminated plates. In the present formulation, a thick laminated plate is treated as a three-dimensional inhomogeneous anisotropic elastic body. Particular attention is focused on the prediction of transverse shear stresses. The plane of a laminated plate is first discretized into conventional eight-node elements. Various through-thickness interpolation is then denned for different regions of the plate; layerwise local shape functions are used in the regions where transverse shear stresses are of interest, while an ad hoc global-local interpolation is used in the region where only the general deformation pattern is concerned. For satisfying the displacement compatibility between these two regions, a transition zone is introduced. The model incorporates the advantages of the layerwise plate theory and the single-layer plate theory. Details of formulation will be presented together with several numerical examples for demonstrating the proposed scheme.

Laminar flow hydrodynamics of rotary dynamics filters

Shear stresses have a strong effect on the filtration rate in dynamic filtration. The numerical simulation of fluid flow in a dynamic filter chamber has been investigated. The applied model describing flow of a Newtonian fluid in the laminar regime uses the Navier—Stokes equation form in cylindrical coordinates. Comparisons of the results of frictional torque and shear rate obtained from a simulation with experimental measurements confirmed the validity of the applied model as far as prediction of shear stresses at the filtration surface is concerned.

Charged network constitutive equation

We have considered a charged network theory as a model of polyelectrolytes. The charges are placed at the junctions. The formalism of a convected coordinate system is used to deduce the constitutive equation via the Helmholtz free energy. Steady viscometric and elongational flows as well as small-amplitude oscillatory flows are examined. The predicted shear stress is compared with experimental data and good agreement is achieved. The relation between elongational viscosity and viscometric functions is deduced. In small-amplitude oscillatory flow one recovers linear viscoelasticity.

Fundamental load transfer patterns for press-fit, surface-treated intramedullary fixation stems

To extend our understanding of the concentric cylinder idealization of a cementless hip stem, we used finite element analysis to study the effects of various types and amounts of surface treatments on the mechanical environment of the bone-stem interface for different load cases in the early post-operative situation. All analyses used no-tension interface conditions with various values of the frictional coefficient. We found that the shear stresses along the medial bone-stem interface were most sensitive to the type and amount of surface treatment, while the contact regions were relatively insensitive to the surface treatment. Consequently, the surface treatment had a negligible effect on the transfer of bending loads. By contrast, the axial load (when combined with a bending load) was transferred by shear stresses at the lateral stem tip for fully coated stems, but by shear stresses at the medial coating junction for partially coated stems. These findings therefore indicate that transfer of bending loads from the stem to the diaphysis cannot be controlled in the early post-operative situation by surface treatments, while transfer of axial loads can be controlled with the appropriate choice and distribution of a coating. In addition, the correspondence between the predicted shear stress distributions at the porous coating junction of partially coated devices and observed bone hypertrophy patterns that are apparently biased towards the medial aspect of the junction suggest that bone remodeling at the interface around porous coated hip implants may be initially stimulated by the development of small shear stresses.

On the electrokinetics of shear stress behavior in fluid‐mud suspensions

The variability of rheological properties in fluid‐mud suspensions is studied as a function of salinity and sediment concentration. It was found that the steady state shear stress increases exponentially with increasing sediment concentration and increases logarithmically by increasing the salinity of the suspension. An analytic model predicting shear stress as a function of electroviscous properties is developed. The model shows that the effect of salts in the suspension is to decrease the zeta potential by compressing the electric double layer and, thereby, elevating the shear stresses acting on the shearing planes at each particle‐fluid interface in the suspension. These stresses increase with the increase in salt content. The model incorporates the classical double‐layer theories of Gouy‐Chapman and the Helmholtz‐Smoluchowski theory for electrokinetics of charged particles. The model shows good correlation with experimental data at low sediment concentrations where the basic assumptions of the Gouy‐Chapman formulation are satisfied. At progressively higher sediment concentrations, there are increasingly larger departures between the model predictions and the experimental data due to violations of these basic assumptions. The advantages and limitations of the model are discussed.

Evaluation of rheological models and application to flow regime determination

Rheological models are frequently used to predict the shear stress-shear rate behavior of drilling fluids. However, none of these models can accurately predict the rheological behavior of all drilling fluids over all ranges of shear rates. In this study, the following rheological models were used to predict shear stress as a function of shear rate in several mud samples: Bingham Plastic, Power Law (2 point method and least-square method), Herschel-Bulkley and Robertson-Stiff. The first objective of this study was to identify the model that provided the best overall match of the experimentally observed rheological data. This was done by democratic ranking of the rheological models based on error analysis. The Robertson-Stiff model provided the best, and the Bingham Plastic model provided the worst overall prediction of rheological behavior. The second objective of the study was to develop a new method for determination of flow regimes in pipe flow using the Herschel-Bulkley and Robertson-Stiff models. The proposed method has been shown to predict the onset of turbulence in pipe flow more accurately than the conventional method for Bingham Plastic and Power Law models.

Discussion of “ Measurement and Prediction of Surface Shear Stress in Annular Flume ” by D. I. Graham, P. W. James, T. E. R. Jones, J. M. Davies, and E. A. Delo (September, 1992, Vol. 118, No. 9)

Discussion of “ <i>Measurement and Prediction of Surface Shear Stress in Annular Flume</i> ” by D. I. Graham, P. W. James, T. E. R. Jones, J. M. Davies, and E. A. Delo (September, 1992, Vol. 118, No. 9)

Closure to “ Measurement and Prediction of Surface Shear Stress in Annular Flume ” by D. I. Graham, P. W. James, T. E. R. Jones, J. M. Davies, and E. A. Delo (September, 1992, Vol. 118, No. 9)

Closure to “ <i>Measurement and Prediction of Surface Shear Stress in Annular Flume</i> ” by D. I. Graham, P. W. James, T. E. R. Jones, J. M. Davies, and E. A. Delo (September, 1992, Vol. 118, No. 9)

Dynamics of shearing in flocculating fine sediment suspensions

AbstractThe variability of rheological properties in cohesive sediment suspensions are studied and related to the flocculation process. It was found that the steady state shear stress increases exponentially with increasing sediment concentration and increases logarithmically by increasing the salinity of the suspension. The salinity dependence of the shear stress was correlated with changes in the floc‐size. These results reflect the dominant influence of fluid‐sediment interactions on the flocculation behavior of the suspension. An analytic model predicting shear stress as a function of the physical and electrochemical properties of the fine sediment suspension is developed.

Determination of tectonic stress field from fault slip data: Toward a probabilistic model

A model based on probability theory is proposed to determine the orientation of the tectonic stress field from fault slip and earthquake focal mechanism data. On the assumptions that (1) slip and shear stress direction on the fault plane coincide, and (2) measured slip direction and fault plane orientation are random variables following the von Mises and the Fisher distribution, respectively, the effects of measurement errors in both variables on stress field inversion are considered. The distribution of shear stress direction on the fault plane can also be approximately modeled by the von Mises distribution, with the concentration parameter varying from infinity to zero according to the orientation of the fault plane, the direction of the principal stress axes, and the stress shape parameter. Measurement errors in both slip direction and fault plane orientation give rise to misfit angles between the predicted shear stress and the measured slip direction even if the tectonic stress field is uniform. A new inversion method is proposed that takes both measurement errors simultaneously into account. This method makes it possible to evaluate statistically the extent and significance of the deviations of the stress field from uniformity, i.e., the likelihood that a given fault population originates from a constant tectonic stress state. For sufficiently large sample size, misfit angles should belong to a von Mises family if the stress field is uniform. A significant deviation from a von Mises distribution implies that the tectonic stress field is not uniform. A few examples of application of the new inversion method are presented, together with a comparison with the results obtained from different methods and an assessment of the uncertainties in the inverted stress field.

Best fit for differential constitutive model parameters to non-linear oscillation data

Non-linear, transient model parameters of non-linear constitutive equations can be fitted objectively with large amplitude oscillatory shear flow by minimizing the function ▪ where σ m J is the stress amplitude of the jth harmonic of the experimentally measured shear stress response and σ p J is the stress amplitude of the jth harmonic of the predicted shear stress. Minimizing this function gives unique, best fits for non-linear differential constitutive theories to the measured shear stress response of a low density polyethylene melt in large amplitude oscillatory shear.

Characterization of in vivo strain in the rat tibia during external application of a four-point bending load

This paper describes a technique for characterizing strains and stresses induced in vivo in the rat tibia during application of an external four-point bending load. An external load was applied through the muscle and soft tissue with a four-point bending device, to induce strain in a 11 mm section of the right tibiae of ten adult female Sprague-Dawley rats. Induced strains were measured in vivo on the lateral surface of the tibia. Inter-rat difference, leg positioning and strain gage placement were evaluated as sources of variability of applied strains. Beam bending theory was used to predict externally induced in vivo strains. Finite element analysis was used to quantify the magnitude of shear stresses induced by this type of loading. There was a linear relationship between applied load and induced in vivo strains. In vivo strains induced by external loading were linearly correlated ( R 2=0.87) with the strains calculated using beam bending theory. The finite element analysis predicted shear stresses at less than 10% of the longitudinal stresses resulting from four-point bending. Strains predicted along the tibia by finite element analysis and beam bending theory were well-correlated. Inter-rat variability due to tibial size and shape difference was the most important source of variation in induced strain (CV=21.6%). Leg positioning was less important (CV=9.5%).

Measurement and Prediction of Surface Shear Stress in Annular Flume

Cohesive sediment beds occur in a variety of natural and man‐made environments. A parameter that has a very significant influence on the sediment behavior is the critical shear stress. This is the shear stress at the sediment surface above which erosion will take place. The critical shear stress can be evaluated in the laboratory under conditions closely resembling those found in the field by use of an annular flume. The main purpose of the work described in this paper is to determine experimentally and numerically the velocity and surface shear stress fields generated by the flow of water in an annular flume. Very good agreement is found between measured circumferential velocity profiles, obtained by laser doppler anemometry, and profiles predicted by the computational fluid dynamics program HARWELL‐FLOW3D. Measurements of the bed and wall shear stresses are made using hot‐film probes and these also agree reasonably well with numerical predictions. Also of interest is the dependence of the sediment shear...

Local bridging to predict aerodynamic coefficients in hypersonic, rarefied flow

A computational method is given for the prediction of local pressure and viscous shear stress on windward surfaces of convex, axisymmetric or quasi-axisymmetric, hypersonic bodies in the transitional, rarefied flow regime. Overall aerodynamic forces and moments are computed by integration of the local quantities. The method is based on a correlation of local pressure and shear stress computed by the direct simulation Monte Carlo (DSMC) numerical technique for cold-wall, real-gas conditions and some supplemental data from low-density, hypersonic wind tunnels. Two-dimensional shapes and leeward surfaces are not included in the scope of the method as it is presented here. Results are compared with DSMC and viscous shock layer computations for both local and overall coefficients. Also included are sphere and blunt cone drag obtained from both computation and experiment, as well as lift and pitching moment coefficients for the NASA Aeroassist Flight Experiment vehicle at various angles of attack. It appears that the method presented here will prove adequate for relatively bluff bodies approximately defined by wetted length-to-nose radius ratios of less than 10.

Reissner’s New Mixed Variational Principle Applied to Laminated Cylindrical Shells

Reissner’s new mixed variational theorem, which allows independent interpolation, through the thickness, of the three transverse stresses besides that of the three displacements, is applied here to derive a higher-order theory of laminated orthotropic cylindrical shells. The accuracy of the theory is verified by comparison with three-dimensional elasticity solutions. It is shown that Reissner’s principle does not directly lead to accurate transverse shear stress predictions, but requires the use of the equilibrium equations of three-dimensional elasticity as is common in the conventional displacement approach.