Journal of Engineering Mechanics

This study accurately predicts cases of turbulent flow around a surface-mounted two-dimensional rib of varying length. The numerical method employs a finite-difference scheme for integrating the elliptic Reynolds-averaged Navier-Stokes equations and the continuity equation. The two-equation k − ε turbulence model is employed to simulate the turbulent transport quantities and solve the problem. The near-wall regions of the separated sides of the rib are resolved by a near-wall model in a two-layer approach instead of the wall-function approximation. Computations for flow over a surface-mounted rectangular rib are conducted for varying rib lengths. Results indicate that upstream of the obstacle the length of the recirculating region remains unchanged with varying rib length, while the downstream length of the recirculating region is a strong function of rib length and changes nearly linearly as B/H varies from 0.1 to 4.0. Reattachment on top of the rib, owing to its increasing length, affects the downstream boundary layer development.

The purpose of this paper is to derive and apply the relationships of the dynamic substructure synthesis method, based on the subregion variational principle of elastodynamics in discrete form. Two theorems are derived for discretized systems and are used to demonstrate the interface compatibility condition of dynamic substructure synthesis. This enables the dynamic substructure synthesis method to be derived from the subregion variational principle. A complete modal expansion is used to derive the residual modes for both the free and fixed interface methods. The alternative formulations of the hybrid, free interface, and fixed interface methods, as well as Guyan-Irons reduction, are shown by coordinate transformations to be degenerate cases. These cases are all reasonable representations of the Rayleigh-Ritz method, and if they use constraint modes and/or attachment modes, good convergence can be assured because the static modes are included in the substructure reduction. The relationships between these cases are explored, and illustrative examples are solved.

Dynamic buckling properties of simply supported columns under axial fluid-solid slamming are experimentally investigated in this study. By observing the elastic-plastic responses of columns, the dynamic buckling criterion and the dynamic plasticity criterion of columns are defined and the relevant critical impulses are determined. The effect of the slenderness ratio of the column on the elastic-plastic dynamic buckling properties is also examined. The dynamic buckling characteristics of fluid-solid slammed columns are compared and discussed with respect to those of columns under solid-solid impact. It is found that they are different from those of columns subjected to either impulsive impact or impact owing to suddenly applied load.

An experimental stretch bending study is presented in this paper. A total of 29 tests on 2 m long rectangular hollow section aluminum specimens were performed in a purpose-built stretch bending rig. The tests were carried out under different tensile force combinations, or tensile sequences, in order to investigate the influence of the force on certain response parameters. Stretch bending is an important industrial forming process, and die force, sagging, and springback are thus considered the most relevant response parameters. The tests show that the sagging is very sensitive to the applied tensile sequence. Furthermore, a close correlation between sagging development and strain evolution is observed. The springback is controlled by the tensile force level immediately before unloading. Finally, the difference in response between two tests performed with different constant, tensile force levels is insignificant.

It is important to understand the rheological properties of an extrudate of short fiber-reinforced cementitious (SFRC) composites to achieve a successful extrusion of SFRC composites. This paper presents the preliminary results on the study of the rheology field of SFRC extrudate. The paper started with the analysis of cementitious flows in a shallow flight extruder in which the height of the flight to the width of the channel ratio is small (H/W < 0.1). The fresh cementitious flow inside was considered as a 2D steady shear flow with nonlinear viscoelastic properties. By the fact that the Deborah number is small for the cementitious flow in an extruder, the constitutive equation of “retarded-motion-expansion” was adopted. The formula of the flow volume rate for a shallow flight screw extruder was derived and numerically solved by the finite-difference method. The velocity profiles and pressure gradient of the flow were presented. Then, a correction factor was used to modify the obtained results for the case of the deep flight screw extruder (H/W > 0.1). The differences between the results predicted by the Newtonian theory and those by the nonlinear viscoelastic theory were also investigated and analyzed.

Tangent stiffness equations for a beam-column, which is subjected to either uniformly or sinusoidally distributed lateral loads, are presented. The equations have been derived by differentiating the slope-deflection equations under axial forces for a member. Thus, the tangent stiffness equations take into consideration axial forces, bowing effect, and laterally distributed loads. As a numerical example, elastic buckling behavior of parallel chord latticed beams with laterally distributed loads is investigated to compare the results obtained from the present method with those from the conventional matrix method in which the distributed loads are considered as a series of concentrated loads at additional intermediate nodes of a member. Furthermore, buckling tests were carried out to confirm the equations derived as well as to clarify the buckling behavior of space frame structures. In conclusion, it can be said that the new equations can provide a good efficient way of estimating the equilibrium paths and buckling loads. They can also lead to a significant savings in core storage and computing time required for the analysis of space frame structures.

A model is presented to determine the threshold shear stress for noncohesive sediment (uniform and nonuniform) motion on horizontal and stream-wise sloping sedimentary beds, under a unidirectional steady-uniform streamflow. Hydrodynamic and particle-mechanic forces on a solitary sediment particle, resting over a sedimentary bed under the slip-spinning condition, are analyzed including the effect of turbulent fluctuations. Hydrodynamic forces such as drag, shear lift, and Magnus lift are taken into consideration. The drag coefficient is determined using an empirical formula. The inclusion of Magnus lift is significant because spherical particles spin just before dislodging downstream from their original position due to the differential hydrodynamic force along the vertical. The experimental data of sediment threshold are used to calibrate the model making the lift coefficient as a free parameter. The dependency of normalized threshold shear stress on particle parameter for various angles of repose and stream-wise bed slopes is presented graphically. The results obtained using the present model are compared with the curves proposed by different investigators and the experimental data of sediment (uniform and nonuniform) threshold for horizontal and stream-wise sloping beds.

This paper develops a model to simulate the distributed thermal cracking of concrete structures with frictional constraint. This model is developed primarily for the thermal cracking asphalt-concrete (AC) pavement structures; however, with some modifications, it is also applicable to similar problems such as shrinkage cracking of concrete and cracking of reinforced concrete in uniaxial tension. This model reflects the multiscale nature of these problems: microcracking or damage on the mesoscale and localization or redistribution on the macroscale. Randomly distributed fictitious cracks are introduced to represent the inhomogeneities and damage in the material at the mesoscale. Friction is recognized as the mechanism leading to stress redistribution and, therefore, damage localization on the macroscale. When the problem is assumed to be 1D and Coulomb friction is used, a semianalytical numerical scheme is developed. The formation of stress-free open cracks is due to the combination of continuous crack growth and unstable jumps, which involve a nonlinear stability analysis. Equilibrium solutions and stability conditions are given in the paper. Displacement controlled analysis is used to follow the unstable equilibrium path after the structure has lost stability. Numerical simulations clearly show that, with slight mesoscale inhomogeneities and in the presence of a constraining frictional force, microcracking or damage on the mesoscale localizes and finally leads to open cracks distributed at a spacing on the order of the macroscale.

Measurements show that silo wall pressures exhibit large fluctuations in time and space during discharge of the silo. This observation is important for the design of the silo wall because spatial pressure variations may impose substantial bending moments in the silo wall that otherwise may be small or vanishing due to the carrying ability of the membrane forces in the silo wall. Information about the stochastic properties of this pressure variation cannot be obtained from any existing continuum model for the silo medium flowing within the confinement of the silo. Therefore the modeling must presently be tied to statistical analyses of the empirical evidence combined with simple mechanical principles. This paper analyzes the same data set as that analyzed by Munch-Andersen et al., but on the basis of a completely different and physically less disputable stochastic pressure field model than the one considered by them. It is shown that an explicitly constructed gamma distribution type of field in equilibrium with itself fits well to the measurements made in the Swedish Karpalund silo.

The probability density function (PDF) and the mean up-crossing rate of the responses for nonlinear ship roll oscillations excited by random sea waves are examined. The excitation of random sea waves is approximated as white noise. The ship roll motion is described by a nonlinear stochastic differential equation that includes a nonlinear wave drag force and a nonlinear restoring moment. The PDF and mean up-crossing rate solution of the nonlinear oscillator are investigated with a new approximate method that expressed the PDF as an exponential function with an exponent in the form of a polynomial in the response variable and its derivative. A special measure is taken such that the Fokker-Planck-Kolmogorov equation is satisfied in the weak sense of integration with the assumed PDF. Numerical examples and a comparison with Monte Carlo simulation are given to show the effectiveness of the method in the study of randomly excited nonlinear ship roll motion.

This paper presents a simple a posteriori error estimator and an effective adaptive mesh refinement procedure for the symmetric Galerkin boundary element method. The “hypersingular residuals,” developed for error estimation in a standard collocation BEM, are extended to the symmetric Galerkin setting. This leads to the formulation of “Galerkin residuals,” which are intrinsic to the symmetric Galerkin boundary integral approach and form the basis of the present error estimation scheme. Several computational experiments are conducted to test both the accuracy and the reliability of the proposed technique. These experiments involve potential theory and various problem configurations including mixed boundary conditions, corners, and nonconvex domains. The numerical results indicate that reliable solutions to practical engineering problems can be obtained with this method.

In this technical note we analyze the free vibration of M undamped oscillators attached to an arbitrarily supported, linear elastic structure. Using the assumed-modes method with N component modes, the frequency equation governing the free vibration for this combined system is typically obtained as the characteristic determinant of a generalized eigenvalue problem of size (N + M) × (N + M). In this note we will show that by algebraically manipulating the generalized eigenvalue problem associated with free vibration, we can reduce it to a simple secular equation consisting of the sum of N terms, the roots or natural frequencies of which can be obtained either numerically or graphically. In addition, the resultant secular equation lends itself to the solution of an inverse problem that cannot be easily solved by analyzing the original generalized eigenvalue problem.

Simple correction factors are given for improving the second-order reliability estimates. The correction factors are applied to Hohenbichler and Rackwitz's formula. The factors are obtained based on the main curvature of the limit state function at the design point. The proposed approximations can also be applied in the point-fitting approach for second-order reliability analysis. The accuracy of the proposed approximations is illustrated through examples.

This study presents a relationship between the buckling loads of sectorial plates based on the Kirchhoff (or classical thin) plate theory and the Mindlin plate theory. Whereas the former plate theory neglects the effect of transverse shear deformation, the latter plate theory allows for it. This effect becomes significant when dealing with moderately thick plates and sandwich plates. The relationship allows easy and accurate deduction of the buckling loads of the Mindlin plates from their corresponding Kirchhoff solutions.