Journal of Engineering Mechanics

In this study, the characteristics of near-bed turbulence were experimentally investigated for three distinct roughness regimes, namely (1) isolated; (2) wake interference; and (3) skimming. Spherical particles of the same size and density were placed upon a rough sediment bed to simulate the three regimes. Experimental runs for the aforementioned regimes were performed in a tilting water-recirculating flume. Flow measurements atop the spherical particles were performed by means of a 3D laser Doppler velocimeter. The aim of the tests was to provide further evidence that the structure of turbulence is affected throughout the boundary layer by the presence of roughness geometry. The measurements reported here include velocity profiles of the mean streamwise and vertical velocity components and of the Reynolds shear stress distribution. To further quantify the differences in turbulent structure under various surface roughnesses, a quadrant analysis was performed.

Measurements of the mean and turbulence characteristics in nonuniform open-channel flows were carried out using a 3D acoustic Doppler velocimeter. Both accelerating and decelerating flows were investigated. Analyses based on the Reynolds equation and the continuity equation of 2D open-channel flow show that a flow will be in equilibrium if the pressure-gradient parameter β is a constant at different sections along the flow direction. The experimental data show that all the flows investigated are in equilibrium. The effect of the flow nonuniformity on the mean velocity and turbulence profiles was also examined. The study shows that (1) the log law is still valid for both accelerating and decelerating flows in the inner region. The Coles law can be used for the entire region, but the wake-strength parameter Π depends on the β-value; and (2) the turbulence intensities and the Reynolds stress decrease in accelerating flow and increase in decelerating flow, when compared with those in uniform flow. Finally, using the Reynolds equation and the continuity equation of 2D open-channel flow, the theoretical expressions for the distribution of vertical velocity and the Reynolds stress have been developed. The measured vertical velocity and the Reynolds stress profile compare well with the derived expressions.

A response spectrum based stochastic approach is developed for analyzing the earthquake response of structures with uncertain properties. For this purpose, expressions for the variances of root-mean-square values of various response quantities at different levels of a multi-degree-of-freedom structure are derived in terms of the covariances of the modal parameters of the structure. The required covariances are defined as a function of the standard deviations of structural properties; i.e., mass, stiffness, and damping ratio. The validity of the proposed method has been established by computing a large number of example results and comparing them with the corresponding exact results obtained by the Monte Carlo simulation method. It is found that there may be significant variations in the response amplitudes for commonly associated uncertainties with the structural properties. The present study provides a simple, practical method to quantify such variations.

Buckling of a heavy elastic column loaded by a concentrated force at the top is analyzed. It is assumed that the base of the column is fixed to a rigid circular plate that is positioned on a homogeneous, isotropic, linearly elastic half-space. The plate has adhesive contact with the half-space. The constitutive equations for the column are assumed in the form that allows axial compressibility and takes into account the influence of shear stresses. It is shown that eigenvalues of the linearized equations determine the bifurcation points of the full nonlinear system of equilibrium equations. The type of bifurcation at the lowest eigenvalue is examined and is shown that it could be super- or subcritical. The postcritical shape of the column is determined by numerical integration of the equilibrium equations.

Series solutions to the differential equations for a complete cylindrical shell under various point loads are developed. Instead of expanding the solution series in both axial and circumferential directions, the solution obtained here is only expanded in circumferential coordinates. Each term in the series represents an exact solution to the set of basic equations under a decomposed ring loading.

Presented herein are the exact axisymmetric buckling solutions of Reddy circular plates on the Pasternak foundation and subjected to a uniform radial load. The boundary conditions of the circular plates covered in this study are (1) simply supported edges; (2) clamped edges; and (3) simply supported edges with elastic rotational restraints. The Reddy buckling solutions are expressed in terms of the corresponding well-known Kirchhoff buckling solutions of circular plates without the elastic foundation. Sample buckling results of Reddy plates are also presented, which should be useful as benchmark solutions for testing numerical solutions and techniques.

The problem of calculating the dynamic response of a one-dimensional distributed parameter system carrying multiple moving oscillators is examined. A solution procedure is suggested that reduces the problem to the integration of a system of linear ordinary differential equations governing the time-dependent coefficients of the series expansion of the response in terms of the eigenfunctions of the continuous structure. The program implementation of the solution procedure is discussed and numerical results are presented. Numerical illustrations clearly demonstrate that the incorporation of even one additional oscillator into the model makes the dynamics of the system vibration considerably more complicated.

The performance of a tuned liquid damper (TLD) with a sloped bottom of an angle of 30° with the horizontal is investigated experimentally. The sloped-bottom TLD was found to be just as effective in dissipating energy as the familiar box-shaped TLD. While the liquid motion of a box-shaped TLD resembles that of a hardening spring, the behavior of the sloped-bottom TLD resembles that of a softening spring. These different behaviors are due to different nonlinear effects: the amplitude dispersion effect and the wave runup effect onto the sloped surface, respectively. The sloshing force created by the motion of the sloped-bottom TLD was found in limited shaking table experiments to be comparable with that created by the equivalent box-shaped TLD, even though the net fluid mass of the sloped-bottom TLD is less than one half that of the box-shaped TLD. This behavior appears to be caused by the greater effective liquid mass involved in the sloshing motion in the sloped-bottom TLD.

A nonlinear cracked hinge model is developed, aimed at the analysis of the bending fracture of fiber-reinforced concrete beams. The model is based on the fracture mechanics concepts of the fictitious crack model with a bilinear stress-crack opening relationship. Closed-form solutions are presented for the moment-rotation relationship of the hinge as a crack propagates, and the case of a nonzero normal force is covered. Special shapes of the stress-crack opening relationship are treated separately. These shapes are the so-called drop-linear and the drop-horizontal for which simplified expressions are obtained. The applicability of the hinge model is demonstrated through analysis of the bending fracture process in the case of a three-point bending beam and an infinitely long beam on a Winkler foundation, the latter analysis comprising the effect of a constant tensile normal force.

Using the experimental background of 130 triaxial tests conducted on cylindrical specimens, a plasticity-based constitutive model of concrete behavior is developed. Parameters of the reference experimental database include the water:cement ratio (i.e., $\mathit{f}{\prime }_{\mathit{c}})$, degree of saturation at testing, and load path used in the tests. In the model, damage is quantified by the volumetric expansion that builds up progressively in the material as it approaches failure and is caused by propagation of microcracks. This behavioral index is calibrated with reference to the available tests and subsequently used as the primary state variable in the model, determining for any stress state the degree of stiffness and strength degradation and the ductility in the response. Because failure is modeled as a damage-driven continuous process rather than a distinct event, the characteristic failure envelope is expanding (hardening) or contracting (softening) as a function of a scalar measure of plastic deformation. A nonassociated plastic flow rule calibrated against the experiments is used to describe the direction of plastic deformation. The model was tested against published triaxial test series and empirical confinement models. It was also used in the context of a finite-element formulation to study the mechanical behavior of reinforced-concrete circular columns. This particular test problem was selected because it is a real-life example of the experimental conditions used to derive the model.

An experimental procedure is presented to quantify damage in terms of microcrack density. This is accomplished by experimentally evaluating the components of a second-order damage tensor for a metal matrix composite material. The procedure involves the use of a scanning electron microscope and image analyzing software to quantify physical damage features found on a representative volume element. These features are quantified in terms of crack density, which is used in developing the second-order damage tensor. The procedure could be applied to voids in a similar fashion. This procedure is applied to the following two different balanced symmetric layups: (1) (0/90)_S; and (2) (±45)_S. Uniaxial tensile loads are used to induce damage in test specimens for each of the layups. Damage evolution is obtained by loading specimens over a range of load intensities from rupture load down to 70% rupture load. A good comparison is obtained between experimentally evaluated and numerically calculated damage values. A companion paper by Voyiadjis and Deliktas used the experimental data presented here in order to verify their proposed formulation for a coupled anisotropic damage model for the inelastic response of composite materials. A physical interpretation of the second-order damage tensor, ;qf, is presented in their work.

A theory of transfer function method for separating two-dimensional wave data obtained in laboratory experiments into incident and reflected waves is presented in this paper. Based on the linear wave assumption, specific transfer functions are derived from mathematical manipulations of the composite wave field, and the corresponding impulse response functions are obtained by implementing the inverse Fourier transform of transfer functions. These response functions are used to perform convolution integrals with time series data measured by fixed wave gauges at different locations in a wave flume and then to separate the incident and reflected waves. Compared with other available methods, the phase difference between two wave signals is considered in the transfer functions. Thus, the separation of waves does not involve the phase calculation and the corresponding error is avoided. The validity of the present method is examined through numerical examples and laboratory experiments of physical models carried out in a wave flume. A comparison of results from physical experiments shows that the present method gives much better estimates of incident and reflected waves than other methods available in the literature.

In this technical note, an infinite thick plate on Winkler's foundation is studied. The effect of shear between the plate and the foundation on the deflection and the stresses is analyzed. It is assumed that the foundation has a stiffness k (the force needed to produce a unit displacement per area) and reacts in compression as well as tension. The effect of a concentrated normal unit force is investigated. The solution is based on the Airy stress function formulation. The Hankel transformation is employed to solve the biharmonic equation for the stress function. The transformed solution is subject to the transformed boundary conditions and the application of the inversion theorem leads to the final solution in the integral form. Judiciously selected dimensionless parameters make this solution relatively simple. Numerical results are obtained for some values of those parameters. In particular, the following two special cases are studied: (1) deflections of a relatively thin plate are compared to the results obtained by Timoshenko and Woinowsky-Krieger, giving an excellent correlation; and (2) with the thickness becoming infinite, the solution of Boussinesq's problem is readily recovered.