Journal of Engineering Mechanics

Rutting, one of the primary distresses in asphalt pavement, is influenced by the nonlinear deformation of its constituents and their microstructural features such as the directional distribution of aggregates and cracks. This study develops a nonlinear elastoviscoplastic model to systematically account for the aggregate directional distribution and damage propagation during the accumulation of permanent deformation. This is accomplished by incorporating a fabric tensor for aggregates and a direction-dependent damage parameter into the yield and potential functions and by the use of Perzyna’s viscoplastic formulation. The comparison of indirect tensile test results with the predictions from the model show that the model captures the permanent deformation of asphalt mixtures well.

This study presents formulas for determining structural properties by which the maximum ductility factors and strain energies stored in elastic-perfectly plastic springs composing a structural system subjected to static monotonic loadings are perfectly controlled. The structural system consists of parallel units comprising elastic springs, elastic-perfectly plastic springs, and units arranged in series with them. The proposed formulas are expressed in terms of the target ductility factors and ratios of the strain energies stored in the springs to the total stored energy in the system. The performance of a structural system with properties determined by employing the formulas in an example application is verified with a conventional step-by-step numerical computation. A noniterative technique to determine the properties of structural components by using the formulas is of great advantage for the recently prevalent performance-based design of various industrial products.

A new formulation of multibody dynamics, the momentum cloud method (MCM), is presented. The method is based on applying the conservation of momentum directly to a complete system, and makes use of prescribed motions between each contiguous body. The absolute translation and rotation of a prescribed base body within the system are chosen to be reference point coordinates. The relative rotations between contiguous bodies along the kinematic chain within the system are chosen to be relative coordinates, the effect of which are captured as a series of cascading transformation matrices. The final result is that the motion of an N-body system can be represented conveniently using only six equations of motion (EOM). Numerical integration of these EOM is facilitated by representing the mass matrix of the entire system as two $3\times 3$ matrices. The solutions to three coupled rotational EOM based on conservation of angular momentum of the system are Euler angles describing the rotation of the base body. The solutions to three coupled translational EOM based on conservation of linear momentum of the system are the translation of the system measured at its center of mass (CM), which are then transferred into translation of base body. Additionally, the inverse dynamic analysis can be used to obtain internal forcing between any two contiguous bodies. The new method is derived for a generalized serial N-body system connected by revolute joints with prescribed relative rotation, and then expanded to more complicated forms and joints. A simulation example is presented for a six-body floating wind turbine system.

In this paper, the formulation of a lower-bound limit analysis for axisymmetric problems by means of finite elements leads to an optimization problem with a large number of variables and constraints. For the Mohr-Coulomb criterion, it is shown that these axisymmetric problems can be solved by second-order cone programming (SOCP). First, a brief introduction to SOCP is given and how axisymmetric lower-bound limit analysis can be formulated in this way is described. Through the use of an efficient toolbox (MOSEK or SDPT3), large-scale SOCP problems can be solved in minutes on a desktop computer. The method is then applied to estimate the collapse load of circular footings and uplift capacity of single or multiplate circular anchors. By comparing the present analysis with the results reported in the literature, it is shown that the results obtained from the proposed method are accurate and computationally more efficient than the numerical lower-bound limit analysis incorporated with linear programming.

An approach to interrogate changes in flexibility regarding the severity of damage is presented. The approach is built on two results. The first shows that the influence lines of stress resultants at damage locations are a basis for the difference in the displacement field between the damaged and reference states for arbitrary loading. The second result shows that the coefficients that combine the basis are the magnitudes of discontinuities in the differential displacement field at the damage locations. The approach quantifies the damage severity by finding changes in sectional stiffness that justify, over reasonable smearing distances, the computed discontinuities. It is shown that at damage locations where the relevant stress resultant is statically determinate the solution is in closed form, while in the indeterminate case it is the fixed point of a nonlinear function.

This study presents the buckling analysis of a radially loaded, solid, circular plate made of porous material. Properties of the plate vary across the thickness. The edge of the plate is either simply supported or clamped and the plate is assumed to be geometrically perfect. The geometrical nonlinearities are considered in the Love-Kirchhoff hypothesis sense. The equilibrium and stability equations, derived through the variational formulation, are used to determine the prebuckling forces and critical buckling loads. The equations are based on the Sanders nonlinear strain-displacement relation. The porous plate is assumed to be of the form where pores are saturated with fluid. The results obtained for porous plates are compared with the homogeneous and porous/nonlinear, symmetric distribution, circular plates.

This paper presents the results of a laboratory study on the subaqueous deposition of sand particles from sediment-laden circular jets on horizontal and inclined beds. Four sets of experiments were carried out to investigate the effects of jet characteristics, bed slope, sediment size, and sediment concentration on the growth and development of the sediment mound. Three distinct flow regimes can be identified as developing regime, spreading regime, and backup regime. It was found that in the developing regime, deposition height and width formed by the continuous release of sediment particles grow faster than the mound length. Slurry jet flow in the spreading regime was diverted from the axial direction to the sides and caused more deposition on both sides of the mound. Backup regime started when the deposition height and width reached their maximum values. In this condition, a slurry jet pushed sediment back to the nozzle and eventually blocked the flow. The initiation of sediment deposition was estimated, and predictions were compared with experimental results. Variations of the deposition length scales, mound base area, and angle of deposition with time were measured. Empirical formulations were introduced to predict deposition development with time.

The time-domain response of a randomly parameterized structural dynamic system is investigated with a polynomial chaos expansion approach and a stochastic Krylov subspace projection, which has been proposed here. The latter uses time-adaptive stochastic spectral functions as weighting functions of the deterministic orthogonal basis onto which the solution is projected. The spectral functions are rational functions of the input random variables and depend on the spectral properties of the unperturbed system. The stochastic system response can be accurately resolved even when using low-order spectral functions, which are computationally advantageous. The time integration required for the resolution of the transient stochastic response has been performed with the unconditionally stable single-step implicit Newmark scheme using a stochastic integration operator. A semistatistical hybrid analytical and simulation-based computational approach has been utilized to obtain the moments and probability density functions of the solution. The simulations have been performed for different degrees of variability of the input randomness and different dimensions of the input stochastic space and compared with the direct Monte-Carlo simulations for accuracy and computational efficiency.

To analyze the dynamic failure process around a circular cavern in hard and brittle rock under high and increasing natural stress conditions, an $800\times 800\times 800\text{-}\text{mm}$ physical model with a $\mathrm{\varphi }$ 160-mm circular cavern in the center was produced by using the self-developed physical model material and tested in the self-developed model test machine under plane-strain conditions. From the physical simulation, when $P_x=P_z=600\hspace{0.17em}\text{kN}$ (${\sigma }_X={\sigma }_Z=3.75\hspace{0.17em}\text{MPa}$), shallow skinlike flakes appeared on the cavern wall, and large-scale abrupt failure occurred during a limited loading-zone for a short time until $P_x=P_z=630\hspace{0.17em}\text{kN}$ (${\sigma }_X={\sigma }_Z\le 3.94\hspace{0.17em}\text{MPa}$). Then, a relatively steady state was followed by a long period with the load increasing. To understand the mechanical behavior around the circular cavern better, in the light of the physical simulation, a numerical simulation was also applied for comparative analysis. Both the numerical simulation and the physical simulation were consistent with each other, and they presented the same failure mechanism.

An approach is proposed for modeling and simulating nonstationary earthquake ground motions that utilizes stationary wavelet and Hilbert transforms. The proposed model is based on the time-frequency representation of a process, which is essential for capturing the nonstationary characteristics of earthquake ground motions. Stationary wavelet transform is first utilized to decompose a sample of a multicomponent nonstationary random process into a set of monocomponent signals. These signals are subsequently transformed to analytic signals using the Hilbert transform, which yields the instantaneous amplitudes and frequencies. Without the customary assumption of piecewise stationarity or reliance on an assumed modulation function, this approach is able to simulate nonstationary random processes, such as earthquake ground motion, based on a sample realization of the process and its instantaneous features. The method is extended to the simulation of multivariate random processes utilizing the proper orthogonal decomposition. Example simulations of measured ground-motion records are presented to demonstrate the efficacy of the proposed scheme. Utilization of this method for simulation of gust fronts is also discussed, further emphasizing the utility of this new framework for the simulation of a host of nonstationary processes with their respective features.

Based on experimental investigations, the literature proposes different methods for modeling the behavior and capacity of foundations subjected to combined loading. Generally, two methods are used to predict the behavior of foundations: traditional approaches and hardening plasticity solutions. The first method is only capable of determining the capacity of the foundations and not the prepeak behavior. Thus, a new strain-hardening criterion is developed by calibrating failure criteria by employing data from small-scale tests on bucket foundations subjected to static loads. The shape of the yield, potential, and failure surfaces are found to be dependent on the embedment ratio (i.e., ratio of skirt length to the diameter) and load path. For the models tested, associated flow is observed to be plausible in the radial planes, whereas nonassociated flow is observed in the planes along the $V\text{-}\text{axis}$.

In this paper, a new quasi-three-dimensional (3D) hyperbolic shear deformation theory for the bending and free vibration analysis of functionally graded plates is developed. By dividing the transverse displacement into bending, shear, and thickness stretching parts, the number of unknowns and governing equations of the present theory is reduced, and hence makes it simple to use. The present plate theory approach accounts for both transverse shear and normal deformations and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. Unlike any other theory, the number of unknown functions involved in displacement field is only five, as against six or more in the case of other shear and normal deformation theories. A comparison with the corresponding results is made to check the accuracy and efficiency of the present theory.

This paper deals with structural static reanalysis with added degrees of freedom. An efficient reanalysis method is proposed. The Cholesky factorization of the stiffness matrix corresponding to the newly added degrees of freedom is completed first, and then the algorithm of updating the Cholesky factorization following a rank-one modification is employed to obtain the factorization of the stiffness matrix for the modified structure. The method preserves the ease of implementation. Numerical examples show that the calculated results of the proposed method are the same as those of direct analysis, while the computational times can be reduced significantly.

Based on the experimental background of 75 true triaxial compression tests conducted on cubic specimens, a plasticity constitutive model for hybrid steel-polypropylene fiber-RC (HFRC) is developed in this study, aiming to accurately predict the strength and deformation of HFRC under various loading scenarios. A five-parameter Willam-Warnke failure surface is modified to account for the presence of hybrid fibers. The evolution of the loading surface is characterized by uncoupled hardening and softening regimes determined by the accumulated equivalent plastic strain, and a Drucker-Prager nonassociated plastic flow is used to describe the plastic deformation. Various model parameters are mainly calibrated on the basis of true triaxial compression test data. Subsequently, the responses of the constitutive model are verified by multiaxial compression test results of both plain concrete and fiber-RC reported by various researchers. It is observed that a good estimation of the strength and the deformation capacity of HFRC with varying fiber volume fractions and aspect ratios can be achieved by the proposed model.

It has been experimentally identified that a stationary crowd or an individual acts like a mass-spring-damper in structural vibration. However, experiments have shown that only one resonance frequency or damped natural frequency of human–structure systems are observed on structures, such as grandstands or floors with crowds. This paper studies the presence of the two resonance frequencies in a heavily damped, two-degree-of-freedom (TDOF) system in theory and in experiment. The invisibility, or nonpresence, of a resonance frequency is defined by investigating a heavily damped single-degree-of-freedom (SDOF) system subjected to a harmonic load. By using frequency response functions (FRFs) for acceleration, it is demonstrated that the observable presence of the two resonance frequencies of the TDOF system depends on the mass ratio and frequency ratio of the upper SDOF model to the lower SDOF model and the damping ratio of the upper SDOF model. The conditions for the presence of the two resonance frequencies are presented graphically based on a study of over 5,000 cases that covered reasonable ranges for these three parameters. Two sets of human–structure interaction experiments, whose design was based on the conditions for observing the resonance frequencies, demonstrated qualitatively the effect of the mass ratio of the system and damping ratio of the human body on the presence of the resonance frequencies, thus verifying the theoretical results. These limiting conditions are discussed and the observation of only one resonance frequency in experiments on some human–structure systems is explained.

A new rectangular orthotropic finite element including drilling rotations and nonnodal degrees of freedom for plane stress analysis is developed, and is fully compatible with a refined frame element; therefore, the membrane and the frame actions are coupled. This plane stress element in combination with a refined beam-column element can accurately model steel plate shear wall (SPSW) systems. The stresses and displacements obtained from numerical examples demonstrate the good accuracy and performance due to the combination of both elements when modeling SPSW with only one plane stress element between the building floors instead of using a dense mesh; therefore, an easier output is obtained to provide a final detailed design. This refined plane stress element provides another analytical tool for practicing structural engineers for the analysis of SPSW. The thin web infill plate design is based on the shear demand obtained directly from the analysis.

Recent developments of a distributed mass damper (DMD) system integrate structural and environmental control systems for buildings. This system simultaneously improves building safety and sustainability by using external shading fins as mass dampers, controlling the amount of sunlight coming into the building for energy efficiency, and reducing structural movements during strong motions. Unlike traditional mass dampers, which are usually placed at the tops of structures, the shading fin mass dampers (SFMDs) are distributed throughout structures because fins are placed along the entire heights of buildings. A recent paper by the authors shows that the passive DMD system is as effective in response mitigation as a conventional tuned mass damper (TMD). In this paper, active control strategies for mass damper control are analyzed and simulated to show further response reductions. Nonpassive controls are of interest for the SFMD system because actuators are already needed to control the positions of the shading fins to affect sunlight for energy efficiency. Several active control strategies [linear quadratic regulator (LQR)-based] are compared with an optimal passive strategy. A 20-story shear structure with 20 DMDs is used as a testbed for active control. The results illustrate that the active DMD system can outperform conventional active systems (e.g., a fully active system and a single active mass damper system) while using a similar level of control forces.