Journal of Engineering Mechanics

The availability of methods for the identification of nonlinear hysteretic systems is crucial for the assessment of the health and the repair of civil infrastructures during and after severe earthquakes. However, most methods used to identify hysteretic systems suffer from two problems: (1) the structural responses at all dynamic degrees of freedom (DOFs) must be measured, which is obviously impractical for real applications; and (2) the nonlinear model of a system is assumed to be known, and only the model parameters are to be identified, meaning that the nonlinear characteristics of the underlying structures may not be captured accurately. To overcome these two problems, this paper proposes a novel method that does not assume a nonlinear model and that does not require measurements at all DOFs. The new approach alternately uses the extended Kalman filter (EKF) and wavelet (W) multiresolution analysis. Within each time step, the identification can then be divided into two stages. In stage one, based on limited-state observations and the structural model at previous step, the structural responses at all DOFs are estimated using the EKF method. In stage two, based on the estimated full states, wavelet multiresolution analysis is used to identify the tangent stiffness matrix and the hysteresis-restoring force curves of the structure (i.e., the structural model is updated using the estimated full states). Two model structures with various nonlinearities at different locations, and with various state-observation schemes, are employed to conduct the numerical study. The numerical results verify the efficiency and accuracy of the proposed method. The best location for state observation is also discussed in the numerical study.

Based on a generalized variational principle of magnetoelasticity and Hamilton’s principle, a dynamic theoretical model is developed for magnetoelastic vibration of a soft ferromagnetic plate with nonlinear magnetization being in a stationary magnetic field. The fundamental equations of the magnetic field and the motion of the ferromagnetic plate are derived together with the expression of equivalent magnetic force acting on the ferromagnetic plate as a result of the reciprocity between the magnetizable ferromagnetic plate and the applied field. There involve twofold nonlinearities in which one is from the magnetoelastic coupling and the other arises from the nonlinear magnetization of the ferromagnetic medium. A numerical technique that combines the finite-element method for magnetic-field distribution with the finite-difference and Newmark methods for vibration of the ferromagnetic plate is proposed. Analyses of the dynamic behaviors and stability characteristics of a ferromagnetic cantilevered beam-plate vibrating in an applied stationary magnetic field are implemented numerically, which show that the frequency of magnetoelastic vibration of the ferromagnetic beam-plate increases with the intensity and the incident angle of the applied magnetic field, and that the magnetization nonlinearity obviously influences the magnetoelastic dynamics behavior. Especially for strong magnetic fields and certain geometrical parameters of the ferromagnetic plate, the magnetoelastic dynamic behavior of the ferromagnetic plate, taking into account nonlinear magnetization, exhibits distinctive magnetoelastic characteristics compared with that of the ferromagnetic plate with linear magnetization.

For the first time, a theoretical formulation is presented for the load-transfer analysis of an elastic cylindrical thin-walled pile immersed in a transversely isotropic half-space under axisymmetric excitations. By generating a set of weakly singular Green’s functions for the embedding medium and using a shell theory for the pile, it is shown that similar to the related interaction analysis in isotropic medium, the soil-structure interaction problem under consideration is reducible to two coupled Fredholm integral equations. Regarding the singular nature of stress transfer, a newly developed adaptive-gradient elements family is employed in the development of an accurate numerical scheme. The effect of soil material anisotropy on the dynamic interaction process is explored by presenting a set of numerical results for various material and geometrical conditions and various excitation frequencies. To confirm the accuracy of the proposed analytical and numerical scheme, numerical results are compared with benchmark solutions for the corresponding isotropic problem.

The screening effects of trenches on train-induced ground vibration are investigated by an analytical method. The embankment and soil banks beside the trench are modeled as elastic layers with appropriate widths. A fully saturated poroelastic half-space is first utilized in the investigation of the isolation of train-induced ground vibration. Biot’s theory is applied to characterize the saturated poroelastic half-space, considering the coupling between the soil skeleton and the fluid. Based on Fourier transforms and Fourier series, the governing equations are solved. The various performances of the trenches on the single-phase elastic half-space and saturated poroelastic half-space as screening barriers to mitigate the ground vibration are specially investigated. It is found for the vibration generated by the axle train load with supercritical speed that the discrepancy between the screening efficiency of the trenches on the poroelastic half-space and elastic half-space is significant; the single-phase elastic half-space model may significantly underestimate the screening effect of the trench. In addition, an excellent screening effect can be achieved by an open trench to the ground vibrations generated by the dynamic wheel-rail load.

A Fourier series method (FSM) of simulating spatial averages of stationary Gaussian random fields is presented. The FSM is able to simulate spatial averages over nonequally spaced rectangular cells, and by adopting Gauss quadrature, it can be further applied to nonrectangular cells. It is also capable of simulating line averages over any prescribed line segment in two dimensions. The former (spatial averaging over cells) is essential for finite-element analysis, while the latter (line averaging over line segments) is essential for slope-stability analysis using limit equilibrium. To resolve the issue of unrealistic periodical correlation pertaining to the FSM, a rule of thumb is provided to extend the simulation space. For cases with nonrectangular cells, the required number of Gauss points to achieve a prescribed accuracy is calibrated for both one-dimensional (1D) and two-dimensional (2D) cases and for both the single-exponential (SExp) and squared-exponential (QExp) autocorrelation models. The consistency of the FSM is verified through 1D and 2D examples for both SExp and QExp models.

Gravelly soils are used extensively for a wide range of engineering applications. One example is railway ballast, and another is the fill for rock-filled dams. These soils are usually subjected to complicated loading, including high pressure, repeated loading from trains, and earthquake loading. Depending on the natural characteristics of soil particles and the level of external loading, gravelly soils may undergo particle breakage, which modifies the strength and deformation properties of the soils. To better estimate the response of earth structures with gravelly soils, it is necessary to describe particle breakage properly, its relation with external loading, and its effect on soil properties. In this study, a generalized plasticity framework, based on critical-state soil mechanics and following the associated flow rule, was developed based on the unique responses of gravelly soils. Particle breakage and its effects were described by a translating critical-state line that was related to dissipated plastic energy through a hyperbolic function. The responses of six gravelly soils along different stress paths were simulated using the proposed model. It was shown that with 12 parameters, the constitutive model was capable of describing the responses of gravelly soils over a wide range of initial void ratios and initial confining pressures, as well as along different stress paths. The model parameters, most of which have definite physical meanings, can be calibrated through conventional triaxial compression tests. This framework will provide a basis for simulating the cyclic responses of gravelly soils.

The nonlinear inelastic stress-strain relationship of concrete is a result of changes to the fabric of the material caused by several damage mechanisms. Existing experimental research on concrete provides very little information on the evolution of these mechanisms. Instead, most experimental studies are limited to measuring the external loads and deformations of concrete specimens. The aim of the research presented here is to provide a direct link between macroscopically observed global stress-strain behavior and the development of damage mechanisms within the specimens. A novel experimental procedure is introduced to monitor the changes in the material during a conventional multiaxial compression test. This procedure, comprising small stress probes repeated at selected points of the stress-strain history, is designed to provide data on the tangent stiffness operator and the associated acoustic tensors. The acoustic tensor with the minimum value of its determinant provides information on both magnitude and orientation of the damage. The stress-probing methodology and some of the key practical aspects and limitations of the experimental procedure are illustrated by using five multiaxial compression tests as examples of different stress-strain histories. The results of the test methodology presented in this paper give an indication of the extent of damage and accurate information about its orientation. This paper therefore shows that the stress-probing procedure can be incorporated in multiaxial tests designed to monitor the relationship between damage evolution in the material and macroscopically observed stress-strain response of the specimen.

Rounding of the corners of a polygonal bar (or a polygonal tube conveying fluid) is unavoidable in practice. This paper studies the effect of rounding on the torsional rigidity by introducing a family of homotopy cross sections and an improved Ritz method. Rounding decreases both rigidity and cross-sectional area. For a given mass, there exists an optimal shape for maximized rigidity.

The detection of changes in vibrational behavior has long been applied as a potential means of damage detection. However, existing damage diagnosis techniques are primarily limited to linear models in which the stiffness of some of the elements is reduced to represent damage. Although these methods appear to be adequate for locating and quantifying the present damage in the structure, they are not sufficient for determining future performance of the structure, which can only be determined using nonlinear models. This paper focuses on the challenging task of updating nonlinear models for reinforced concrete civil engineering structures. A nonlinear hysteretic material model is applied to accurately portray the fundamental hysteretic behavior of concrete structures. A systematic methodology to perform damage detection and, more importantly, update the nonlinear model for prediction is proposed. This new method is designed to use low-level ambient vibration data to detect changes in the modal parameters. With the acquired modal information, the damage parameters that control the nonlinear material model are updated. The final updated nonlinear model may be utilized not only to evaluate the structure’s current damage state but also to predict its future behavior. A concrete shear wall is analyzed numerically to demonstrate the proposed method.

One of the most critical components in the oxygen-generation and water-processing assemblies for human habitation in space is the deionizing (DI) bed—a packed bed of ion-exchange resin beads—that purifies water. The DI bed shrinks during the course of its operation, and therefore, for the bed to work satisfactorily, it must be kept properly compressed. To understand the force-transferring mechanism along the bed, sets of experimental programs were developed and conducted on the individual particles and bed samples of a DI granular material, Amberlite IRN-78. The presence of water reduced the load-bearing capacity of the individual particles, because most of the wet (water submerged) particles tested failed under relatively small crushing force, whereas the dry particles withstood a much higher load. The particle crushing force was found to be closely represented by normal and Weibull distributions. The DI material bed has a relatively small internal friction angle (shear strength). The lateral pressure coefficient was found to be relatively high. The material exhibited time-dependent behavior, creep, and stress relaxation, possibly through particle deformation and rearrangement. The friction force between the DI medium and the wall of the housing cylinder was significant, and increased rapidly in a nonlinear fashion with increasing sample length. The effect of friction was more significant for more densely packed beds. The loading and unloading tests showed that the compacted material bed exhibited an anelastic type of hysteresis behavior. The uncompacted bed was seen to have nonlinear load-deformation behavior, with a rapid increase in displacement with load, whereas the compacted bed showed linear or near-linear, load-displacement behavior.

In the current study, a semianalytical closed-form solution is presented for the first time for buckling analysis of two-directional, functionally graded (FG) circular plates with variable thickness supported by both constrained edges and two-parameter elastic foundations. It is assumed that the material properties of the functionally graded material (FGM) vary in the transverse and radial directions, simultaneously. While variations of the elasticity modulus in the transverse direction is described by a power-law, variations of the material properties and the thickness in the radial direction are assumed to obey exponential laws. Mindlin’s shear deformation plate theory and the differential transform technique are employed to develop the governing equations. A sensitivity analysis including evaluation of effects of various edge conditions, geometric parameters, coefficients of the elastic foundation, and material heterogeneity is performed. Results reveal that the strength degradation caused by the radial thickness reduction may be compensated by an appropriate increasing of the elasticity modulus in the radial direction. Furthermore, the elastic foundation may significantly affect the buckling load in some circumstances.