Journal of Engineering Mechanics

The sustained progress in the study of the hysteretic behavior of structural and mechanical systems has led to the adoption of increasingly sophisticated and reliable mathematical representations. Models based on the distributed elements (hysterons) appear to be quite versatile. Among these, the Preisach hysteretic model has received considerable attention in the field of engineering mechanics. In this paper, the stochastic response of a Preisach hysteretic system driven by a white noise process is investigated. In this regard, the method of stochastic averaging is modified to be applicable for the determination of the probability density of the stationary system response envelope. Remarkably, this probability density expression in conjunction with the response of an auxiliary linear system can also be used to determine the power spectrum of the system response. The approximate theoretical solutions are validated by data derived by a pertinent Monte Carlo study.

An exact analytical solution based on the propagator matrix method and a semianalytical solution based on a higher-order mixed approach (displacement and stress interpolation) have been presented in this paper to evaluate the natural frequencies as well as the stress and displacement mode shapes of simply supported, cross-ply laminated and sandwich plates. Continuity of the transverse stresses and displacements has been maintained at the laminae interfaces. Results have been presented for orthotropic plates, symmetric as well as nonsymmetric cross-ply composite and sandwich laminates. Results from the propagator matrix agree well with the published results for frequencies as well as displacement and stress mode shapes. Furthermore, the frequencies and displacement and stress eigenvectors obtained from the proposed layerwise mixed method are in excellent agreement with those obtained by three-dimensional elasticity theory. Results obtained from the present equivalent single layer theory are in good agreement with those obtained from the displacement based higher order methods. The high accuracy of the present methods is further confirmed by comparing the response of a sandwich plate with significantly different layer properties for which the conventional displacement based formulations yield inaccurate solutions.

This paper presents an experimental investigation on the applicability of the empirical mode decomposition (EMD) for identifying structural damage caused by a sudden change of structural stiffness. A three-story shear building model was constructed and installed on a shaking table with two springs horizontally connected to the first floor of the building to provide additional structural stiffness. Structural damage was simulated by suddenly releasing two pretensioned springs either simultaneously or successively. Various damage severities were produced using springs of different stiffness. A series of free vibration, random vibration, and earthquake simulation tests were performed on the building with sudden stiffness changes. Dynamic responses including floor accelerations and displacements, column strains, and spring releasing time instants were measured. The EMD was then applied to measured time histories to identify damage time instant and damage location for various test cases. The comparison of identified results with measured ones showed that damage time instants could be accurately detected in terms of damage spikes extracted directly from the measurement data by EMD. The damage location could be determined by the spatial distribution of the spikes along the building. The influence of damage severity, sampling frequency, and measured quantities on the performance of EMD for damage detection was also discussed.

In-plane shear and compression are important modes in masonry walls, both in load bearing structures and in framed structures. By these mechanical actions shear forces caused by wind and earthquakes are resisted. Upon shear-slipping along bed joints, brick units in masonry also undergo upward translation, or dilatancy, causing global volume increase. If this dimensional change is prevented, large compressive stresses may build up, increasing the resistance to slip by the Coulomb-friction nature. If this shear-compression interaction is not modeled correctly, large errors may be made. In the extreme case, unlimited shear resistance may be predicted by computational models. A discrete crack modeling approach for masonry, which captures the shear-compression dilatational behavior realistically, is elaborated. Shear-compression experiments on small masonry specimens as well as 1 m×1 m masonry walls are analyzed as validation.

Timoshenko and Euler beam formulations, using energy approach, have been used to estimate the influence of crack size and location on the natural frequencies of cracked beams. Fracture mechanics approach has been used to consider the effect of cracking on the dynamic response of the beam. Galerkin’s approach has been used to solve the problem numerically. It is shown that for slender beams the deep beam influence is felt only when the $\left[\right(\mathrm{basic}\mathrm{bending}\mathrm{length})/h]$ ratio of the fundamental sinusoid of a beam becomes very small for higher modes. When the $(l/h)$ ratio becomes small $\left(<10\right)$, the influence of shear rotation and rotary inertia effects become dominant; the inclusion of these effects makes the beam less stiff than a Euler beam. The crack influence on Euler and Timoshenko beams are similar for beams with $l/h>10$; but when $l/h<10$, the results of cracked Euler and Timoshenko beams slowly become different and diverge. The frequency contour method identifies the crack size and location properly, using the lower order frequencies. When structural symmetry gives an ambiguity regarding the crack location, the vibration behavior of the same beam with an asymmetrically placed mass, in conjunction with the frequency contour method, would uniquely identify the crack size and location.

A rigorous mathematical formulation is presented for a flexible tubular pile of finite length embedded in a semi-infinite soil medium under lateral loading. In the framework of three-dimensional elastostatics and classical beam theory, the complicated structure–medium interaction problem is shown to be reducible to three coupled Fredholm integral equations. Through an analysis of the associated Cauchy singular kernels, the intrinsic singular characteristics of the radial, angular, and vertical interfacial load transfers are rendered explicit and incorporated into a rigorous numerical procedure. Detailed results on the three-dimensional load–transfer process, as well as their resultant one-dimensional analogs, are also provided for benchmark comparison and practical applications.

A sand plasticity constitutive model is presented herein, which accounts for the effect of inherent fabric anisotropy on the mechanical response. The anisotropy associated with particles’ orientation distribution, is represented by a second-order symmetric fabric tensor, and its effect is quantified via a scalar-valued anisotropic state variable, $A$. $A$ is defined as the first joint isotropic invariant of the fabric tensor and a properly defined loading direction tensor, scaled by a function of a corresponding Lode angle. The hardening plastic modulus and the location of the critical state line in the void ratio—mean effective stress space, on which the dilatancy depends, are made functions of $A$. The incorporation of this dependence on $A$ in a pre-existing stress-ratio driven, bounding surface plasticity constitutive model, achieves successful simulations of test results on sand for a wide variation of densities, pressures, loading manners, and directions. In particular, the drastic difference in material response observed experimentally for different directions of the principal stress axes with respect to the anisotropy axes, is well simulated by the model. The proposed definition and use of $A$ has generic value, and can be incorporated in a large number of other constitutive models in order to account for inherent fabric anisotropy effects.

A high-order model for the analysis of reinforced concrete (RC) slabs strengthened with externally bonded composite laminated patches of a general layup is presented. The model follows the concepts of the high-order theory and it is based on variational principles, equilibrium, and compatibility requirements. The classical lamination theory is adopted for the composite patch and it yields a set of coordinate dependent constitutive relations. The governing equations form a set of partial differential equations with variable coefficients. The solution procedure adopts the Galerkin and the multiple-shooting methods in the circumferential and radial directions, respectively. The proposed model is used for the numerical study of a square RC slab strengthened with a circular cross-ply laminated patch. The results focus on the overall behavior of the slab and the localized shear and vertical normal stresses near the edge of the bonded patch. Comparison with results obtained using a simplified axisymmetric model is also presented and discussed. The study reveals that the anisotropy of the bonded patch affects the overall and the localized response of the strengthened slab. It also shows that the simplified axisymmetric analysis tends to underestimate the stresses and stress resultants, and thus may be considered unsafe.

This paper introduces a new fault identification method that uses pseudomodal energies to train probabilistic neural networks (PNNs). The proposed procedure is tested on a population of 20 cylindrical shells and its performance is compared to the procedure which uses modal properties to train probabilistic neural networks. The PNNs trained using pseudomodal energies provide better classification of faults than the PNNs trained using the conventional modal properties.

A new method of estimating flutter derivatives using artificial neural networks is proposed. Unlike other computational fluid dynamics based numerical analyses, the proposed method estimates flutter derivatives utilizing previously measured experimental data. One of the advantages of the neural networks approach is that they can approximate a function of many dimensions. An efficient method has been developed to quantify the geometry of deck sections for neural network input. The output of the neural network is flutter derivatives. The flutter derivatives estimation network, which has been trained by the proposed methodology, is tested both for training sets and novel testing sets. The network shows reasonable performance for the novel sets, as well as outstanding performance for the training sets. Two variations of the proposed network are also presented, along with their estimation capability. The paper shows the potential of applying neural networks to wind force approximations.

The behavior of Hostun RF sand on proportional strain paths at low confining pressures (20 to 100 kPa) is considered in this paper. In such paths, a constant dilation rate is imposed during shear. The usual features of pore pressure increase (contracting material) or decrease (dilating material) are here observed depending upon whether the imposed dilation rate is respectively greater or smaller than the “natural” dilation rate at failure (as measured in a drained test). Particular attention is given to the static liquefaction phenomenon, which is seen to occur for loose as well as dense sand provided the imposed dilation rate is large enough to lead to a continuous pore pressure increase during shear. Instability tests performed at low confining pressures on proportional strain paths show that the instability line is strain path dependent. It does not coincide with the peak deviator stress line in proportional strain paths tests, in general, but does coincide with the line $d^{2}W=0$ (nil second increment of total work).

The buckling problem of a column weakened at an interior location is studied for the first time. The weakness is modeled by a rotationally restrained junction. Exact buckling load values are obtained for the weakened column with various end conditions. Depending on the end conditions of the column, the buckling loads show sensitivity (and insensitivity) to junction location and rotational stiffness. The optimum location of the junction could be at the midpoint, at the ends, or somewhere in between.