Journal of Engineering Mechanics

This paper first extends a classical solution concerning the shape optimization of a hanging bar. The well-known solution determines the optimal cross section of a homogeneous bar that minimizes elongation under its own weight and a given applied force, subject to a total volume constraint. Herein, the analytical solution is generalized to materials with a variable density and elastic modulus along the bar, subject to a total mass constraint. A gradient-based numerical optimization algorithm is developed and then used to solve the inverse problem to validate the analytical results. The approach is then extended to two-dimensional structures through the parameterization of the external boundary using nonuniform rational B-splines (NURBS) functions and the solution of repeated forward problems with updated meshes. Three different cases are studied: (1) homogeneous elastic, (2) homogeneous hyperelastic, and (3) inhomogeneous elastic materials. The results show the differences between the optimal shape of one- and two-dimensional models and the effect of material models on the optimal solutions.

A constitutive model is presented for brittle granular materials based on a recent reformulation of the breakage mechanics theory. The primary objective of the study is to capture peak strength with subsequent strain softening in dilatant specimens under shearing and the simultaneous evolution of breakage and dilation. The predictive performance of the model is assessed relative to two experimental datasets from the literature. The influence of the model parameters on the overall material response is described through a detailed calibration procedure based on a benchmark experimental dataset. Comparison of the results of drained triaxial compression experiments on two sands with the predictions of the model indicates that the enriched model can successfully capture the evolution of stress-strain behavior at different confinement levels. The predicted response of dilatant specimens exhibits stress- and density-dependent peak strength and strain softening toward the critical state, which is in agreement with experimental evidence. The simulations of Kurnell sand can reproduce the transition of the volumetric strain from $-0.05$ to 0.14 as the confining pressure increases from 760 to 7,800 kPa. The predicted breakage of specimens subjected to different confining pressures is slightly higher than experimental measurements, whereas they exhibit similar trends. The proposed framework is capable of qualitatively reproducing many aspects of the experimentally observed stress-dilatancy-breakage relationship in brittle granular materials.

In this paper, a new approach is proposed to estimate the probability of failure in structural reliability analysis. This method is based on the law of total expectation and variance in subintervals, and it combines the conditional Monte Carlo method and the importance sampling method. The conditional input variable can be chosen from the estimates of variance-based sensitivity measures with one set of samples. In addition, the optimal sample size in each subinterval can also be estimated with the same set of samples. The proposed method has a higher rate of convergence compared to the importance sampling method. The numerical and engineering examples show the efficiency of the proposed method.

The self-centering brace (SCB) is a high-capacity structural component for lateral force resistance and recentering. This paper focuses on modeling the magnetorheological self-centering brace (MR–SCB). Full-scale cyclic tests of the MR–SCB under sine waves are conducted. Results indicate that the MR–SCB exhibits a full flag-shaped force-displacement response with high energy dissipation and recentering capabilities. Three mechanical models of the MR–SCB are proposed to reproduce the hysteretic behaviors. Predicted errors of the modified Bouc–Wen-based model are smaller than those of the other two models. Considering high numerical convergence and low computational cost, the modified Bouc–Wen-based model is the best choice for prediction, and 12 model parameters are analyzed to determine reasonable values. Due to earthquake excitation, the hysteretic response of the MR–SCB is fuller than that of the existing SCB, indicating greater energy dissipation.

Full-depth lock-exchange experiments of saltwater with a lock length $x_0$ of 40 m were conducted in a horizontal open channel in order to gain insight into the gravity currents of long lock releases. Without the effects of backreflected waves and initial volume on their development, the experiments showed that the front spreading distances and front velocities developed very smoothly without any transitions. But they were significantly affected by drag and friction. Their variations with time in later periods were different from the previously published results for gravity flows of small-volume release. The current was analyzed using one-layer open-channel hydraulics. The theoretical results show that the front traveling length $x_f$ over time is a quadratic function and the front velocity $u_f$ decreases linearly based on the initial speed, which is related to the drag coefficient. Similarly, the front height $h_f$ also decreases linearly from half of the total water depth. The rate of the decrease depends on drag and friction, which can be represented by the velocity coefficient $\alpha$ at a gate section and the dimensionless Chezy’s coefficient $C$. The resulting expressions reveal the effects of drag and friction on all the current processes in the slumping phase. The theoretical and experimental results are in satisfactory agreement. Comparison of previous and present results indicates that a power law does not fit well all the flow processes of the experiments. It is found that the experiments in a later period are close to the gravity current of constant discharge in the buoyancy-viscous phase.

This paper is dedicated to the nonlinear finite-element analysis of the dynamic behavior of beams on foundations under moving loads. The goal of the study is to generalize, for more realistic foundation behaviors, the analyses performed in other studies. The foundations are considered to be nonlinear with different tensile and compressive behaviors. Tensionless foundations lead to large beam deflections. Accordingly, the finite-element formulation of the problem is derived taking into account the geometrical nonlinear behavior of the beam. Critical velocities of the moving loads are computed, and the effect of the physical and geometrical nonlinear behavior of the system on their values is analyzed.

Researchers in the structural health monitoring field have recently focused on using instrumented vehicles, usually equipped with accelerometers, as mobile bridge inspection instruments. The vehicle plays two roles: that of the measurement device and that of the excitation source. Permanent changes to the bridge’s stiffness due to damage or wear may manifest as changes in the bridge’s fundamental frequencies. In vehicle-based inspection, bridge frequencies are extracted from vehicle responses. These bridge frequencies may be estimated periodically as a continuing bridge condition assessment. This paper establishes closed-form solutions for bridge and vehicle vibration as a vehicle traverses a two-span continuous bridge and provides a method of bridge frequency extraction from vehicle response. Results are validated using finite-element simulations and compared against the literature. Results show that bridge frequencies observed by the vehicle manifest as two peaks shifted below and above the fundamental bridge frequency. These shifts are linear functions and the average of these shifted bridge frequencies approximates the fundamental bridge frequency to within 7% error; this error decreases to 2% for equal spans.

The simulation and peak value estimation of non-Gaussian wind pressures are important to the structural and cladding design of the building. Due to its straightforwardness and accuracy, the moment-based Hermite polynomial model (HPM) has been widely used. However, its effective region for monotonicity is limited, resulting in its unsuitability for non-Gaussian processes whose skewness and kurtosis are out of the effective region. On the other hand, the Johnson transformation model (JTM) has attracted attention due to its larger effective region compared with that of the HPM. Nevertheless, the systematic study of its application to the simulation and peak value estimation of non-Gaussian wind pressures is less addressed. Specifically, its comparison with the HPM is not well discussed. In this study, a set of closed-form formulas to determine the relationship between correlation coefficients of the non-Gaussian process and those of the underlying Gaussian process was derived, and they facilitate a JTM-based simulation method for the non-Gaussian process. Analytical expressions for the non-Gaussian peak factor were developed. Furthermore, the JTM was systematically compared with the HPM in terms of the translation function, which helps to understand the ensuing performance evaluation on these two models in the simulation and peak value estimation based on the very long wind pressure data. Results showed that the JTM-based peak value estimation method performs well for wind pressures with weak to mild non-Gaussianity, even those beyond the effective region of the HPM, although it may provide slightly worse estimation for strong softening processes compared with the HPM.

Characterizing the time-domain response of a random multiple-degree-of-freedom dynamical system is challenging and often requires Monte Carlo simulation (MCS). Differential equations must therefore be solved for each sample, which is time-consuming. This is why polynomial chaos expansion (PCE) has been proposed as an alternative to MCS. However, it turns out that PCE is not adapted to simulate a random dynamical system for long-time integration. Recent studies have shown similar issues for the frequency response function of a random linear system around the deterministic eigenfrequencies. A Padé approximant approach has been successfully applied; similar interesting results were also observed with a random mode approach. Therefore, the latter two methods were applied to a random linear dynamical system excited by a dynamic load to estimate the first two statistical moments and probability density function at a given instant of time. Whereas the random modes method has been very efficient and accurate to evaluate the statistics of the response, the Padé approximant approach has given very poor results when the coefficients were determined in the time domain. However, if the differential equations were solved in the frequency domain, the Padé approximants, which were also calculated in the frequency domain, provided results in excellent agreement with the MCS results.