Journal of Engineering Mechanics

This paper investigates the possibility to enhance the seismic response of a frame structure by the combined use of an external rocking wall and some inerters attached to both the frame and wall. This innovative mechanical assemblage is introduced by means of a reduced-order three-degrees of freedom model. The latter is constituted by a two-degree of freedom linear system, used as a model for a multistory frame structure, and a rigid block, which represents the rocking wall. The frame–wall connection is represented by an elastic link that spans the top of the block to the first story of the frame structure. Some inerters attached to both the frame and the block are considered to provide some apparent inertia forces. The nonlinear equations of motion are obtained and successively numerically integrated, considering seismic base motions. An extensive parametric analysis is performed and the results are summarized in gain maps that show the ratio of the maximum displacements or drifts of coupled and uncoupled systems, thus providing a measure of the seismic enhancements that derive from the coupling. It is found that there are wide regions of the adopted base parameters where coupling is effective. Results also show that the use of inerters increases the effectiveness of coupling with block, thus enabling the use of smaller blocks. Finally, the proposed procedure, based on the spectrum-compatibility criterion, appears able to serve as a useful preliminary design tool for selecting the main characteristics of a system.

The physical mechanism of the static–dynamic combined (S–DC) multiaxial strength of concrete is investigated considering cohesive and frictional strength. It is determined that the strain rate effects and stress state effects on the shear strength of concrete can be decoupled. An effective initial static stress is defined to distinguish the part of the cohesive strength that is dependent on the strain rate; the other part is consumed by the initial static stress. Furthermore, the strength parameter, which reflects the coupled effects of the initial static stress and the strain rate on the strength, is obtained based on the effective initial static stress and dynamic increase factor ($DIF$). Combining the proposed strength parameter and nonlinear dynamic multiaxial strength criterion, a new S–DC multiaxial strength criterion for concrete is presented. The proposed strength criterion is applied to analyze the S–DC strength rules of concrete under multiaxial stress conditions and is further verified using five groups of test results.

With the increasing use of high-strength steel, structures are becoming more resistant but also more slender. Therefore, the phenomenon of structural instability must be considered and prevented. It is imperative for the structural engineer to understand in detail, analytically and numerically, the detection and classification of critical points in the primary equilibrium path of slender structural systems. For this purpose, this work uses the total Lagrangian formulation to describe the kinematics of a three-dimensional biarticulated bar element. Through this formulation, the internal force vector and the tangent stiffness matrix, including the geometric nonlinearity effects, are obtained. An elastic linear constitutive model is assumed for the uniaxial stress-strain state. This constitutive model uses the natural logarithm strain and the Kirchhoff axial stress, which are energetically conjugate tensors. For developing the analytical approach, as a study case, the article presents a simple structural system with three degrees of freedom made up of two biarticulated prismatic three-dimensional (3D) bars and an out-of-plane lateral linear spring. Finally, for the numerical approach, an in-house program was developed to perform geometrical nonlinear analyses using the 3D truss element.

The real-time estimation of structural deformations using discrete strain data, known as shape sensing, is critical to the health monitoring of structures such as bridges. An innovative methodology called the inverse finite-element method (iFEM) is proposed to solve this issue. In this paper, a novel two-node inverse beam element, iBeam3, is developed for two-dimensional deformation monitoring of beam type structures. The present iFEM formulation is derived based on the least-squares variational principle involving section strains of Euler-Bernoulli beam theory for stretching and bending. The iBeam3 element is able to reconstruct deformed shapes without any prior material and/or loading information because only the strain-displacement relationship is used in the formulation. Static and dynamic validation cases regarding steel beams with different boundary conditions subjected to transverse force are discussed in detail. In the tests, different discretization strategies are used to perform the iFEM analysis, and the effects of sensor positions, number of sensors, and measurement errors are evaluated with respect to iFEM-predicted accuracy. The experimental results demonstrate that the iBeam3 element is accurate, robust, and highly efficient. The present methodology provides promising potential in the real-time shape sensing of civil infrastructures.

It is of great significance to incorporate various uncertainties into the design optimization of structures and other engineering systems. Many reliability-based design optimization (RBDO) methods have been developed, but their practical applications can be limited if the reliability consideration entails a large number of evaluations of performance functions, especially for those requiring time-consuming simulations. To overcome the challenge, this paper proposes a new RBDO method that employs quantile surrogates of the performance functions to identify the admissible domain, termed the probability-feasible design domain. Gaussian process models of the quantile surrogates are updated adaptively through an exploration-exploitation trade-off based on inherent randomness and the model uncertainty of the surrogate. The method guides the computational simulations toward the domain in which the quantile estimation can make the greatest contribution to the optimization process. The validity and efficiency of the proposed RBDO method using quantile surrogates by adaptive Gaussian process (QS-AGP) are demonstrated using several numerical examples. The results confirm that QS-AGP facilitates convergence to a reliable optimum design with a significantly reduced number of function evaluations compared to existing RBDO approaches.

A novel Hencky bar-grid model (eHBM) was developed to address plane stress elasticity problems. This model comprises rigid bars arranged in a grid which are joined by frictionless hinges, frictionless pulleys, elastic primary and secondary axial springs, and torsional springs. Based on the energy approach, the in-plane displacements at the joints were determined and the in-plane stress resultants were obtained from the stress resultant–displacement relations. This paper calibrated the elastic spring stiffnesses for the eHBM for the first time by matching them with the finite-difference governing equation for elasticity problems. Some rectangular plane elasticity problems were solved by using the newly developed eHBM. The solutions obtained from the eHBM converged to the exact solutions for the continuum plane body with respect to decreasing the eHBM segment size. It was shown that the eHBM readily can handle any boundary conditions, and furnishes accurate solutions for plane elasticity problems with any complex geometry, such as a rectangular plane body with cutouts.

The interaction and mixing of twin particle clouds in stagnant water were studied by a series of laboratory experiments. The importance of source separation distance and sand particle mass was investigated by introducing nondimensional parameters. The frontal positions of twin particle clouds were compared with the corresponding single particle cloud frontal positions and a critical source separation distance was reported based on the maximum frontal velocity and minimum mass loss of twin particle clouds. The maximum frontal velocity of the critical twin particle cloud was found to be correlated with the depletion of the ambient entrainment in a region between the two clouds. The maximum cloud width took place in nondimensional time of $t/T=0.5$ and the boundary depth between thermal and swarm regimes in twin particle clouds occurred in $t/T=1.4$ irrespective of the initial condition of the clouds as well as source separation distances. In twin clouds with the large mass of sand particles, the swarm width of twin particle clouds became 1.5 times larger than that of the corresponding single particle clouds. The maximum centerline velocity inside the twin clouds occurred once the source separation distance became five times the nozzle diameter. The radial velocity variations inside the twin clouds showed a 30% higher time duration, indicating that the trailing part of a single particle cloud remained longer in the water than the twin particle clouds. The entrainment coefficient attenuated by increasing the aspect ratio of particle clouds and an empirical equation was adopted for prediction of the entrainment coefficient. The turbulent intensity of particle clouds was assessed and it was observed that the velocity fluctuations were higher in closer distances from the nozzles in larger aspect ratios.

This paper considers the case of a relatively large number of parallel columns that buckle simultaneously. The close proximity between columns results in the possibility of contact between adjacent columns as buckling proceeds, and this brings with it some interesting observations on load-carrying capacity. Some experimental results verify the theoretical development based on the versatility of high-fidelity 3D printing, but also highlights the difficulty of applying purely axial loading. The sensitive nature of initial geometric imperfections (slight lack of straightness) and load eccentricity strongly influence postbuckled contact, load-carrying capacity, and, as the number of columns is increased, a statistically based evaluation of anticipated behavior is explored and ultimately found to be unrealistic.

Accurate residual life evaluation is crucial for maintenance of corroded bridge wires, and a stress-life ($S\text{-}N$) curve is determined for the fatigue strength of steel wires after corrosion. The $S\text{-}N$ curve is established based on assumptions that the maximum pit depth can qualify as an indicator of the corrosion level, and the residual life primarily depends on the crack growth of the corroded wire. By means of the Paris law, the $S\text{-}N$ curve is derived for the corroded wires. Intensive reported experimental results from both corrosion acceleration wires and artificially notched wires as well as the corresponding numerical simulation are then used to validate the proposed model. A sensitivity study is also presented to prove the wide applicability of the proposed $S\text{-}N$ curve under different factors, including the corrosion pit shape, stress ratio, fatigue loading frequency, and corrosive environment.

This paper proposes new semianalytical solutions to one-dimensional consolidation of unsaturated soils with a multilayered system under the partially permeable boundary condition, in which a time-decaying exponential function is applied to represent the variations of excess pore pressures for both water and air at the boundary. The general solutions are explicitly presented by the aid of the Laplace transform. Based on the general solutions, interfacial continuity between layers, and boundary conditions, the transfer matrix approach is adopted to deduce the analytical solutions of the multilayered unsaturated soil consolidation in the Laplace space, and the numerical inverse computations of Laplace transform in terms of Crump’s technique are carried out to obtain the final analytical solutions. Then, the existing solution for single-layered soils and the numerical solutions for two-layered unsaturated soils performed by finite-difference methods are utilized to demonstrate the validity of the present methodology as well as semianalytical solutions. Finally, a case study considering two distinct soil profiles is implemented to illustrate the influence of the impeded boundary parameters on the settlement of two-layered unsaturated soils.

Superelastic shape memory alloys (SMAs) have attracted considerable interest in the field of earthquake engineering recently due to their excellent self-centering and moderate energy dissipating capabilities. This unique feature provides promising solutions that can be used in the passive control of structures under strong earthquakes. However, the hysteresis properties of the SMAs have a great influence on the response of the structures. A prominent problem of most previous SMA constitutive models is that they do not consider the strain-rate-dependent effect, especially the mechanical behavior in the typical frequency range of interest for seismic applications. Moreover, the variability effect of the SMA’s hysteresis parameters on the performance in seismic applications is not addressed comprehensively. For this reason, it is important to explore the response sensitivity analysis of an improved SMA constitutive model and gain insight into the effects of various thermomechanical parameters. This paper presents an efficient and accurate sensitivity analysis method for the strain-rate-dependent model of SMAs based on the direct differentiation method (DDM). The constitutive model of SMAs involves three coupled quantities, i.e., stress, martensite fraction, and temperature. The model is expressed numerically using the first-order ordinary differential equations and is solved by the fourth-order Runge–Kutta method. Both the consistent tangent modulus and the stress sensitivity of the SMAs are derived and integrated into the DDM framework. The newly developed algorithms are implemented in a general nonlinear finite element analysis program, OpenSees, and are further verified by the time history analyses of a multi-story steel frame designed with SMA braces. The results demonstrate that the developed DDM-based sensitivity algorithm is accurate and efficient and can provide an excellent solution to the response sensitivity analysis of the thermomechanical strain-rate-dependent model of SMAs.

An innovative procedure was proposed to simulate the viscoelastic mechanical behavior of asphalt mixture. The existing fractional viscoelastic models were quantitatively analyzed, and the fractional Zener model was adopted. The model parameters were obtained by fitting the storage modulus and loss modulus simultaneously. The relaxation modulus of the fractional Zener model in the time domain was deduced using the Mittag-Leffler function. The numerical algorithm of the fractional Zener model was proposed and implemented into finite-element (FE) software ABAQUS version 6.9. Simulations of the relaxation test were conducted to verify the effectiveness of the numerical algorithm and the FE implementation. Then dynamic modulus tests were simulated, and the master curve of the storage and loss modulus was calculated. The simulation results indicated that the fractional Zener model can be effectively applied to FE analysis and accurately predict the storage modulus and loss modulus master curve of asphalt mixture in a wide frequency or temperature range.

In site investigation, it is common to conduct some soundings to explore greater depths that are not explored by remaining soundings. This produces the scenario of nonlattice data, meaning that not all soundings measure identical depths. Recently in 2020, the first and third authors of the current paper developed a probabilistic site characterization method based on sparse Bayesian learning (SBL). This SBL method assumes lattice data (all soundings measure identical depths) to take advantage of the Kronecker-product derivations. These Kronecker-product derivations significantly improve computation efficiency, so the resulting SBL method can be scaled up to address full-scale three-dimensional problems. However, this SBL method is not applicable to nonlattice data, which are common in practice. The purpose of the current paper is to modify the SBL method developed in 2020 to accommodate nonlattice data, while retaining the crucial computational advantage of the Kronecker-product derivations. One real-world case study of underground stratification is used to demonstrate the usefulness of the modified method.