Journal of Engineering Mechanics

The existing literature on Bayesian updating of structural models has assigned equal variances (homoscedasticity) in the measured observables across all modes by assuming a Gaussian error distribution. This paper relaxes the assumption by allowing the error distribution to be conditionally heteroscedastic but marginally follow the Student’s $t$-distribution. Modeling heteroscedasticity in structures is necessary because higher modal parameters are prone to higher uncertainty—an idea that is supported by experimental data obtained from a scaled building model. We adopted a hierarchical modeling framework for system equations and employed Bayesian techniques to update the parameters. Estimation used Gibbs sampling, a well-known Markov chain Monte Carlo (MCMC) algorithm. The proposed framework is illustrated in various simulated data obtained from a 10-story shear building for varying levels of noise contamination. The model was also implemented for experimental data from an eight-degrees-of-freedom spring-mass model tested at the Los Alamos National Laboratory. We show that our framework provides several advantages over the homoscedastic model, including a more stable and accurate inference about the stiffness and modal parameters and a noticeable improvement in noise immunity compared to those reported in the literature. The importance of the heteroscedasticity is also highlighted because it leads to a better exploration of the associated uncertainty in the observables, not captured by its homoscedastic counterpart. The paper also discusses some limitations and provides possible extensions for future research.

In recent decades, fiber reinforced polymer (FRP) wrapping has become a common technique to retrofit reinforced concrete (RC) columns. Numerous research works have sought to verify analytically and experimentally its effectiveness in terms of enhancement of axial load bearing capacity and ductility. These studies highlighted that in the case of sharp-cornered sections, the maximum allowable confinement pressure is limited by premature failure at corners and, consequently, stress in the FRP, as well as the distribution of the confinement pressure, is not uniform. The prediction of this phenomenon is not straightforward, and existing theoretical studies propose complex numerical simulations, whereas technical codes provide simplified or empirical relationships for its assessment. This paper presents an analytical model for the evaluation of the effective distribution of confinement pressure in FRP confined concrete members with rounded corners. The model allows considering the interaction with the concrete core and different brittle failure modes, including FRP rupture and debonding. It leads to determining the distribution of the confinement pressure along the section. Results are compared with those achieved by finite-element (FE) analyses and with numerical and experimental data available in the literature. Good agreement is obtained in all cases, showing the reliability of the proposed model.

The characteristic receptance method of analyzing the free wave propagation of a finite monocoupled periodic system with a single disorder is applied to study the vibration transmission through the periodic bearing, due to horizontal ground motion, into which the shear modulus or thickness disorder of a rubber layer has been introduced. The upper building and laminated rubber isolator are respectively modeled as two different types of periodic systems. The superstructure model is formulated according to the Euler-Bernoulli beam theory for the walls, while the floors are considered as lumped masses. The shear beam theory along with the lumped-mass model is used to describe the bearing with the rubber layers, reinforced by periodically placing vulcanized steel shims. The point impedance of the superstructure obtained from the indirect receptance and propagation constant is utilized in the development of the displacement transmissibility function of the bearing. The study of the seismic response and dynamic transmission characteristics of the bearings shows that a small shear modulus or large thickness in the disordered element generally enhances the isolated capability. The presented analysis indicates how disorders can be used most effectively for vibration isolation in existing laminated rubber bearings or the design of new laminated rubber bearings.

We are concerned with controlling wave propagation in an elastic medium by engineering its dispersive properties. To this end, we discuss a flexible and systematic framework for designing the material composition of the unit cell of a periodic medium when given a target dispersion relation or, equivalently, a target group velocity profile at a user-defined frequency range. We cast the inverse medium design problem as a dispersion-constrained optimization problem that minimizes the distance between the target and the computed group velocity profiles. We rely on the Hellmann–Feynman theorem to obtain the computed group velocity of a trial unit cell, and use a gradient-based algorithm to drive the engineered medium’s material properties to convergence. We numerically demonstrate the capabilities of the approach using scalar waves in one and two dimensions. We also use the method to design metamaterials exhibiting user-defined omnidirectional band gaps and to provide numerical evidence of the metamaterial’s intended performance via time-domain simulations.

In this work, monolithic and staggered schemes using a locking-free solid-shell element are proposed to analyze the behavior of thin-walled structural components subjected to combined thermal and mechanical loads. The enhanced assumed strain method, assumed natural strain method, and reduced integration with hourglass control are incorporated into the formulation of the eight-node solid-shell element to seek accurate predictions of the structural response of the elastodynamic systems. The thermal field (the solution of the heat conduction problem) is obtained using a standard eight-node solid-element formulation with full integration. Element formulations for monolithic, isothermal, and isentropic staggered schemes are presented. The use of different element formulations in the structural and thermal fields brings difficulties in implementing the isentropic scheme; hence, special efforts are made to preserve its convergence properties and numerical stability. Numerical examples demonstrate the accuracy and efficiency of the present locking-free solid-shell element in conducting large-deformation thermoelastic analyses of thin-walled structures. In particular, the isentropic scheme with only a one-pass strategy presents equal robustness but superior efficiency to the monolithic element in simulations considering weak, as well as strong, couplings.

For the seismic design of structures in which the respective supports are located at long distances from each other, the assumption of uniform ground motion may be inadequate. In this study, an efficient time domain method is proposed to determine seismic structural response considering the effect of stochastic multiple-support excitation (MSE). This method improves the Markov vector method by considering the frequency-dependent coherence function of the excitations, proposing a new modeling framework and solving strategy. The location of the time-modulating function is studied theoretically, the and the calculation method of the time-modulating function for an arbitrary excitation envelope of the MSE is studied. A natural way of calculating support damping is given. Based on the principle that a model built in absolute coordinates should be consistent with a model built in relative coordinates, the formulation of a damping matrix in absolute coordinates was studied. The nonstationary response variances were obtained by solving the governing ordinary differential equations. The results were compared with extensive Monte Carlo simulation, demonstrating that the proposed method is efficient and accurate for analysis of stochastically structures considering multiple-support excitation.

The uncoupled alongwind and crosswind responses of base-isolated tall buildings with hysteretic restoring force characteristics are quantified through response time history analysis and statistical linearization approach. The upper building is modeled as a linear elastic multiple-degrees-of-freedom shear building. The story wind forces are represented in their cross power spectra. Response history analysis is carried out to characterize the crosswind response with zero mean component and alongwind response with time-varying mean component. The response statistics including time-varying mean, standard deviation (STD), and extreme and fatigue damage at different wind speeds are quantified. The fluctuating alongwind and crosswind responses can, to some extent, be unified with respect to their corresponding elastic responses, while the alongwind base displacement has a greater low-frequency drift, a larger STD and weaker softening non-Gaussian character. As compared to fixed-base building, the building displacement and acceleration of base-isolated building at higher wind speeds are greatly reduced due to the effect of hysteretic damping. The higher mode contributions can be ignored in building displacement, but are noticeable in building acceleration. Analytical estimations of the response statistics by using statistical linearization approach with Gaussian assumption are also presented and the challenges posed by non-Gaussian response character are pointed out. A comprehensive parametric study is performed to explore the effects of various building parameters on the response of base-isolated buildings.

The miscible displacement of a Newtonian fluid pushed by a nonlinear viscoelastic fluid (viscous fingering instability) has been investigated via a pseudospectral method and Hartley transform. The results of the present study could be useful for enhanced oil recovery (EOR) using chemical flooding technique. Here, the Giesekus model is applied as the constitutive equation of viscoelastic fluid. In addition to the homogeneous media, the simulations are performed for a horizontal layered heterogeneous medium and the results are presented as concentration contours, transversely averaged concentration profiles, mixing length, and sweep efficiency. It is concluded that the heterogeneity of the medium has a great effect on the flow structure. The channeling regime is observed in these media. Higher layers in the heterogeneous medium reduces the intensity of instability while permeability variance acts on the contrary. This is the first attempt in simulation of the viscoelastic-Newtonian displacement (polymer flooding) in heterogeneous media.

Existing axisymmetric slip-line theories for metal are established based on certain hypotheses of circumferential stress and thus lack strictness. This article presents a technique for deriving actual circumferential stress according to circumferential geometric conditions and plastic flow theory. Based on the strict expression of circumferential stress replacing existing hypotheses, a new axisymmetric slip-line theory for metal is developed. Slip lines and stress relations are derived by the transformation of the triangle function. General solutions to two types of boundary conditions are also derived. The new slip-line theory is applied to the problem of indentation by a conical indenter. The slip-line field, the stress fields, and the indentation pressure are calculated, discussed, and compared with those in existing slip-line theories. The derivation and calculation show that the plastic stress fields and the indentation pressure vary with the boundary velocity. The mean vertical pressure on the circular conical surface decreases as the loading rate increases but less so than seen with existing slip-line theories.

A simple structure under earthquake ground motion is modeled as single-degree-of-freedom systems with nonlinear or hysteretic stiffness subjected to modulated Gaussian white noise excitations. A nonstationary response is characterized in terms of probability density and statistical moments. According to the motion equation, a generalized Fokker-Planck-Kolmogorov (FPK) equation is derived. The exponential-polynomial closure (EPC) method, which is proposed previously for stationary solutions of the FPK equation, is further developed and extended by taking into account the time variable and generalized for nonstationary solutions. The solution is assumed as an exponential function of a series of polynomials with time-dependent unknown coefficients. With the Galerkin method, the time-dependent coefficients are then solved from the residual errors of a series of nonlinear differential equations. Thus, nonstationary probability densities and statistical moments are obtained. Finally, two types of nonlinear structural models, that is, structural systems with memory and without memory, under different modulating ground motions are considered. Typical modulating functions, that is, exponential type, box-car type, and Ang and Amin type are taken into account, and are assumed of the same Arias intensity. The proposed procedure is verified using Monte Carlo simulation. Moreover, the influences of the modulating function shape and Arias intensity on structure responses are discussed.

This study presents the finite element–based micromechanical modeling approach to obtain the electromechanical properties of the piezoelectric metamaterial based on honeycomb (HC) cellular networks. The symmetry of the periodic structure was employed to derive mixed boundary conditions (MBCs) analogous to periodic boundary conditions (PBCs). Three classes of hexagonal HC cellular networks, namely, a conventional HC (CHC), a re-entrant HC (RE), and a semi-re-entrant HC (SRE) were considered. The representative volume elements (RVEs) of these three classes of cellular materials were created, and finite element analyses were carried out to analyze the effect of orientation of the ligament on their effective electromechanical properties and their suitability in specific engineering applications. The longitudinally poled piezoelectric HC cellular networks showed an enhanced behavior as compared to the monolithic piezoelectric materials. Moreover, longitudinally poled HC cellular networks demonstrated that, as compared to the bulk constituent, their hydrostatic figure of merit increased and their acoustic impedance decreased by one order of magnitude, respectively, indicating their applicability for the design on hydrophones. Moreover, results showed that cellular metamaterial with tunable electromechanical characteristics and a variety of auxetic behaviors such as negative, positive, or zero Poisson’s ratios could be developed. Such novel HC network-based functional cellular materials are likely to facilitate the design of light-weight devices for various next-generation sensors and actuators.

The beating phenomenon, induced by coupling between translational modes of tall buildings with closely spaced frequencies, may have significant effects on modal identification, especially damping estimation. This paper proposes a new method for attenuating the adverse effects of beating on modal identification for high-rise buildings. Beating in typhoon-induced responses of a high-rise building is clearly observed via both frequency domain and time domain analysis. To eliminate the effects of beating on structural modal identification, a normal coordinates–based modal decomposition method for coupled translational modes is proposed, which is proved to be effective for separating closely coupled translational modes and thereby improving the accuracy of damping estimation for high-rise buildings. This paper aims to provide valuable implications for damping evaluation of high-rise buildings.

This study proposes a methodology to predict the capacity of aluminum welded connections. In order to evaluate the material characteristics within the heat-affected zone, an inverse analysis methodology, using full-field measurements of the strain field using digital image correlation, was developed during uniaxial tensile tests on specimens extracted from gas metal arc welded 6061-T6 aluminum alloy plates. The identification of the constitutive law problem was formulated within the Virtual Fields Method. The inverse analysis methodology was compared with an identification process of the material in the vicinity of the weld using a fully coupled multiphysics simulation considering thermal, metallurgical, and mechanical mechanisms during heating and cooling. The simulation accounts for the nonhomogeneous hardening properties within the heat-affected zone to extract the constitutive material laws of a welded join. The proposed simulation methodology was used to analyze the structural response of a plate–square hollow structural section (SHSS) joint subjected to tensile loading. The predicted capacity of the specimens was compared with the experimental findings as well as analyses using Canadian code recommendations. It is shown that it is possible to improve the prediction of the capacity of welded aluminum connection using the Canadian recommendations if the width of the heat-affected zone is reduced to 15 mm instead of the original 25 mm.

This paper studies the interaction between two cylinders of an identical diameter immersed in quiescent fluid. The master cylinder carries out forced vibration, while the adjacent slave cylinder is elastically mounted and has one degree of freedom along the centerline between the two cylinders. In this study, the geometry of the problem is fixed, with an initial gap ratio of the two cylinders of 0.9 and a nondimensional vibration amplitude of the master cylinder of 0.477. In total, 7,480 two-dimensional cases have been simulated to cover the parameter space of the problem, with the Reynolds number ranging from 10 to 150, the structural damping factor of the slave cylinder ranging from 0 to 0.2, the mass ratio of the slave cylinder ranging from 1.5 to 2.5, and the master cylinder’s oscillation frequency ratio ranging from 0.05 to 3.2. Both the resonance amplitude and resonance frequency are found to increase with the Reynolds number. A critical Reynolds number is discovered, beyond which the vibration center of the slave cylinder drifts away from the master cylinder, but below which the vibration center of the slave cylinder approaches the master cylinder. This effect is amplified when the master cylinder vibrates at a higher frequency.

We present a novel framework for nonlinear stochastic dynamic analysis under generalized (Gaussian and non-Gaussian) loading. First, the actual system involving high-dimensional stochastic inputs is reduced to multiple low-dimensional systems by using graph structure. Subsequently, Gaussian process (GP) is utilized as a surrogate for the low-dimensional systems. The GP associated with the low-dimensional systems obtained using the graph-theoretic approach can be trained in parallel, and hence the proposed approach is highly efficient. In order to illustrate the performance of the proposed approach, four nonlinear stochastic dynamic problems have been solved. All the problems selected are high dimensional in number of stochastic dimensions. Results obtained using the proposed approach are compared with benchmark solutions obtained using Monte Carlo simulation. It is observed that the proposed approach yields highly accurate results for all the problems. Moreover, the number of training points required is also quite a bit less, indicating that the proposed approach is highly efficient.

Existing procedures for determining the minimum separation distance between adjacent buildings are based on the approximations of the peak relative horizontal displacement of the buildings, which are characterized by unknown pounding probabilities. The present study proposes a probabilistic performance-based procedure for determining the critical separation distance (CSD) between adjacent buildings exhibiting linear elastic behavior. Pounding events are expressed in the form of single-barrier first-passage reliability problems according to the performance-based seismic design theory. With the random vibration theory, the nongeometric spectral characteristics of the relative displacement response of adjacent buildings are deduced, and the approximate analytical solutions of the seismic pounding fragility are obtained, employing analytical approximations. Based on the seismic pounding fragility of adjacent buildings, the calculation of CSD is described as an inverse reliability problem, and the specific CSDs corresponding to a target probability of pounding during the design life of the given adjacent buildings are derived by a proposed piecewise fitting iterative search algorithm. The proposed procedure is applied to several different buildings modeled as linear elastic single-degree-of-freedom (SDOF) and multidegree-of-freedom (MDOF) systems. Referencing to the importance sampling using elementary events (ISEE) method, the accuracy and efficiency of the proposed methodology are verified. Furthermore, the results obtained based on the proposed procedure are validated against shaking table test results.

In this paper, the nonlinear sloshing behavior of a liquid in a partially filled tank is studied using the finite-element method (FEM) based on new spherical Hankel shape functions. The liquid free surface is one of the important parameters in the modeling of the sloshing problems. The main aim of this study is the determination of the free surface location using a new finite-element technique. In this new method, the finite-element method with new shape functions is developed and reformulated. These shape functions are derived using the first and second kind of Bessel functions and have properties such as piecewise continuity. Using these new functions, the number of elements can be reduced, while the accuracy of the results can be increased. The application and accuracy of the proposed method are investigated by several problems related to the sloshing behavior of the liquid. The obtained results indicate that the new method is capable of computing the free surface elevation with a lower number of elements with good accuracy.

Viscoelastic dampers are a kind of energy-dissipation device with good damping performance. They are also extensively utilized in earthquake mitigation for structures in civil engineering. In the present work, mechanical behavior tests of a viscoelastic damper are conducted with varying loading frequencies and excitation displacement amplitudes. The results demonstrate that viscoelastic dampers have a high damping performance. The micromorphological structures of the viscoelastic material are investigated with scanning electron microscope (SEM) technology. A new mathematical model for viscoelastic materials, the equivalent fractional-order microstructure Zener (EFMS-Zener) model, is formulated depending on the micromolecular structures and the amplitude-temperature equivalent principle. The EFMS-Zener model is validated with test data, which show that the newly formulated model can accurately reflect the mechanical performance and damping capability of a viscoelastic damper, which are importantly influenced by loading frequency and excitation displacement.

During hydraulic fracturing, the filtration of fracturing fluid increases the pore pressure in the vicinity, resulting in pore pressure–induced stress in the reservoir. In order to study the evolution of pore pressure–induced stress during fracturing, based on Biot’s theory, a dynamic simulation model of single-fracture or multifracture propagation was established through coupled fluid flow and geomechanics. In the model, the heterogeneity of the reservoir and the influence of pore elasticity of reservoir rock were considered. Further, the finite volume and iterative methods were used to solve the model. The results show that the heterogeneity of reservoir permeability and porosity has a great influence on the distribution of pore pressure–induced stress, and it will make the induced stress distribution more complicated, resulting in local stress prominence. The distribution of pore pressure–induced stress during fracturing is quite different from that of hydraulic fracture opening–induced stress. With the increase of fracturing time, the distribution of pore pressure–induced stress shows a certain regularity, and the minimum horizontal principal stress shows a higher level near the fracture and a lower level on the left and right sides. However, the maximum horizontal principal stress is higher near the fracture and lower at the fracture tip (upper and lower parts of the fracture). Under certain conditions, pore pressure–induced stress will reverse the horizontal principal stress in the local area. Considering the influence of pore elasticity, the pore pressure will increase because of the fracturing fluid filtration, resulting in further increase in reservoir permeability and porosity, which in turn will increase fracturing fluid filtration. Through this study, the distribution of induced stress in the hydraulic fracturing process can be described more accurately, which can provide some guidance for hydraulic fracturing design and theories.