Journal of Engineering Mechanics

A new interface element constitutive model is proposed in this study for analyzing masonry using the simplified micromodeling (SMM) approach, in which mortar and two unit–mortar interfaces are lumped into a zero-thickness joint (modeled using an interface element) between expanded masonry units. The new model is capable of simulating tension cracking, shear slipping, and compression failure, and is defined by a convex composite failure surface consisting of a tension-shear and a compression cap failure criterion. It removes the singularity in the tension-shear region but not in the compression-shear region. In addition, the proposed model is based on the hypothesis of strain hardening. The robustness and computational cost of the proposed model were compared with different constitutive models (which are based on three, two, and one failure criteria) that have been widely used in the literature to describe masonry behavior through a series of one-element tests and through the comparison of finite-element (FE) response simulation of an unreinforced masonry shear wall. The FE response results indicate that the proposed constitutive model is more efficient than and at least as accurate as the other constitutive models for analyzing masonry using the SMM approach.

Based on the fast Fourier transform (FFT), an efficient and accurate algorithm was developed for improving the computational efficiency of structural responses under nonstationary stochastic excitations. In this method, the FFT technique was first adopted to accelerate the evaluation of time integration terms involving significant computational effort in the nonstationary stochastic response analysis of linear structures. Then, the proper orthogonal decomposition was used to assist the application of FFT for the generally modulated excitation by separating the frequency item of nonuniform modulation functions from the time integration terms. Further, the proposed method was extended to the nonstationary stochastic response analysis of nonlinear structures based on the equivalent statistical linearization method. Finally, numerical examples with respect to linear structures, Duffing systems, and hysteretic systems illustrated that the proposed method performs well.

This paper presents a novel copula-based approach to model the joint cumulative distribution function (JCDF) of wind speed and direction for wind-resistant design of engineering structures. Copula functions enable the JCDF to be obtained with the corresponding marginal distributions of wind speed and wind direction. The daily maximum wind speed recorded during 1971–2017 in Dali, China, was collected and used as the data source. The Weibull distribution was applied to represent the marginal distribution of wind speed; meanwhile, the marginal distribution of wind direction was modeled by the von Mises distribution. The Farlie-Gumbel-Morgenstern (FGM) and four commonly used Archimedean copulas were employed to construct the continuous bivariate JCDF of wind speed and direction. The simulation results were compared with those obtained using the traditional methods, i.e., the approaches based on multiplication rules and angular-linear (AL) model. The statistics of the coefficient of determination $R^2$ and root-mean-squared error (RMSE) obtained in the regression analysis were used to judge the goodness of fit of each approach. The analytical results show that the approach based on copulas can not only yield good JCDF estimations of wind speed and direction, but also provide an effective and practical way to predict the extreme wind speed at a certain return period. Moreover, the estimated extreme wind speed varies significantly in the 16 directions and the predicted extreme wind speed in the studied region will be unreliable when neglecting the joint effect of wind speed and direction.

The influence of occupants on the dynamic properties of structures is not totally understood and can lead to overdesign, extreme vibrations, or even the collapse of buildings, stadiums, and other structures subjected to the action of standing large crowds. Several numerical models have been proposed to represent the effects of people on the structure, showing that there is not yet a consensus between the different approaches. Most of the models use masses, springs, and dampers to model the human in a standing position. Arguably, the human model could be more complex. The motor system of the human body is a complex interaction of systems (musculoskeletal, nervous, proprioceptive, etc.), all responding at distinct levels of excitation, a phenomenon that is difficult to model with a spring-mass-damper (SMD) system. This paper proposes the use of a closed-loop controller system to model the interaction of a standing human on a structure. The model is updated in a probabilistic sense using experimental data collected in a laboratory setting. The probabilistic approach allows exploration of dependencies between parameters, as well as a probabilistic estimation of the model parameters. The proposed model obtained is validated by predicting the dynamic characteristics of the combined human–structure interaction system after the mass of the structure has been modified. The closed loop controller model is able to predict the dynamic behavior of the human–structure system for a specific individual more closely than traditional SMD models found in the literature.

Computational fluid dynamics (CFD) and fluid–structure interaction (FSI) are growing disciplines in the aeroelastic analysis and design of long-span bridges, which, with their bluff body characteristics, offer major challenges to efficient simulation. In this paper, we employ isogeometric analysis (IGA) based on nonuniform rational B-splines (NURBS) to numerically simulate turbulent flows over moving bridge sections in three dimensions (3D). Stationary and dynamic analyses of two bridge sections, an idealized rectangular shape with aspect ratio $1:10$ and a $1:50\text{-}\mathrm{scale}$ model of the Hardanger bridge, were performed. Wind tunnel experiments and comparative finite-element (FE) analyses of the same sections were also conducted. Studies on the convergence, static dependencies on the angle of attack, and self-excited forces in terms of the aerodynamic derivatives show that IGA successfully captures the bluff-body flow characteristics and exhibits superior per-degree-of-freedom accuracy compared to the more traditional lower-order FE discretizations.

A hysteretic shell finite element for the nonlinear, static, and dynamic analysis of structures is presented, formulated on the basis of classical theory of plasticity and finite deformation. The generalized smooth, rate-independent three-dimensional (3D) Bouc-Wen model is expressed in tensorial form incorporating the von Mises yield criterion and different types of nonlinear hardening laws. Based on this approach, a hysteretic shell finite element is derived in which the shell is considered as a number of fully bonded layers along the thickness. The elastic mixed interpolation of tensorial components with nine nodes (MITC9) element is extended by considering as additional hysteretic degrees of freedom the plastic strains, backstresses, and the variable yield stress. These are considered at the Gauss points of two faces and all interlaminar interfaces, the evolution of which is described by Bouc-Wen-type equations. Using this formulation, the effect of the nonlinear hardening on the response of a shell structure and in particular the phenomenon of ratcheting is investigated. The developed hysteretic shell element accounts for geometric nonlinear analysis and incorporates two constituent functionally graded materials. Numerical results are presented, demonstrating the efficacy, accuracy, and generality of the proposed approach.

This paper investigated the nonlinear, rocking seismic response of slender, free-standing columns when equipped along their sides (or at their pivoting points) with vertical energy dissipation devices which offer either hysteretic or viscous (linear or nonlinear) dissipation. The paper derived the nonlinear equations of motion and then revisited the transverse response of the South Rangitikei Rail Bridge. The analysis showed that the 72-m-tall stepping bridge piers exhibit remarkable seismic performance even when excited with recorded ground motions that are much stronger than the known strong motions at the time of the design of the bridge. Subsequently, the paper showed that there are isolated examples of earthquake excitations in which the response of the rocking bridge pier when damped with either hysteretic or viscous dampers is more aggravated than the undamped response. This phenomenon may also manifest when idealized mathematical pulses are used. The paper concluded that the effectiveness of supplemental hysteretic or viscous damping in suppressing rocking response depends strongly on the local kinematic characteristics of the ground motion. Whenever the damped response exceeds the undamped response the exceedance is marginal, and in most cases the damped response is lower than the undamped response.

Structure-dependent integration algorithms have been implemented for pseudodynamic testing because they are very promising for this type of test due to the combination of unconditional stability and explicit formulation simultaneously. Although their numerical properties have been assessed and their feasibility for pseudodynamic tests has been corroborated, the choice of an appropriate structure-dependent pseudodynamic algorithm might be a difficult task. This is because some undiscovered, adverse properties were found for specific structure-dependent algorithms, although their basic properties have been well explored. Because the adverse properties are not well disclosed for these structure-dependent pseudodynamic algorithms, they might lead to inaccurate test results. This paper summarized both the favorable and adverse numerical properties of the pseudodynamic algorithms so that appropriate pseudodynamic algorithms can be identified. This paper assessed and compared most structure-dependent pseudodynamic algorithms, and recommended some structure-dependent pseudodynamic algorithms for engineering practice. Both recommended nondissipative and dissipative structure-dependent algorithms are very suitable for pseudodynamic tests because they possess favorable properties but exhibit no adverse properties. It was also substantiated that numerical damping cannot be used to overcome an overshoot caused by weak instability.

Initiation toughness, propagation toughness, and arrest toughness can be considered as threshold values to predict the dynamic behavior of cracks in initiation, propagation, and arrest. For rock materials, initiation toughness has been studied extensively, whereas propagation toughness and arrest toughness have received less attention. In this study, a single cleavage semicircle compression (SCSC) specimen was proposed, and Ya’meng black sandstone was selected to make the SCSC specimens. Impact tests were conducted using the SCSC specimens and a split Hopkinson pressure bar (SHPB) test system. Crack initiation time, propagation time, and propagation speed were measured using crack propagation gauges (CPGs). A high-speed photography (HSP) system was also used to observe the dynamic behavior of crack propagations and arrests. Dynamic stress intensity factors (SIFs) were calculated using ANSYS code, and the crack propagation path was simulated using AUTODYN code. The simulation results generally agree with the test results. Dynamic initiation toughness, propagation toughness, and arrest toughness were determined using an experimental–numerical method. The results show that crack propagation speeds vary during crack propagations, and cracks may arrest for one or more periods during propagation. Dynamic initiation toughness is proportional to the loading rate applied to the specimens, and arrest toughness is less than both initiation toughness and the propagation toughness for the Ya’meng sandstone.

It is important from the safety and economical perspectives that a suspension bridge should have minimal deformation under the self-weight of the bridge while the tension forces of the main cable and hangers remain at the lowest required level to achieve this goal. Most existing studies require establishing force equilibrium equations on the main cable joints and substituting equivalent forces. A new iterative nonlinear shape-finding technique is developed for suspension bridges to seek the target bridge profile under gravity. Different from most existing studies, nonlinear analysis is conducted on the whole bridge structure directly to avoid the complexities and induced errors associated with existing approaches. A detailed analyzation of a three-dimensional catenary cable element is first conducted based on the analytical equilibrium equations of elastic catenary. Two iteration schemes are proposed to find the solutions of cables with known undeformed length or known tension force at one end to serve different design needs. The proposed shape-finding technique is composed of iterations in three levels to comprehensively consider the nonlinear effects involved in the process. Numerical studies are conducted to demonstrate the behavior of a single cable element and the proposed shape-finding process on a prototype suspension bridge. The iteration results show that the proposed direct shape-finding technique is effective and accurate to determine the optimal target bridge profile by overcoming the limitations of the existing approaches. Although developed for suspension bridges, the proposed iteration technique for target cable shape and cable tension can also be extended to the optimal design of other types of cable-supported structures.

A nonlinear diffusion model for the drying of concrete, previously developed at Northwestern University and embedded in some design codes, was improved and calibrated on the basis of recent more extensive experimental data from the literature as well as theoretical considerations. The improvements include a new equation for the dependence of the self-desiccation rate on pore humidity and hydration degree; an updated equation for the decrease of moisture permeability at decreasing pore humidity; new equations to predict the permeability and diffusivity parameters from the $\text{water-cement}$ and $\text{aggregate-cement}$ ratios, hydration degree, the type of concrete; and new equations to capture the nonlinearity of the sorption isotherm as a function of pore humidity and water-cement ratio. Furthermore, the recent idea that the pore humidity drop is the driving force, rather than a side effect, of the autogenous shrinkage is verified.

To understand the inelastic behavior of functionally graded materials (FGMs) containing aluminum particles in high-density polyethylene (HDPE), a micromechanics-based elastoplastic model was developed. It was assumed that the particle phase was in a linearly elastic state while the matrix phase could be in a plastic stage. The corresponding yield function for the matrix phase was investigated, where the pairwise interaction term and probabilistic spatial distribution of particles were used to accommodate the gradation of particle volume fraction. Accordingly, the overall elastoplastic stress-strain response was established through homogenization of the stress and strain fields. The modeling prediction was validated with experiments on a specific functionally graded material. Good agreement was observed between the model and experimental results. In this paper, the effect of various particle distribution functions and relative material stiffness on the elastoplastic behavior of FGMs is addressed and discussed.

Two novel surrogate-based approaches have been developed for uncertainty quantification of engineering systems. In doing so, two well-known techniques, namely, high dimensional model representation (HDMR) and Kriging, have been integrated. Specifically, the trend portion of Kriging has been replaced by HDMR such that the approximation accuracy may be enhanced. The improvement in accuracy is the result of the fact that the proposed hybrid surrogate model performs a two-tier approximation, first capturing the global variation in the functional space using a set of component functions by HDMR and subsequently interpolating the local fluctuations by Kriging. Additionally, to improve the computational cost of this proposed model, feature selection approaches, namely, least absolute shrinkage and selection operator and least angle regression have been employed. These efficient schemes utilized to determine the relevant unknown coefficients induces adaptive sparsity for the proposed surrogate models. The performance of the proposed approaches has been assessed by solving an analytical and practical engineering problem. The results illustrate excellent performance of the proposed approaches in terms of both approximation accuracy and computational effort.

The maximum value of a random field over a subdomain is a random variable whose probability distribution can be determined from the first-order marginal probability density function and autocorrelation function of the random field given that certain assumptions hold. It is shown in this work that this formulation, which traditionally has been applied to wind engineering problems, can express the probability distributions of the maximum values of mechanical response quantities of structures subjected to the boundary conditions applied in computational homogenization. Once the expression for the maximum value distribution is determined, the convergence of the maximum value to a deterministic value as a function of structure size can be easily computed. This may have implications in determining the representative volume element for mechanical properties driven by the extremes of the response quantities from which they are derived, such as in upscaling damage parameters. The concept is demonstrated by comparing the results using the maximum value formula to brute-force Monte Carlo simulation for a stochastic bar.