Journal of Engineering Mechanics

The state space method has been widely used to analyze the static and dynamic characteristics of homogeneous, laminated, functionally graded, or even intelligent structures. However, the solution of the state equation using the traditional transfer matrix generally encounters the problem of numerical instability. This work, therefore, derives the general solution to the state equation by making use of similarity transformation to convert the system matrix into a matrix in Jordan canonical form (including the diagonal matrix as a special case), so as to avoid the previously stated problem. A special form of the exponential function is also introduced according to the characteristics of the eigenvalues of the system matrix. Furthermore, the undetermined coefficients in the general solution—rather than the original state variables—are considered as the primary unknowns. Consequently, a new solution with numerical robustness to the state equation is obtained. Finally, numerical examples for the free vibration analyses of beams and plates as well as interfacial shear stress analysis of fiber-reinforced polymer (FRP)-strengthened concrete beams are presented to verify that the proposed procedure can circumvent numerical instability completely.

This paper presents a floor-vibration-based step-level occupant-detection approach that enables detection across different structures through model transfer. Detecting the occupants through detecting their footsteps (i.e., step-level occupant detection) is useful in various smart building applications such as senior/healthcare and energy management. Current sensing approaches (e.g., vision-based, pressure-based, radio frequency–based, and mobile-based) for step-level occupant detection are limited due to installation and maintenance requirements such as dense deployment and requiring the occupants to carry a device. To overcome these requirements, previous research used ambient structural vibration sensing for footstep modeling and step-level occupant detection together with supervised learning to train a footstep model to distinguish footsteps from nonfootsteps using a set of labeled data. However, floor-vibration-based footstep models are influenced by the structural properties, which may vary from structure to structure. Consequently, a footstep model in one structure does not accurately capture the responses in another structure, which leads to high detection errors and the costly need for acquiring labeled data in every structure. To address this challenge, the effect of the structure on the footstep-induced floor vibration responses is here characterized to develop a physics-driven model transfer approach that enables step-level occupant detection across structures. Specifically, the proposed model transfer approach projects the data into a feature space in which the structural effects are minimized. By minimizing the structure effect in this projected feature space, the footstep models mainly represent the differences in the excitation types and therefore are transferable across structures. To this end, it is analytically shown that the structural effects are correlated to the maximum-mean-discrepancy (MMD) distance between the source and target marginal data distributions. Therefore, to reduce the structural effect, the MMD between the distributions in the source and target structures is minimized. The robustness of the proposed approach was evaluated through field experiments in three types of structures. The evaluation consists of training a footstep model in a set of structures and testing it in a different structure. Across the three structures, the evaluation results show footstep detection F1 score of up to 99% for the proposed approach, corresponding to a 29-fold improvement compared to the baseline approach, which do not transfer the model.

The size-dependent strength of individual particles controls several key aspects of the constitutive response of brittle granular materials. Capturing this factor in numerical analyses is essential to accurately model the mechanical behavior of assemblies with particles of different size. In this study, a three-dimensional discrete element method (DEM) model is proposed to reproduce the size dependence of the particle strength by means of a bonded particle framework. Particle fragmentation is modeled explicitly through the disintegration of agglomerates made of bonded elementary spheres. Diametric and oedometric compression tests performed on different sands are used for the calibration and validation of the model. The size effect and variation of the particle strength evaluated in terms of stress and energy measures are interpreted via Weibull statistics. The DEM model calibrated with a set of diametric compression experiments successfully captures the particle strength variability and the size dependence of the failure and yielding strength at particle- and assembly-scale, respectively. The degree of fragmentation during the confined compression of sand and agglomerate assemblies are compared by quantifying the evolution of particle size distribution and a relative breakage index. The satisfactory agreement between experiments and numerical results suggests that the proposed DEM approach can be used to simulate the comminution of crushable granular solids, thus being particularly useful to study size reduction processes in cases where direct testing is impractical.

A thermodynamics-based energy analysis approach for pressure-dependent materials is presented. Formulation of plastic free energy and plastic dissipation for the nonassociated Drucker-Prager plasticity model is derived based on thermodynamics. It is proven that the proposed energy computation formulation always gives nonnegative incremental plastic dissipation, as required by the second law of thermodynamics. The presented methodology is illustrated using numerical simulations of Toyoura sand and Sacramento River sand under different loading conditions. Multidirectional loading and pressure dependency effects on plastic dissipation are investigated. The continuous, nonnegative dissipation of mechanical energy in pressure-dependent frictional materials under complex three-dimensional cyclic loading was properly modeled.

A critical analysis of the hysteresis models of wooden connections has led to an alternative analytical formulation of the pinching phenomenon. Starting from the generalized Bouc-Wen model, the six-degrees-of-freedom formulation has been extended to an eight parameters formulation, which is a better representative of the connection’s cyclical degradation. The information given by the two additional parameters and also energy-dependency of the parameters provide a faithful representation of the actual hysteresis cycles of wooden connections. The model has been calibrated on experimental data, following an identification procedure, based on an Ordinary Least Squares (OLS) operator.

The paper investigates the role of masonry infills on the progressive collapse response of reinforced concrete frame structures. A wide parametric investigation is carried out to assess the influence of frame aspect ratio, seismic detailing, and lateral constraint degree for the cases of bare and infilled frames. Numerical pushdown tests simulating a column-loss scenario are carried out on reference two-bay frames extracted from different 5-story frame buildings. Infill-frame systems are modeled by means of a refined nonlinear finite-element modeling approach experimentally validated. Bearing capacity under the column-loss scenario is compared with the expected dynamic load demand, highlighting most influencing parameters and determining capacity/demand ratios by means of an energetic approach. Results show a significant increase in strength and stiffness of infilled frames to vertical collapse with respect to bare frames, accompanied by substantial modification of damage framework, resisting mechanism, and overall safety margins. The adaptability of the common equivalent-strut modeling approach as a simple assessment method is finally tested, comparing results from refined finite-element models and simplified fiber section models.

An analytical elastic continuum model is developed for the settlement of end-bearing piles in a two-layer soil over a rigid stratum. The model has its roots in the point-load solution of Westergaard, which was later extended by Tajimi to deep foundations and lies on the assumption of a vanishing soil stress or displacement component. For piles in homogeneous soils, such solutions were elaborated on by Nogami and Novak. Contrary to these solutions, the proposed generalized formulation can handle layered soils using, for the first time, two sets of eigenfunctions (static “modes”) that are different for the soil and the pile. Stresses and displacements are determined in the form of Fourier series with coupled coefficients obtained by solving a system of algebraic equations of rank equal to the number of modes considered. This is in contrast with existing models, where the Fourier coefficients are obtained individually. Pile-head stiffnesses obtained from this model are verified against results from rigorous finite-element analyses and other solutions. Results for pile settlement, pile stresses, side friction, and Winkler moduli are presented.

The coaxial and totally noncoaxial parts of a tensor in regard to another reference tensor are derived in closed analytical form based on representation theorems of tensor-valued isotropic functions. In the process a new interpretation is obtained for a singular case of representation theorems. As a first application, the coaxial and noncoaxial parts of a stress rate tensor in regard to the stress tensor are analytically expressed, and the findings applied to the following two cases: analytically express the part of a stress rate tensor that induces change of stress principal axes at fixed principal stress values, and change of stress principal values at fixed stress principal axes such that the stress orbit on the stress $\pi$-plane is circular. A second application refers to enhancing the definition of the fabric anisotropy variable $A$, a quantity of cardinal importance for anisotropic critical state theory in granular mechanics, so that the orthogonal coaxial and noncoaxial parts of the fabric tensor in regard to the plastic strain rate direction participate in the definition of $A$.

Traffic signal structures are very susceptible to wind-induced vibration because of their slenderness and low damping. In the wind, the vertical vibration is usually dominant, which affects driving safety and structural fatigue life. To suppress the vibration, a new type of pounding tuned mass damper (PTMD) is proposed in this study. It is specially designed for a cantilevered traffic signal structure with two improvements based on the original PTMD. First, the proposed PTMD has a hidden design and is housed inside the cantilevered mast arm of traffic signal structures, which can avoid visual interference and potential safety risks to drivers and pedestrians. Second, the static equilibrium position of PTMD is relocated so that its mass block just touches the lower boundary of mast arm, which makes it effective at any level of amplitude. Concretely, the mass block pounds the lower boundary of the mast arm under small-amplitude vibrations, while it pounds both the lower and upper boundaries under large-amplitude vibrations. The model experiment on a traffic signal structure was designed to verify the performance of the proposed PTMD in free and forced vibrations. Further, the corresponding numerical simulations were also carried out, where a nonlinear viscoelastic model was established to model the impact force and the related model parameters were obtained by the experimental results. Both numerical and experimental results show that the proposed PTMD is very effective in reducing the vibration of traffic signal structures.

This paper presents a new approach for extracting nonlinear aerodynamic damping of crosswind-excited tall buildings from response statistics at different levels of structural damping obtained from aeroelastic model tests. The aerodynamic damping at a given wind speed was modeled as a polynomial function of the amplitude of the harmonic building motion, which leads to analytical solutions of the standard deviation (SD) and kurtosis of the crosswind response under stochastic load excitation. As an inverse problem of response analysis, the nonlinear aerodynamic damping model coefficients can be identified from known response SD and kurtosis through a nonlinear optimization algorithm. The crosswind loading spectrum at the structural frequency can be determined from rigid model testing or treated as an unknown. The accuracy of this identification scheme is first illustrated using crosswind response of a tall building calculated from a given nonlinear damping model. It is then applied to a square-shaped tall building using aeroelastic model testing data under boundary-layer flows. The limitation of the conventional approach, which did not account for the response kurtosis, is highlighted. With the proposed approach, the effect of approaching flow characteristics on crosswind aerodynamic damping is examined.