Journal of Engineering Mechanics

An accurate determination on the acceleration response of a long-span and lightweight steel-concrete composite floor is essential for assessing the floor’s human-induced vibration serviceability, in which the interaction between human and structure should be considered. In the theoretical analysis, the human and floor subsystem are idealized as the linear oscillator model and anisotropic rectangular plate, respectively. This paper presents an analytical approach to determine the acceleration response induced by the walking activity on a steel-concrete composite floor with two opposite edges simply supported and the other two edges clamped. The proposed approach is based on the combined weighted residual and perturbation method. Implementation of this method is simple and avoids cumbersome mathematical calculations. The theoretical solution is validated with experimental results. A sensitivity study using the analytical solution was also conducted to investigate the effects of walking path, damping ratio, and walking frequency on the peak acceleration.

In order to accurately assess the reliability of a real-world complex system, the joint distribution of component events is needed. In reality, however, such complete information to model the joint distributions of system components is rarely available. As a way to resort only to the available information while excluding any assumptions on the form of distributions, a linear programming (LP) bounds method was developed in 2003, which computes the narrowest bounds possible for given information regarding marginal and joint failure probabilities. However, the number of variables of the optimization problem exponentially increases as that of component events increases, requiring an insurmountable memory for larger systems. In order to overcome such memory issue, an alternative formulation of the LP bounds method is proposed in this paper. Specifically, an iteration of binary integer programming (BIP) is formulated based on the inclusion relationships between the events of consideration. As a result, the memory requirement can be significantly alleviated with the trade-off of the computational cost required for repeated optimizations of smaller BIP problems. Then, the major bottleneck is changed from the number of component events to that of constraints given as information to narrow the bounds. This paper also provides empirical suggestions on the selection of a subset of constraints to further extend the applicability of the proposed methodology to even larger systems. Five numerical examples of series, parallel, and general system reliability problems are provided to demonstrate the method and its applications.

Digital image correlation (DIC) is a commonly used full-field technique for measuring surface deformations in experimental solid mechanics. It directly provides full-field displacements by comparing digital images of the speckle pattern subsets painted on a structure’s surface in the undeformed and deformed states, respectively. Although DIC measures displacements in solid structures, it is often necessary to determine the individual stress components for proper fatigue and failure analysis. Hybrid digital image correlation (hybrid-DIC) is an experimental-analytical approach where theoretical formulations are combined with DIC displacement data for the identification of the full-field stress components. The present paper demonstrates the ability in providing reliable full-field stresses in numerous two-dimensional (2D) plane stress engineering situations involving circular and irregular geometric discontinuities in isotropic or orthotropic composite materials. Hybrid-DIC’s main advantages are (1) it does not require the differentiation of measured displacements, and (2) it provides stresses at the edges of discontinuities, often the location of maximum stress magnitudes.

This paper uses long-term bridge monitoring data to quantitatively assess the composite action exhibited in slab-on-girder highway bridges and investigates the potential relationship between composite action and deck deterioration over negative bending regions. A three-span highway bridge in Michigan is instrumented with a structural monitoring system to observe the flexural response of the spans to vehicular loads. The monitoring system is designed to offer data for quantitative assessment of the degree of composite action in composite and noncomposite sections of the bridge spans using the position of neutral axis and the magnitude of slip strain as key response parameters correlated to composite action. It is shown that unintended nonlinear partial composite action exists in negative bending regions of the bridge. A calibrated analytical model and a finite-element model are developed based on empirical observation allowing tensile strains in the deck to be estimated under load. Estimated surface strains are compared with those with the design assumption of no composite action at the slab–girder interface. It is concluded that the observed partial composite action results in higher tensile strains in the deck which is a likely culprit to accelerated deck deterioration.

Dynamic sensor networks have the potential to significantly increase the speed and scale of infrastructure monitoring. Structural health monitoring (SHM) methods have been long developed under the premise of utilizing fixed sensor networks for data acquisition. Over the past decade, applications of mobile sensor networks have emerged for bridge health monitoring. Yet, when it comes to modal identification, there remain gaps in knowledge that have ultimately prevented implementations on large structural systems. This paper presents a structural modal identification methodology based on sensors in a network of moving vehicles: a large-scale data collection mechanism that is already in place. Vehicular sensor networks scan the bridge’s vibrations in space and time to build a sparse representation of the full response, i.e., an incomplete data matrix with a low rank. This paper introduces modal identification using matrix completion (MIMC) methods to extract dynamic properties (frequencies, damping, and mode shapes) from data collected by a large number of mobile sensors. A dense matrix is first constructed from sparse observations using alternating least-square (ALS) then decomposed for structural modal identification. This paper shows that the completed data matrix is the product of a spatial matrix and a temporal matrix from which modal properties can be extracted via methods such as principal component analysis (PCA). Alternatively, an impulse-response structure can be embedded into the temporal matrix and then natural frequencies and damping ratios are determined using Newton’s method with an inverse Hessian approximation. For the case of ambient vibrations, the natural excitation technique (NExT) is applied and then structured optimization (Newton’s method) is performed. Both approaches are evaluated numerically, and results are compared in terms of data sparsity, modal property accuracy, and postprocessing complexity. Results show that both techniques extract accurate modal properties, including high-resolution mode shapes from sparse dynamic sensor network data; they are the first to provide a complete modal identification using data from a large-scale dynamic sensor network.

A stabilized meshfree formulation for modeling nonlinear, multiphase porous media with application to landslide simulation is presented. To effectively capture the hydromechanical couplings between solid and fluid phases, an efficient equal-order approximation pair is adopted in conjunction with the fluid pressure projection in the mixed formulation, which avoids spurious pressure oscillations caused by the violation of the inf-sup condition. Although semi-Lagrangian meshfree methods are well-suited for modeling extremely large deformation phenomena, their performance is severely impacted by improper domain integration techniques. In this work, the naturally stabilized nodal integration (NSNI) technique is employed to achieve a stable and efficient reproducing kernel mixed formulation. By using the implicit gradient approximation, the gradients of strain and fluid flux fields are added into the mixed formulation to eliminate spurious low-energy modes of nodal integration. This procedure adds little computational effort to the overall analysis. In addition, a set of modified test functions is introduced to ensure the variational consistency in the Galerkin formulation for multiphase porous media. The convergence, stability, and effectiveness of the semi-Lagrangian meshfree formulation are examined and demonstrated in several numerical examples, including the post-failure modeling of a partially saturated levee.

This study proposes a numerical method to solve the snap-through problem of elastic shallow inextensible circular arches. Specifically, the snap-through behavior of arches subjected to a downward load at a point along the span was systematically evaluated for variable elastic horizontal supports under unilateral displacement control. Through theoretical analysis based on a dimensionless formulation, the critical state of snap-through can be determined by embedding ordinary differential equations into the nonlinear unconstrained optimization. Then, critical stiffness lines for horizontal springs and snap regions with varying loading position were systematically analyzed to judge whether a snap-through phenomenon will occur. Parametric analysis was further carried out to investigate the influence of variable horizontal spring stiffness and different arch length on the overall deformation and the critical displacement of critical states. The results show that the critical stiffness increases with the decrease of arch length and the decrease of horizontal stiffness and arch length can both expand the snap region. This study highlights the important role of stiffness of supports in snap-through behavior control and provides a numerical method for more accurate evaluation of the snap-through behavior of arches under various supports and loading conditions in engineering applications.

The harmonic-enriched reproducing kernel (HRK) approximation together with collocation method is introduced to circumvent the discretization restriction for highly oscillatory partial differential equations (PDEs). It is first shown that to embed the harmonic function with a desired frequency in the HRK, both sine and cosine with the same frequency should be included in the basis vector for construction of HRK approximation. The HRK and its implicit derivatives are then used in the collocation method to effectively obtain solutions of oscillatory PDEs. The standard monomials can be included together with harmonic functions in the HRK and the reproducing conditions can be exactly satisfied with a complete set of basis functions. For PDEs with semi-harmonic solutions, the present method yields more accurate results compared with the standard reproducing kernel (RK) when a coarse discretization is used. On the other hand, when the discretization is refined, the HRK exhibits a similar convergence behavior as the standard RK. The effectiveness of the present method is demonstrated using highly oscillatory 2nd order and 4th order PDEs. The accuracy and performance of this method are compared with standard RK with the collocation method and the finite element method (FEM).

In this paper, a displacement-based weak-form quadrature element (WQE) is formulated and implemented for long-term response analysis of steel–concrete composite beams. The effects of creep and shrinkage taking place in reinforced concrete slabs are considered by using an integral type viscoelastic model. Timoshenko and Kant higher-order beam theories are applied to depict the reinforced concrete slab and steel beam, respectively, so as to achieve accuracy close to that of the 3D shell model, but at a much lower computational cost. The proposed model and program are verified through comparisons with the 3D shell and classical beam models. To investigate the improvement of convergence performance contributed by the differential quadrature technique, detailed comparisons are made between the WQE and conventional finite element. Numerical results show that the composite beams modeled with the Timoshenko-Kant kinematical assumption can achieve accuracy close to that of the 3D shell model; due to the ability to conveniently adjust interpolation order, the proposed WQE acquires much higher computational efficiency than the conventional finite element; the severe numerical smoothness problem common in the displacement-based finite element model (FEM) is significantly alleviated by the higher-order WQE method.

Clutching inerter damper (CID) is an innovative damping device with inherent nonlinearity. In this paper, the description of the CID system is firstly made followed by the analyses of free vibration and harmonic response. Secondly, the equivalent linearization method (ELM) based on statistical linearization is studied to linearize the CID system. Thirdly, the layout of the CID in a multidegree-of-freedom (MDOF) structure is discussed and the ELM is extended to the MDOF structure based on modal reconstruction. Finally, the spectra-based seismic assessment and performance design are discussed via the equivalent linearization system (ELS), which proves to be a simplified way for the assessment and design of structures with CID. Results have shown that the ELS is accurate and convenient to approximate the CID system, and it is suggested that the CID should be mounted in the weak layers of the MDOF structure.

This study describes step-by-step analytical closest-point projection (CPP) implicit return mapping solutions for von Mises, Drucker-Prager, and Hyperbolic Drucker-Prager yield surfaces in rotated energy-mapped stress space (REMSS) along with discussion, nonlinear finite-element implementation and examples within the Wolfram Mathematica environment. The CPP in conventional stress space does not give the closest point in the Euclidean norm, but in the energy norm. In REMSS, the correct return trajectory is a closest-point return, allowing the constitutive relations to be simplified and turning the determination of a CPP solution in a systematic task. The obtained finite-element results are in excellent agreement with the analytical solutions.

Given a limited number of time histories of a non-Gaussian random process, it is of interest to reproduce a much greater number of samples while retaining homogenous statistical characteristics. In structural engineering, this matters to extrema prediction and fatigue assessment. Particularly when the given data exhibit strong non-Gaussianity, the issue of how to capture such stochastic characteristics while retaining the original spectral profile of the underlying process needs to be resolved. This study is an extension of the translation method that employs Hermite models to establish the relationship between the non-Gaussian process and underlying Gaussian process. Thus, unlike many other works, no information regarding a probability density function (PDF) is mandated for the translation in the present study; only central and linear moments are required. Specifically, for highly non-Gaussian processes, quartic and quintic Hermite models are discussed because the commonly used cubic Hermite model cannot yield an accurate approximation. For spectral restoration, the explicit relationship between the autocorrelation of the transformed process and that of the underlying Gaussian process is presented to retain homogeneity in the non-Gaussian characteristics. This explicit relationship also allows for more straightforward implementation of the proposed method in the time domain than the conventional PDF-based translation method. Furthermore, to remove negative power spectral contents incurred by incompatible and numerical errors, a correction procedure inspired by the iteration algorithm is used. Through comprehensive analyses of three offshore engineering problems (Morison drag force, total wave load on a jack-up platform, and stress response of a typical offshore wind turbine), the robustness and accuracy of the proposed homogeneous reproduction method in capturing both extrema and fatigue damage are affirmed.

A novel theoretical framework for the interpretation and modeling of the critical-state behavior of granular soils is proposed in this paper. The theory is built upon the hypothesis that the fabric state of granular assemblies is attracted by a critical fabric surface under continuous shearing. A fabric ratio-stress ratio relation and a fabric-porosity relation are proposed based on recent discrete element modeling (DEM) experimental results. It follows that the existence of a critical-state line in the conventional $e\text{-}p\text{-}q$ space can be derived by combining the aforementioned elements, offering a new perspective on the critical-state phenomenon. Simple fabric evolution laws are proposed to capture the first-order features of the stress-strain-fabric behaviors of granular soils. The basic evolution laws are then enhanced to capture the behavior of natural sand. The computed results agree well with the data from Toyoura sand under a wide range of pressure and density conditions. This exploratory study reveals a promising pathway to integrate various microstructure information in the continuum modeling of granular soils. The generality and limitations of the model is also discussed at the end of this paper.

The use of rocking members in earthquake-resistant structural systems has gained attention in recent years due to their inherent benefits, including the limitation of damage, recentering capabilities, and reduction of seismic forces transmitted to the rest of the structure. In this paper, the ideas behind the elastic macroelement formulation proposed by the authors in previous works, able to account for the deformability of the member along its height and across its base, are extended in order to predict the planar cyclic response of inelastic rocking members. To this end, the rocking interface is discretized and a nonlinear compression-only stress distribution is determined so that the sum of the induced elastic member displacements, calculated using the provided solutions based on the theory of elasticity, and the plastic ones induced in inelastic regions, agrees with the target displacements. Characteristic example cases are presented, and the results produced by the proposed macroelement are compared with experimental ones, showing that the form of the response of various rocking member configurations found in the literature can be adequately captured.

Exact solutions for steady fully developed dry granular and saturated granular–liquid mixture flows down rough inclined planes are presented with an emphasis on nonlocal effects. The particle rheology of both dry granular and saturated granular–liquid mixtures is described by a recently developed nonlocal granular fluidity (NGF) model. The fluid rheology of a saturated granular–liquid mixture is represented by the eddy viscosity, and the contacting forces between the fluid and grains are drag and buoyancy forces. The problems are then reduced to solving the resulting partial differential equations (PDEs). Closed-form solutions for the critical stopping layer height of dry granular and saturated granular–liquid mixtures are derived by analytically solving the linearized equations of the NGF model. Moreover, exact solutions for velocity profiles are acquired by solving the coupled equations with a PDE solver.

Recently, the wavelet finite element has been introduced to solve wave propagation problems because of its outstanding compact support, multiscale, and multiresolution characteristics. In this research, the accuracy of a multiscale wavelet element using B-spline wavelet on interval (BSWI) for two-dimensional (2D) elastic wave propagation was theoretically studied through dispersion analysis. The Rayleigh quotient technique was introduced to overcome the difficulties caused by the wavelet element with large internal nodes. The numerical dispersion curves of different wave types (P- and S-waves) for different BSWI elements were provided, and the phase errors and numerical anisotropy were discussed. The effects of material parameters and element distortions on the numerical dispersion were elucidated. The BSWI element and other high-order finite elements were compared. The BSWI element of order four and scale three can almost completely suppress the numerical dispersion and anisotropy when no less than five nodes exist per wavelength. Element distortions can severely aggravate numerical dispersion and anisotropy, but the accuracy can be significantly improved with a local lifting scheme without altering the initial mesh and polynomial order.

For suppression of vibration of structures modeled by a spring-mass system, we propose an innovative vibration absorber comprising a hanging heavy column attached to the mass by a pinned joint with an elastic rotational spring. The governing equation of the vibrating heavy column is derived and solved using the shooting-optimization method for the vibration amplitude of the spring-mass system under an oscillatory force. The validity of the theoretical formulation is confirmed by comparing the computed results with existing solutions for the special case of a hanging heavy column with its end fully fixed to the mass. An example is given to demonstrate the reduction of the vibration amplitude of the spring-mass system under a given exciting forcing frequency. It can be shown that one can achieve a zero amplitude of vibration of the spring-mass system by choosing a rotational spring stiffness that will tune the frequency of the hanging heavy column to the exciting frequency of the driving force.