Journal of Engineering Mechanics

Forum papers are thought-provoking opinion pieces or essays founded in fact, sometimes containing speculation, on a civil engineering topic of general interest and relevance to the readership of the journal. The views expressed in this Forum article do not necessarily reflect the views of ASCE or the Editorial Board of the journal.

The load-carrying capacity of circular sandwich panels under the quasi-static loading applied in the central area is investigated in this paper. The panels consist of two metallic face sheets and a metallic foam core, and they are simply supported or fully clamped at the edges. A velocity field is assumed to estimate the large deflection response, which is defined according to the initial deformation mode of the flat panel and boundary condition. In order to validate the analytical solution a finite-element simulation has been performed. Good agreement confirms that the quasi-static behavior of circular sandwich plates is well captured by the analytical model. A parametric study is then carried out to examine the effect of the boundary condition, face-to-core thickness ratio, and core strength on the structural response. It is shown that membrane effect caused by large deflection has a significant influence on the postyield response, especially in the case of a fully clamped boundary. Using the analytical model, a comparative study is carried out between the sandwich panels and monolithic plates, on their energy-dissipating performance.

The devastating low-frequency ground motions of the 2011 Great East Japan Earthquake produced large displacements in low-frequency structures previously thought to be safe, including base-isolated structures. Rate-independent linear damping (RILD) is a promising damping model for low-frequency structures because it provides direct control over displacement. Because the control force generated by RILD is proportional to displacement (advanced in phase by $\pi /2$ radians) and independent of frequency, it performs well under both low-frequency ground motions and more common higher-frequency ground motions (relative to the structure’s fundamental natural frequency). The phase advance makes RILD noncausal, which has hindered its practical applications. This paper proposes a causal filter-based method to approximate RILD that can be easily implemented in time-domain or frequency-domain analyses. The calculated force can be tracked in real-time (due to causality) through semiactive or active control methods. The approach is applied to a base-isolated structure with supplemental control provided by a magneto-rheological (MR) damper. Both numerical simulations and shake table tests are conducted to demonstrate the performance of the proposed causal approach. The results compare well to noncausal simulations in both the achieved forces and structural responses.

Investigations of earthquakes have shown that piles in soft or liquefiable soils are more susceptible to problems arising from ground amplification or excessive soil movements. However, because of the complexity of dynamic pile-soil interaction during seismic shaking, the seismic response of piles embedded in soft soils has yet to be fully understood. Based on a series of centrifuge tests and three-dimensional (3D) finite-element analyses, a relevant study has provided a framework for the prediction of seismic pile bending moment response for piles embedded in clays in an average (i.e., mean value) sense. In this paper, this relevant study was extended by considering seismic ground motion as a nonstationary Gaussian stochastic process. By doing so, the coefficient of variation and probability distribution of the pile bending moment were examined through 3D finite-element analyses incorporated with Monte Carlo simulations. The findings from this study likely will provide some useful guidance for practical reliability-based design of piles embedded in soft clays subjected to seismic shaking.

Minimum void ratio is an important soil property in the practice of geotechnical engineering. It correlates with the volume change tendency, the pore fluid conductivity, and the shear strength of the soil. Minimum void ratio for granular soil is highly dependent on its particle size distribution. However, very few analytical models are available for predicting minimum void ratios as a function of particle size distribution. This paper develops a mathematical model that can predict the minimum void ratio for granular soil with arbitrary particle size distribution based on a more fundamental approach using the concept of dominant particle network. The developed model is evaluated by the simulation results using a discrete element method (DEM) and by the experimental results on granular soil with four different gradations to illustrate the applicability of model. The results predicted by the model show very good agreement with the data from DEM simulations and experiments.

The nonlinear wave-current propagation over a submerged rectangular breakwater on a flat seabed was investigated both experimentally and numerically. Experiments were conducted in a two-dimensional wave flume and numerical simulations were performed using the higher-order boundary element method (HOBEM) based on potential flow theory. Comparisons between the numerical results and experimental data indicate that the numerical model is capable of accurately modeling wave interactions with a submerged structure in uniform currents. Parametric studies were conducted to examine the effects of a current and the submerged breakwater on the wave profile, higher-order harmonic waves, and reflection coefficient.

A probabilistic framework to draw real-time inferences on the maximum response of an uncertain nonlinear structural system under stochastic excitation based on sensor measurements is proposed. The primary contributions are twofold: first, an exact discretization solution is derived for the system evolution equation for the nonlinear case. This is validated against a Taylor expansion discretization solution. Second, a methodology for robust Bayesian estimation of the time-evolving system state is proposed. The system is instrumented by sensors placed on the structure with inferences drawn using Kalman-based approaches. The sensor observations are used in real time to estimate system state without any knowledge of the time history of the input motion. The distribution of the maximum response is assessed. The proposed methodology is applied to a 10-story shear-type sample structure under earthquake loading. The interstory drift is analyzed with measured data collected through accelerometers placed on the building. A simulation approach is used to demonstrate the ability of the proposed methodology to accurately estimate nonlinear structural response based on sensor measurements. In addition, the method is shown to be robust to varying system characteristics. This includes uncertainties in the structural, ground, and input motion parameters, as well as varying measurement characteristics.

Based on the Euler–Bernoulli beam theory and the generalized Hamilton’s principle, this paper presents piezoelectric energy harvesting (PEH) from vibrations of a functionally graded (FG) beam induced by multimoving forces and multimoving masses. Various moving loads are analyzed by considering various parameters. The finite element method is used to analyze the electromechanical behavior of a piezoelectric harvester in a unimorph configuration. For the transient analysis, the Newmark’s explicit integration technique is adopted. It is assumed that material properties of the beam and piezoelectric patch vary continuously in the thickness direction according to the power-law form. The effects of different material distributions, velocities of the moving loads, and time lags between each moving load on the produced power are discussed. The present work shows that a remarkable electrical power can be generated from the vibrations of an FG beam subjected to moving loads and masses.

The classical spectral representation method for simulation of multivariate nonstationary Gaussian random processes may be less efficient due to difficulty in a straightforward application of the fast Fourier transform (FFT). Although several attempts have been made to invoke the FFT, there remains the need to further improve the efficiency for cases where a large number of points need to be simulated. In this paper, a stochastic wave-based simulation scheme for the multivariate nonstationary random process along a straight line is introduced in conjunction with either a direct summation of cosine functions or the application of a two-dimensional (2D) FFT. Central to the proposed schemes is the transformation of the simulation of a multivariate nonstationary random process to that of a nonstationary one-dimensional stochastic wave. The stochastic wave can be simulated based on a direct summation of cosine functions or by invocation of a 2D FFT. The latter requires that the points to be simulated are evenly distributed. To implement FFT, proper orthogonal decomposition (POD) is employed to factorize the time-dependent and space-dependent 2D decomposed evolutionary power spectral density of the converted stochastic wave. The proposed hybrid approach of a stochastic wave and POD is quite general, and can be used to simulate nonstationary multivariate random processes with complex coherence functions. Numerical examples show that the proposed hybrid approach is very efficient in comparison with existing approaches when the number of simulation locations is large, and it offers a desired level of simulation accuracy when appropriate discretization parameters are selected.

This paper reveals the consequences of practicing the 2015 National Earthquake Hazards Reduction Program (NEHRP) soil-structure interaction (SSI) provisions, which form the basis of the 2016 edition of the seismic design standard provided by the ASCE. For this purpose, the probability that the practice of SSI provisions, in lieu of fixed-base provisions, increases the ductility demand of the structure computed. It is subsequently investigated whether the NEHRP provisions are indeed an improvement upon the SSI provisions of the current ASCE seismic design standard. To this end, 720 soil-structure systems with different numbers of stories, structural systems, aspect ratios, and foundation embedment ratios on various site classes are studied. A probabilistic framework is employed to account for prevailing uncertainties in ground motion and in the properties of the soil-structure system. It is concluded that both NEHRP and the current provisions result in unsafe designs for structures with surface foundation on moderately soft soils, but NEHRP slightly improves upon the current provisions for squat structures. For structures on very soft soils, both provisions yield conservative designs where NEHRP is even more conservative. Finally, both provisions yield near-optimal designs for other systems.

The wind-resistant design process of roof structures is a complex task due, inter alia, to the temporal-spatial distribution of fluctuating wind loading and to multimode vibration. This process can conceivably be greatly simplified in the case of availability of analytical expressions for the determination of the structural response. In this context, this paper develops analog filter approaches for the representation of wind pressure spectra on large-span roof structures. In conjunction with this representation, integrals which are determinable analytically are used to derive formulas that can be used to compute efficiently the wind-induced structural responses. For this purpose, the cross-spectral model is also approximated by the filter approach for the case of multi-degree-of-freedom roof structures. The validity and efficiency of the approaches are demonstrated by several case studies correlated with wind tunnel tests.

In this paper, development of a thermohydromechanical model for expansive soils including double structure is described. The model is based on the previously developed double-structure hypoplastic model, in which hydromechanical coupling is considered at each of the two structural levels. The model also includes separate effective stress definitions and water retention curves for the two levels of structure, and they are linked through the double-structure coupling function. In the proposed model, thermal effects are considered on the mechanical behavior of both the macrostructure and the microstructure. This is combined with a temperature-dependent water retention curve for the macrostructure and an enhanced double-structure coupling law. Good predictions of the model are demonstrated by comparing the simulations with experimental data on MX80 bentonite taken from the literature.

This paper explores the particle-scale origin of the additional shear strength of unsaturated granular materials in pendular states induced by the capillary effect by applying the stress–force–fabric (SFF) relationship theory to unsaturated granular material stress analysis. The work is based on discrete element simulations with the particle interaction model modified to incorporate the capillary effect. By decomposing the total stress tensor into a contact stress tensor originating from contact forces and a capillary stress tensor due to the capillary effect, the directional statistics of particle-scale information are examined. The observations are used to support the choice of the appropriate analytical approximations for the directional distributions associated with the solid skeleton and water bridges. The SFF relationship for unsaturated granular materials is formulated, and is shown to match the material stress state with good accuracy and is used to interpret the material strength in terms of the relevant microparameters. Macro and micro observations are carried out on both relatively dense and loose samples in triaxial shearing path to the critical state. The capillary force remains nearly isotropic during triaxial shearing. Anisotropy in the water bridge probability density, however, develops alongside the anisotropy in contact normal density, which decreases when the suction level decreases and the water content increases. The anisotropy effect in the water phase is much smaller than the solid skeleton, and a coupling effect with the solid phase makes the fabric anisotropy in wet materials smaller than that in dry materials. Combined with the SFF function, the increased solid coordination numbers and mean contact forces by the water bridge effect are more important factors for the suction-induced shear strength.

Physiochemical forces of attraction and repulsion from clay mineralogy of an expansive soil during hydration contribute to the macro swell behavior of expansive soils. In this research, diffuse-double-layer (DDL) theory–related electrostatic forces from individual clay minerals of an expansive soil and their influence on soil swelling were studied. A fundamental approach for estimating swell potentials using the DDL model is proposed here for improved characterization of soil swelling potential. As a part of this research, 14 natural expansive clays were characterized and studied by performing basic soil characterization and clay mineralogy studies, followed by one-dimensional swell strain and swelling pressure tests. Clay mineralogy data were used to estimate total DDL thicknesses, which eventually transpire as adsorbed layers during the swelling process. Assumptions with respect to clay mineral crystalline alignment and orientation of clay particles were made in order to estimate adsorbed DDL thicknesses. Estimated DDL thicknesses were then converted to DDL strains, which were later correlated with the measured swell potentials of the present soils. Strong correlations between DDL-based strains and measured swell potentials are observed, indicating the importance of using DDL concepts in the estimation of swell properties. Further refinements of the modeling and model coefficients are to be conducted in the progressive studies for better prediction of the swell behavior of soils.

Stay cables are vulnerable to excessive vibration because of their inherently low damping properties. Described in this paper is an experimental investigation of the vibration control performance due to passive negative stiffness dampers (NSDs) installed on a scaled stay cable model. The passive NSD used in the experiment was composed of a viscous damper and a magnetic negative stiffness spring with an adjustable stiffness coefficient installed close to one cable end in the transverse direction. In general, the passive NSD performed much more effectively than conventional viscous dampers in mitigating the vibration of the stay cable. As the negative stiffness strength increased, the cable responses under various dynamic loadings became smaller, thus indicating that high damping had been added to the stay cable. A damping ratio higher than 10% was obtained in the cable vibration tests. The flexural rigidity of the stay cable is a parameter often overlooked. However, after the installation of a passive NSD, this was found to be of importance. The actual influence of flexural rigidity depends on the negative stiffness coefficient, the damper location, and the boundary condition of the stay cable. Numerical simulation results taking account of the flexural rigidity and boundary conditions agreed well with the experimental results.

A new approach for the limit analysis of masonry vaults retrofitted with fiber-reinforced polymers (FRP) based on an upper bound formulation is presented in this paper. In particular, a new genetic algorithm (GA)–nonuniform rational $b$-spline (NURBS)–based general framework for the limit analysis of curved masonry structures tailored upon an upper bound formulation is discussed thoroughly in the present Part I. A given FRP-reinforced masonry vault can be geometrically represented by a NURBS parametric surface, and a NURBS mesh of the given surface can be generated. Each element of the mesh is a NURBS surface itself and can be idealized as a rigid body. An upper bound limit analysis formulation, which takes into account the main characteristics of masonry material and FRP reinforcement, is deduced, with internal dissipation allowed exclusively along element interfaces. The approach is capable of well predicting the load-bearing capacity of any reinforced masonry vault of arbitrary shape, provided that the initial mesh is adaptively adjusted by means of a metaheuristic approach (i.e., a suitable GA) to enforce that element edges accurately approximate the actual failure mechanism. The approach is validated and discussed in Part II, which is devoted to presenting a number of structural analyses of FRP-reinforced vaults.

A new approach for limit analysis of masonry vaults retrofitted with fiber-reinforced polymers (FRPs) based on an upper bound formulation is presented. Part I of this paper was devoted to detailing the theory on which this approach relies. The main idea consists of exploiting properties of nonuniform rational $b$-spline (NURBS) functions to develop a computationally efficient adaptive limit analysis procedure, which allows quick evaluation of the collapse load multiplier of any given FRP-reinforced masonry vault starting from its three-dimensional (3D) model, which can be generated within any free-form modeler natively working with NURBS entities. A suitably devised genetic algorithm (GA) governs mesh adaption. The present Part II is devoted to validating and discussing through numerical simulations the proposed GA-NURBS procedure. Several structural examples of masonry vaults, including two distinct arches (a straight parabolic barrel vault and a skew parabolic arch, respectively), a hemispherical dome, and both cloister and cross vaults are investigated. Each example is analyzed considering both the unreinforced configuration and the presence of FRP reinforcements. Moreover, comparisons with both nonlinear finite-element (FE) simulations and data collected from experiments (where existing) are presented to assess the proposed GA-NURBS limit analysis procedure. It is shown that, for all cases analyzed, this model allows reliable prediction of both collapse mechanisms and failure loads. The present GA-NURBS approach turns out to be a promising tool that may be conveniently used by practitioners who seek a quick and reliable way to evaluate the outcome of restoration interventions based on the application of FRP composites.

This paper presents a numerical procedure based on equilibrium finite elements and conic programming for plastic collapse load computation of reinforced concrete slabs governed by the Nielsen yield criterion. Bending moment fields are approximated using the enhanced Morley elements with an added second-degree moment field, allowing exact equilibrium relations to be achieved when applying a uniform pressure to the slabs. Conic programming, which is robust and efficient, is incorporated into the obtained discrete equilibrium formulation to ensure solutions can be obtained rapidly. Several slabs of arbitrary geometries and boundary conditions are examined, providing accurate collapse load multipliers and distributions of moment fields at the limit state.

An efficient procedure employing the first-order reliability method (FORM) is proposed to evaluate the reliability of engineering systems governed by multiple limit state functions that are correlated due to the correlation among random variables involved in different limit state functions. It is shown that to estimate the system reliability, the FORM analysis for an individual limit state function included in the system needs to be carried out only by considering the random variables involved in the limit state function itself; the design point hereby obtained from the FORM can be mapped to the design point in the space that corresponds to all the random variables in the system. The latter is used as the basis to estimate the needed correlation coefficients among the linearized safety margins at the design points for the system reliability evaluation. The proposed procedure is applicable provided that the correlation matrix of the random variables associated with the system in the normal space is positive definite. Three system reliability examples are included to illustrate the application and efficiency of the proposed procedure.

This study presents new structural formulas for steady-state thermoelastic Green’s functions (TGFs) to a plane-generalized boundary value problem (BVP) of thermoelasticity for a generalized half-strip. The structural formulas for TGFs are expressed in terms of Green’s functions for Poisson’s equation (GFPE). These results are formulated in a special theorem, which is proved using a developed harmonic integral representations method. The development of this method consists in calculating a boundary integral of the product between two GFPEs. This integral was calculated due the proved before statement that the TGFs have to satisfy must have the following two conditions: (1) thermal boundary conditions with respect to points of application of the heat source, and (2) mechanical boundary conditions with respect to the points of finding the displacements. On the basis of derived structural formulas, it is possible to obtain many explicit Green’s functions for termoelastic displacements, deformations, and stresses. An example is presented for a concrete-plane BVP for a half-strip; TGFs are obtained in terms of elementary functions. New analytical expressions for thermal deformations and thermal stresses to a particular plane problem for a thermoelastic half-strip under a boundary constant temperature gradient were obtained. The graphical computer evaluation of thermal deformations and thermal stresses, created by a unit point heat source and by a temperature gradient, also is included.

This study utilizes a computational-experimental method to determine the effective oxygen diffusivity of asphalt concrete based on diffusivities of its constituents, i.e., air void, aggregate, and asphalt binder phases. The proposed method enables the estimation of oxygen diffusivity of asphalt concrete, which is very challenging, if not impossible, to determine experimentally, and addresses various controversial factors, such as consideration of accurate microstructures, high contrast in properties of constituents, and high volume fraction of aggregates. Random particle generation algorithm and X-ray computed tomography techniques are used to reconstruct realistic microstructural representation of asphalt concrete materials. Then, finite-element (FE) diffusion simulations are used and the results are compared with closed-form solutions to estimate the effective oxygen diffusivity. Capabilities of the proposed method are illustrated by comparing the simulation results with relevant analytical solutions, rigorous bounds, and available experimental measurements regarding oxygen diffusivity of fine aggregate matrix (FAM) of asphalt concrete. Finally, the proposed technique is used to simulate two-dimensional oxygen diffusion problem in a dense-graded asphalt concrete.

The lower-bound finite elements limit analysis in combination with semidefinite programming (SDP) has been used to solve stability problems involving a modified Hoek-Brown (HB) yield criterion with the exponent $\alpha =0.5$. In order to demonstrate the applicability of the proposed computational approach, bearing capacities of strip and circular foundations on rock mass have been determined. The results have been given in the form of nondimensional bearing capacity factors as a function of different material input parameters. By comparing the results obtained from the present analysis with that reported in literature, it is noted that the proposed approach remains quite accurate and is highly efficient to deal with any large-scale optimization problem. The method does not require any kind of the smoothing of the yield surface and it can even be implemented to deal with any three-dimensional problem as well.

This study investigates ways to passively suppress wind-induced instabilities such as flutter and torsional divergence. The control system design study is based on a sectional flexible bridge model interacting with a constant velocity airstream. Two strategies are considered, separately and in combination. The first makes use of trailing and leading flaps adjacent to the bridge deck, the motion of which is triggered by the deck’s movement through a combination of springs, dampers, and inerters at the hinged connection. Emphasis is placed on the effect of the flap hinge location and an optimization procedure is used for determining the compensator parameters that result in favorable aeroelastic properties. The second approach reexamines the efficacy and limitations of using tuned mass dampers (TMDs) placed inside the bridge deck for controlling self-excited motion. The paper then combines the two approaches and introduces a kinematic constraint between the masses of the TMD and the flaps. This combined mechanical system, the flap mass damper (FMD), combines favorable aerodynamic properties of the flaps with a driving force provided by the vibrating mass. Consequently it has the advantage of not requiring complex and often impractical linkages in order to transmit the deck motion to the flaps. Special attention is given to ensuring that the passive control system attains optimum robustness properties and maximizes tolerance to uncertainties. Uncertainties are quantified in a series of simulations showing how the alteration of the bridge’s natural frequencies affect the stability of the controlled system. The Humber Bridge in the United Kingdom is chosen as an example for the numerical simulations.

A closed-form analytical solution for ground-borne vibrations from a tunnel embedded in a saturated poroelastic half-space is proposed in this paper. The tunnel modeled as an elastic hollow cylinder is surrounded by the water-saturated poroelastic material. The total wave field in the poroelastic half-space with a cylindrical cavity consists of the outgoing cylindrical waves and the down-going plane waves. In addition to the traction-free condition on the ground surface and the continuous conditions of displacement and stress at the tunnel-soil interface, hydraulic boundary conditions on these two scattering surfaces are required to solve this multiple-scattering problem. The transformation properties between the plane and cylindrical wave functions are employed to apply the boundary conditions expressed in both the rectangular and cylindrical coordinate systems. Numerical results for the displacements of the solid on the ground surface and the pore pressure in the saturated soil attributable to a harmonic point load applied at the tunnel invert are presented. The influence of the soil permeability and the hydraulic boundary at the tunnel-soil interface on the free-field responses is investigated. The proposed solution can serve as a benchmark for other computational methods and as an efficient tool for predicting vibrations from a tunnel embedded in a saturated poroelastic half-space.

The construction of confined masonry buildings has become a good choice to meet the housing needs of low-income families in big cities. Despite this, current building codes for such construction allow the use of highly simplified analysis techniques that have hardly changed in the last 40 years. This paper is based on numerical simulation and discusses the need to combine and improve existing techniques in finite-element method (FEM) analysis for composite materials, to assess the overall structural behavior of reinforced concrete structures with masonry in-fills, and consequently to support the derivation of rational rules for analysis and design. Through the use of a simple yet powerful shell finite element (FE), state-of-the-art theories of mixtures to analyze composite materials, a computational tool to generate the volume fraction of composites, and the Mexican building code, this paper attempts to be a guide to numerical reproduction of the overall behavior of confined masonry structures.

A modified Cook-Mayne method is proposed for extreme wind load estimation. A technique that can simulate true $r$-order extreme values of a correlated random process is adopted in this method to estimate the annual multiorder maximum 10-min mean wind speeds. These estimated extreme wind speeds are then used for extreme wind load estimation on structures. Results show that the autocorrelation of the macrometeorological fluctuating wind can have significant effects on the estimated extreme wind load. A big difference is found when comparing the design fractile of the extreme wind load coefficients obtained from the modified method by considering the autocorrelation of wind speeds and the existing full-order method in which only independent wind speeds are adopted. The order of annual maximum wind speeds required for wind load estimation is also examined. The number of orders that is needed for 50-year return period wind load design varies greatly—from 2 to 50—and depends on the application conditions. The design fractile of extreme wind load coefficient distribution for a 50-year return period can be increased to 93% from the 79% recommended in the existing method.

Laboratory experiments were conducted to investigate the evolution of particle clouds in stagnant water. Nozzle size and released mass of particles were formed to an aspect ratio of $L_o/d_o$, where $L_o$ is a length of sand particles occupied in a pipe with a nozzle diameter of $d_o$. Characteristic length and time scales of $L_i$ and ${\tau }^{*}$ were found to classify the initial regime (sand jets), the transient regime (particle cloud with trailing stem), particle cloud without trailing stem, and swarm of particles. Image analysis indicated that the transition regime occurred for $1<{\tau }^{*}<5$ and swarm of particles occurred for ${\tau }^{*}>15$, where ${\tau }^{*}$ is the characteristic time scale for cloud classification. This classification was found to be applicable for $0.1375\mathrm{mm}\le D_{50}<0.507\mathrm{mm}$, where $D_{50}$ is the mean particle size. It was found that the formation of trailing stem can change the characteristics of transient particle clouds. Power law correlations were developed for progression depth, width, and frontal velocity of particle clouds with $L_o/d_o$ using length and time scales based on initial parameters of particle clouds. The effect of particle size on evolution of particle clouds was considered using Stokes number $S_t$. Wider particle clouds were observed for small $S_t$ because small particles have a higher tendency to follow water eddies. The effects of nondimensional release height of sand particles $\eta$ on spreading of particle clouds were also investigated. A relatively wide range of $\eta$ was tested for $1\le \eta \le 26.5$. For small $L_o/d_o$ (i.e., $L_o/d_o\le 1.5$), experimental results indicated a direct correlation between $\eta$ and the width of particle clouds. An adverse relationship was found for $1.5<L_o/d_o<15$.

This paper investigates statistical errors in the simulation of spatially varying seismic ground motions modeled by evolutionary Gaussian vector processes and simulated by the spectral representation method (SRM). Formulas are derived for both bias and random errors of the simulated evolutionary power spectral density (EPSD), time-varying correlation function, and standard deviation with respect to the target (idealized) ones. The closed-form error formulas for the EPSD are further simplified under specified conditions. It is shown that the simulated nonstationary characteristics are all unbiased, the closed-form random error formulas for the EPSD can reduce to those for stationary simulations, and the predicted random errors match those given by the ensemble average. By using the random error formulas, the factors influencing the random errors are investigated. The results show that the SRM implementation scheme involving both random amplitudes and phase angles would cause larger random errors, and increasing the number of samples and frequency intervals would reduce these errors. Closed-form error formulas are finally used to estimate errors in the simulation of spatially varying seismic ground motions for the Tsing Ma suspension bridge.

The paper studies the effect of nonuniformity and localized degradation of the interfacial conditions on the dynamic debonding mechanism in layered structural elements. In particular, it looks into the effect of a periodic delamination pattern. Such a pattern is observed in masonry or periodically cracked concrete elements strengthened with fiber reinforced polymer (FRP) plates and in other periodic structural forms such as armor plates with ceramic tiles, sandwich plates, and coating for electronic devices. The study focuses on FRP plated beam specimens and combines analytical modeling using a high order multilayered theory with cohesive interfaces, numerical solutions using a specially tailored finite element formulation, and experimental, techniques that are based on high-speed photography and image processing. The combined methodologies reveal the impact of pre-existing periodically delaminated regions on the response of the examined beams. Specifically, it reveals the impact on the critical load and displacement where the dynamic process commences, on the kinematics of the process including the debonding front movement and velocity, on the duration of the process, and on its potential arrest. Altogether, the combined effort sheds more light on the dynamic nature of the debonding failure in layered structural elements and the role it plays in their structural behavior.

To experimentally validate a recently developed theory for predicting the stability of cut slopes under unsaturated conditions, the authors measured increasing strain localization in unsaturated slope cuts prior to abrupt failure. Cut slope width and moisture content were controlled and varied in a laboratory, and a sliding door that extended the height of the free face of the slope was lowered until the cut slope failed. A particle image velocimetry tool was used to quantify soil displacement in the $x\text{-}y$ (horizontal) and $x\text{-}z$ (vertical) planes, and strain was calculated from the displacement. Areas of maximum strain localization prior to failure were shown to coincide with the location of the eventual failure plane. Experimental failure heights agreed with the recently developed stability theory for unsaturated cut slopes (within 14.3% relative error) for a range of saturation and cut slope widths. A theoretical threshold for sidewall influence on cut slope failures was also proposed to quantify the relationship between normalized sidewall width and critical height. The proposed relationship was consistent with the cut slope experiment results, and is intended for consideration in future geotechnical experiment design. The experimental data of evolution of strain localization presented herein provide a physical basis from which future numerical models of strain localization can be validated.

The analysis of structures subjected to earthquake actions can be carried out by means of several methods with different levels of accuracy, among which the nonlinear dynamics is generally recognized as the most reliable one. This paper presents a general treatment to develop approximate solutions for rigid-plastic response of structures subjected to base harmonic pulse, by means of a numerical procedure on-purpose developed. The case study is a vertical cantilever beam, with base support, constant mass, and inertia distribution, subjected to only ground acceleration. The failure is assumed depending on the formation of a single shear hinge and the results are expressed in general terms. As a result, the motion proceeds through successive spreading and contractions of the plastic front and related elastic returns. Possible applications of the method to real structures can be envisaged.

Circular rings are used in various engineering structures because of their nonlinear properties. The use of large assemblies of steel rings in flexible ring nets is widespread in recent technologies of protection structures and their design requires a nonlinear and computationally efficient mechanical modeling. This paper presents an innovative discrete model of steel rings for application in flexible protection structures. The model aims at providing an effective mechanical response of the net at both the local ring scale and the global net scale. Two different uniaxial tension configurations are defined as reference loading cases and the nonlinear analytical response of the ring model to these loading cases is established. A multicriteria numerical method based on the Levenberg-Marquardt algorithm is developed to calibrate the model parameters from experimental data. An experimental campaign on steel wire spliced rings of different dimensions is conducted and permits the calibration and validation of the model.

It is essential to diagnose, i.e., detect and isolate, potential sensor faults for structural health monitoring to guarantee reliable condition evaluations. This paper proposes an innovative method called weighted principal-component analysis for sensor-fault detection and isolation. It is first illustrated that the fault sensitivity of each principal direction of traditional principal-component analysis is different from others for the same fault occurring in a certain sensor. Then, a fault-sensitive factor is theoretically derived to quantify the fault sensitivities. Based on that, a weighted fault-detection statistic determined according to the difference in fault sensitivities is developed and shown to have enhanced fault-detection ability. Bayesian inference is used to integrate all the weighted statistics corresponding to all the sensors to quickly judge whether a sensor fault occurred. Meanwhile, contribution analysis is used to establish a fault isolation index to identify the specific faulty sensor. Case studies using numerical simulation and a benchmark model demonstrate that the new proposed method is excellent and superior to the traditional approach.

The paper focuses on the representation of a classical damping matrix in terms of a Caughey series including only negative or zero powers of (${[m]}^{-1}[k]$). An explicit expression for the series in terms of prescribed modal damping ratios at a set of natural frequencies is derived which avoids the need to solve an ill-conditioned problem for the coefficients of the series. In addition, optimal choices for the coefficients of the series are presented for cases in which the natural frequencies are not known or can change as a result of structural changes. Two optimization procedures are presented: (1) analytical application of a least-squares approach for an expansion of the damping ratio into a power series of the eigenvalues; and (2) expansion of the damping matrix into a series of Legendre polynomials of matrices. Finally, the particular case of uniform damping ratios is given special consideration.

This paper advances the gradient inelastic (GI) flexibility-based (FB) frame element formulation, which focused on monotonic loading conditions, to capture member responses to arbitrary (nonmonotonic) loading conditions. The GI formulation is a generalization of the strain gradient elasticity theory to inelastic continua. Contrary to nonlocal/gradient damage or plasticity models, in the GI theory, nonlocality is strictly decoupled from the constitutive relations; as a result, the GI theory can incorporate any material constitutive law (plastic, hardening, or softening), whereas for linear elastic materials, the GI theory reduces to the strain gradient elasticity theory. In the GI theory, alleviation of strain localization and response objectivity (i.e., convergence with mesh refinements) are achieved through a localization condition applied to the strain field at strain localization locations during strain softening. Strain localization locations are not a priori known and are identified through a localization criterion. This paper advances/refines the GI theory and GI FB element formulation by (1) eliminating (unintended and unphysical) discontinuities in the temporal response of section strains introduced during application of the localization condition; and (2) alleviating false identifications of localization locations in the case of arbitrary and combined (axial/flexural/shear) loading through a new robust localization criterion. Furthermore, this paper assesses (1) various mathematically admissible end boundary conditions to the section strain fields—proper selection of which has been a challenge in higher order gradient theories—in terms of their physical rationale and mesh convergence properties; and (2) higher-order nonlocality relations in terms of the spatial characteristics of the resulting section strain fields and mesh convergence properties. The performance of the proposed formulation is evaluated through examples on frame members subjected to monotonic, cyclic, and seismic loading, and comparisons with experimental data from quasi-static cyclic testing of a reinforced concrete column.

This paper proposes a damage parameter, $M_{\mathrm{int}}$, for evaluation of the surface energy associated with the formation of multiple cracks terminating at a bimaterial interface. The study considers two crack mechanisms, including an inclined crack terminating at the interface with an arbitrary angle and an interface crack lying along the material interface. Based on the concept of the $M$-integral, the parameter $M_{\mathrm{int}}$ is developed by conducting the integration along a closed contour enclosing all the cracks and with respect to a specific reference coordinate system. The formulation is shown to be path-independent, and therefore good accuracy of $M_{\mathrm{int}}$ can be achieved even when elaborate near-tip local solutions are not ensured.

This contribution focuses on the nonsynoptic wind-induced effects on linear bridge aerodynamics. More specifically, the transient nature of the downburst events and its effects on the aerodynamic parameters are investigated. Because an additional timescale is introduced in the wind-structure interaction system attributable to the time-varying transient nonstationarity of the nonsynoptic winds, the conventional one-dimensional (1D) indicial response function needs to be extended to a two-dimensional (2D) case. Buffeting response of a bridge deck based on the time-domain linear analysis framework associated with 2D and 1D indicial response functions, representing aerodynamics under nonsynoptic winds and corresponding synoptic equivalents, was calculated. The results highlighted the important effects of the transient nature on the nonsynoptic wind-induced structural response. The presented approach could provide a straightforward physical explanation on the underlying mechanism of the changing aerodynamics attributable to time-varying transient effects. The study may facilitate a more appropriate design of the flexible horizontal structures considering nonsynoptic wind loads.

The uncertainty involved in the structural parameters inevitably leads to uncertainty in predicting the resulting structural dynamic characteristics, and this relationship is important to quantify. There is a large volume of work dealing with quantifying the overall uncertainty propagated from parameters to the structural dynamic responses, whereas little work has been done in measuring the contributions of the individual parameters and groups of parameters to the overall uncertainty, which is corresponding to the variance-based global sensitivity analysis (GSA). The variance-based GSA allows for providing a robust assessment of the relative influences of individual parameters on the structural dynamic characteristics. Although it is a powerful tool, the variance-based GSA suffers from the limitation of high computational cost, especially when applied to the expensive-to-run complex systems such as the long-span cable-stayed bridge in this study. To alleviate the computational burden, a fast-running nonparametric Gaussian process model (GPM), a fully specified statistical model, is used as a surrogate model. The highlights of the developed metamodel-based approach for the variance-based GSA are: (1) adopting the full GPM, rather than the mean of GPM, where the latter drops the valuable uncertainty information of the prediction variance; (2) enabling the full GPM-based method not to be restricted to the calculation of the first-order sensitivity index, and to be applicable for the computation of sensitivity indices of groups of parameters; (3) generalizing this approach to be suitable for the cases with arbitrarily distributed parameter uncertainty. Then, this full GPM-based approach is applied for sensitivity analysis of structural dynamic characteristics of a long-span cable-stayed bridge.

A variational temperature-dependent formulation is proposed and developed for dynamical problems of thermoplasticity. The variational method is based on a Hamiltonian approach using a weak form of the mixed thermoplastic governing equations. Interestingly, within this framework, when an exponential dependence on temperature is assumed for the material properties (e.g., viscous dashpot and yielding force), the correct viscous and plastic dissipated energy terms are obtained for the entropy-energy equation. With this in place, a discrete variational calculus approach is adopted to represent the nonlinear discrete equations of motion. Next, several case studies are performed with a lumped-parameter thermoplastic model to investigate the exponential dependence of the material properties on temperature. The thermoplastic model is subjected to cycling external forces and external heat sources, for which continuous softening of the material properties is observed per cycle. This suggests that the proposed multiphysics mixed variational formulation may be used to capture a range of complex rate-dependent thermoplastic material behavior. Finally, a discussion on the convexity of the proposed thermoplastic formulation is included.

The equivalent stress concept allows the comparison of arbitrary multiaxial stress states with a uniaxial one. Based on this concept several limit surfaces were formulated. The trend in the formulation lies in the generalized criteria that contain classical hypotheses and are suitable for several materials. In this work, three generalized criteria are discussed. They are rewritten in order to more closely meet a set of plausibility assumptions. A schematic representation of the unified strength theory (UST) of Yu can be given as a convex combination of the classical hypotheses (Tresca, Schmidt-Ishlinsky, and Rankine). For this schema a criterion as a function of the stress angle is proposed. It describes a single surface without plane intersecting in the principal stress space. The introduced criterion is similar to the UST and like the UST is $C^0$-continuous. The Podgórski criterion as function of the stress angle is $C^1$-continuously differentiable and can be used as yield and strength criterion. The parameters of this criterion are real numbers restricted in order to obtain the convex shapes in the $\pi$-plane. The same parameters can be defined as complex numbers. With these complex parameters, this criterion describes an extended region of the convex shapes in the $\pi$-plane. The Altenbach-Zolochevski criterion as function of the stress angle will be modified in order to describe additional convex shapes in the $\pi$-plane. In contrast to the Altenbach-Zolochevski criterion, the modified criterion contains the Schmidt-Ishlinsky hypothesis as extremal yield function. Both criteria are $C^0$-continuous and can therefore be recommended as strength criteria. The suggested modifications of the discussed criteria extend their application area and simplify the fitting procedure. Therefore these criteria are recommended for practical use.

This paper investigates the normal and shear stresses induced due to a load moving on initially stressed irregular heterogeneous isotropic viscoelastic rock medium (sandstone, limestone, and marble) at a free rough surface. Two-dimensional geometry of the rock medium is considered for this purpose. It has been reported through the closed-form expressions of induced stresses that both normal (compressive and tensile) and shear stresses are affected by the irregularity depth, different shapes of irregularity (rectangular irregularity and parabolic irregularity), heterogeneity, horizontal compressive initial stress, horizontal tensile initial stresses, hysteretic damping ratio, velocity of a moving load (in the subsonic range), and viscoelasticity of rock medium. Moreover, friction due to rough upper surface of viscoelastic rocks has a significant effect on shear and tensile stresses induced in viscoelastic rock medium. In addition, some important peculiarities are addressed and depicted by means of graphs.

A Lie-group differential algebraic equations (LGDAE) method, which is developed for solving differential-algebraic equations, is a simple and effective algorithm based on the Lie group $GL(n,\mathbb{R})$ and the Newton iterative scheme. This paper deepens the theoretical foundation of the LGDAE method and widens its practical applications to solve nonlinear mechanical systems with nonholonomic constraints. After obtaining the closed-form formulation of elements of a one-parameter group $GL(n,\mathbb{R})$ and refining the algorithm of the LGDAE method, this differential-algebraic split method is applied to solve nine problems of nonholonomic mechanics in order to evaluate its accuracy and efficiency. Numerical computations of the LGDAE method exhibit the preservation of the nonholonomic constraints with an error smaller than ${10}^{-10}$. Comparing the closed-form solutions demonstrates that the numerical results obtained are highly accurate, indicating that the present scheme is promising.

This paper develops a new symplectic eigenvalue analysis (SEA) method for deriving the symplectic analytical solutions for the bending of Timoshenko beams resting on two-parameter elastic foundations. The SEA method accommodates various beam–foundation models with arbitrary external loads and arbitrary boundary conditions. A generalized Hamiltonian functional is first derived by introducing the Lagrange multipliers into the total potential energy functional, and then the first-order dual equation and its corresponding boundary conditions are obtained. Once the variables are separated, the beam bending is transformed into an eigenvalue problem, and the corresponding eigenvalues and eigenvectors are used to derive the symplectic solutions. In addition, a new hybrid method, which incorporates the singular functions and the variable separation method, is proposed to obtain the particular solutions with respect to arbitrary external loads. The systematic SEA method provides a new general analytical framework for studying beam–foundation interaction problems, and the comprehensive analyses on the symplectic eigenvalues help to deeply understand the characteristics of the symplectic solutions. Three examples are presented to assess the applicability of the SEA method and to validate the accuracy of the symplectic solutions. The differences and similarities between the Pasternak elastic foundation and the generalized elastic foundation are quantitatively and qualitatively investigated by the SEA method.

Uncertain changes in spatial distribution of structural parameters, caused by deterioration or damage, may weaken the structure and result in unexpected losses of properties or casualties. In recent decades, to identify spatial distribution of parameters, various system identification (SI) methods have been developed based on optimization algorithms employing various regularization techniques. However, such optimization-based SI methods may suffer from ill-posedness of the optimization problem under uncertain measurement noises. Moreover, depending on boundary and traction conditions, the accuracy and robustness of SI methods may differ. In this paper, to overcome these technical challenges in identification of spatial distribution, a new SI method is developed by modifying the transitional Markov chain Monte Carlo (m-TMCMC). In addition to the modifications introduced to the sampling algorithm, the proposed method enhances robustness of the SI results by exploiting the results by the maximum likelihood estimation and finite-element updating. To identify general shapes of spatial distribution with a reasonable number of parameters, a spatial deterioration model is proposed based on the modes obtained based on a random field model called Karhunen–Loeve expansion. The proposed SI method is tested and demonstrated through numerical examples of steel plate and B-pillar structure, in which the effects of random measurement errors are also considered. The numerical examples demonstrate accuracy and robustness of the proposed method.

Wave attenuation in vegetated shallow water is mainly attributed to actual drag-induced dissipation and near-resonant triad interactions. The latter is neglected in existing theoretical models for vegetation-induced dissipation. In this study, a set of evolution equations describing the spatial evolution of three near-resonant wave components was extended to include vegetation effects. The contributions of triad interactions to the attenuation of individual harmonics were investigated. The authors found that neglecting the energy cycling caused by triad interactions gives an underestimation of damping rates. The triad interactions have greater effects on the attenuation of higher harmonics. A fully nonlinear, fully dispersive wave model was used to explore the effects of triad interactions on spectral dissipation of random waves. After isolating the energy transfers caused by triad interactions and the actual drag-induced dissipation, the authors found that triad interactions transfer energy to higher harmonics, which experience greater damping. Due to the energy transfers from spectral peak ($f_p$) to high frequencies ($2f_p$), the energy losses in $f_p$ and $2f_p$ are overestimated and underestimated, respectively, by existing models based on linear wave theory.

In this work, a simple and effective finite element-boundary integral equation (FE-BIE) approach for the static analysis of elastic beams and frames in bilateral frictionless contact with an elastic half-plane is extended to include the case of material nonlinearity. Elastic-perfectly plastic behavior is assumed for the supported structure and in particular for the foundation beam. Potential plastic hinges are placed along structural elements and modeled as nonlinear semirigid connections characterized by a rigid-plastic moment-rotation relationship. Incremental, load-controlled analyses of beams and frames resting on an elastic half-plane with several potential plastic hinges along the structural members are then performed. Numerical examples illustrate the effectiveness of the model in determining the stiffness degradation of the structure for increasing loads, together with ultimate loads and collapse mechanisms.

Nonlinear behavior of concrete reinforced by rebars and/or fibers has been studied over decades. In this paper, classical models for flexural behavior are discussed and an improved model is proposed. The model is based on a modified force-based fiber-beam formulation where progressive loading is driven by a curvature at its nonlinear hinge. Such a procedure allows capturing both softening and hardening behavior without any further adjustments. The curvature outside of the nonlinear hinge decreases during a deflection-softening phase, and therefore a damaged constitutive law should be introduced. Rather than using the classical damage model proposed by Mazars, a macroscopic damage model at the moment-curvature level is proposed. The moment-curvature damage model reduces the whole computation of the beam equilibrium to only one numerical loop. Consequently, time efficiency of the proposed model is significantly improved. Hypotheses of the new model such as damage modeling, localization, and shear deflection are discussed and finally practical applications are presented to show the model benefits.

This study develops a homotopy analysis method (HAM) for analytically solving a one-dimensional time-fractional advection-dispersion equation (FADE). The HAM is a powerful method for solving nonlinear ordinary and partial differential equations and does not seem to have been employed in hydrology. The advantage of the HAM is that it does not require much information about the boundary conditions of the aquifer domain. The initial condition may be measured for an aquifer, but the boundary conditions do not always have to be specified. The FADE is employed for modeling the fate of contaminants in heterogeneous porous formations subject to an increasing or decreasing source of contamination that is spatially and temporally dependent. Both solute dispersion coefficient and seepage velocity are considered spatially and temporally dependent, exhibiting the heterogeneity of the porous formation. It is found that the contaminant concentration changes with the order of the FADE. This study aids understanding of the physical meaning of parameters involved in velocity and dispersion because the parameters are not linearized. The analytical solution is also compared with the numerical solution obtained by the finite-element method and is validated with field data available in the literature.

A numerical model based on computational fluid dynamics and kinetic theory of granular material is used to investigate sand-bed erosion due to an upward water jet. After verifying the numerical model, the onset and mechanism of the sand-bed erosion are analyzed. As the the inlet water-jet velocity increases, a cavity around the jet orifice is first formed by the water jet, and the sand bed is eroded with a significant expansion. The numerical simulation shows that the increase in sand particle size and sand-bed height can significantly increase the inlet water velocity, causing sand-bed erosion. In addition, the critical velocity leading to sand-bed erosion is decreased as the sand friction angle decreases. Based on the observation and analysis of the numerical simulation, an analytical model using force equilibrium analysis and Ergun’s equation is proposed. The interaction between the mobilized and static zones in the sand bed is taken into account using granular theory. The critical inlet water velocity leading to the sand-bed erosion can be determined using this analytical model. This study provides a fundamental understanding of the mechanism of sand-bed erosion, and this numerical technique is shown to be an effective and promising way to investigate sand-bed behavior under an upward water jet.

A three-dimensional hydrodynamic analysis founded on the linear water wave theory and separation of variables in elliptical coordinates is undertaken to investigate the free sloshing characteristics in the doubly connected fluid domain of an upright (rigid-walled) cylindrical vessel of elliptical cross section that contains an internal (nonconfocal) elliptical core barrel of arbitrary size, aspect ratio, location, and orientation. The lateral tank boundary (impenetrability) condition is imposed by using the addition theorems for Mathieu functions, and a ($4\mathcal{N}\times 4\mathcal{N}$) truncated set of algebraic equations is eventually obtained after application of the relevant orthogonality relations. Extensive numerical experiments include plots of the first five sloshing wave numbers as functions of the (normalized) barrel eccentricity, for selected tank/barrel aspect ratios, barrel angular locations/orientations, and size. Also, the first four dimensionless natural sloshing frequencies are tabulated for selected liquid elevations and a wide range of geometrical configurations. Moreover, certain two-dimensional images of the liquid free-surface oscillation mode shapes are graphically portrayed. The prominent (moderate) effects of container cross-sectional ellipticity and barrel eccentricity (barrel aspect ratio and angular location/orientation) on the liquid sloshing characteristics are noted. In particular, in the circular tank configuration, several frequency clusters are formed among contiguous frequency branches that progressively merge together as the barrel eccentricity decreases (problem symmetry increases), leading to repeated doublet frequencies. Also, at certain barrel eccentricities, frequency crossovers (mode crossings) between different frequency branches are observed. Accuracy of simulations is confirmed by using a standard finite-element package in addition to comparisons with the existing literature data.

Tikhonov regularization on the integral-type nonlocal plasticity model is proposed to obtain a mesh-independent solution of strain localization. A detailed parametric study on the Tikhonov-regularized model is carried out for a one-dimensional and a two-dimensional problem. The influence of the regularization parameter, the tolerance of the nonlocal yield criterion, and the internal length scale on the finite-element solutions are examined. The width of the localization zone was found to be six times the internal length scale for a Gaussian-type weighting function. The solutions of the two-dimensional shear banding problem are compared with those of the one-dimensional strain localization. With the proposed model, no additional boundary conditions have to be introduced in the constitutive level, and only $C^0$ continuity is needed at element interfaces.

So far, no effective methods have been found to measure shale dual-porosity dual-permeability poromechanical and chemical parameters. This paper presents a practical method to determine such parameters by matching the newly derived two-dimensional transversely isotropic dual-poro-chemo-electro-elastic analytical solutions with laboratory pressure transmission test data of a clay-rich shale. The matching provides estimations of crucial shale parameters, including dual permeabilities, membrane coefficient, ions’ diffusion coefficients, and electro-osmotic permeability. Moreover, this matching includes not only pore pressure but also axial strain and radial strain. Such triple matches provide more confidence in the estimations compared to conventional simulations of only pore pressure measurements. Both the single porosity poromechanics solution and the newly derived dual-poro-chemo-electro-elastic solution are applied to analyze the test. It is shown that the single poro-chemo-electro-elastic simulation could not reproduce the experimental pore pressure or strain responses while the dual-poro-chemo-electro-elastic simulation could capture simultaneously pore pressure, axial strain, and radial strain responses very well. Compared to the single-porosity simulation, the dual-porosity simulation indicates that most of the shale volume change occurred within the clay grains and in between clay layers, pore pressure in between clay layers was higher than that outside of clay grains due to chemical osmosis. Sensitive analysis is implemented to show the confidence of the estimations and to identify parameters with the most influence on the results of the pressure transmission test. This paper also highlights the importance of accounting for shale dual-porosity nature when simulating its responses.

The effect of damping on progressive collapse responses of structures is typically ignored. However, the margin of conservatism resulting from ignoring damping is not well known. Therefore, in this paper, a nonlinear single-degree-of-freedom (SDOF) model is developed with a piecewise linear resistance function, viscous damping, and a loading function consisting of a ramp part and ensuing constant load. The closed-form analytical solutions are derived with Laplace transform techniques and verified with experimental results of steel beam-column assemblies under column-removal scenarios (CRS). The model is then used to investigate the damping effect on the dynamic displacement responses of structures under CRS with different initial conditions, structural resistance types, and levels of applied load. The results indicate that the effect of damping on displacement responses depends not only on the structural resistance but also on the level of applied load. For structural responses involving elastic and plastic hardening resistance, ignoring conventional global damping (e.g., a damping ratio of 3–5%) is reasonably conservative, but it is suggested that for structures with severe plastic softening resistance (e.g., softening stiffness greater than 10% elastic stiffness) and high damping ratio (e.g., more than 10%), the damping should be explicitly considered in the progressive collapse analysis; otherwise, it is too conservative, resulting in unnecessary cost.

This paper focuses on evaluating the vertical movements that appear when a pedestrian is walking on a slender platelike structure. For this, the pedestrian is modeled by a dynamic system consisting of a concentrated mass, located in the pedestrian’s center of mass, supported by two springs that simulate the stiffness of the legs. The success of this simple mechanical model is that the resulting contact forces are well adjusted to those observed experimentally for human gait. In this way, the structure is undergoing the moving mass and is loaded with realistic forces, resulting in a proper assembly to study interaction effects. The dynamic response is obtained at any coordinate by the modal superposition method, considering a finite number of modes. Differential equations of the resulting coupled problem are solved using proper numerical techniques (constant time step Runge-Kutta method). Solutions obtained for different scenarios (depending on the dimensions and boundary conditions of the plate and on the mass of the pedestrian with respect to the mass of the floor) are presented and compared with the response of the structure when the pedestrian load is treated as a moving force, as suggested in some design guidelines.

Mode shape–based structural damage detection is an emerging field of research. This study presents a vibration-based damage localization technique using the derivatives of mode shapes corresponding to undamaged and damaged states of a structure. First, mathematical expressions of the derivatives of mode shapes have been formulated and correlated with the damage location. The mathematical derivation shows that the difference in mode shape slopes attains a Dirac delta function at the location of the damage. Also, the difference in mode shape curvature is discontinuous at the damage location. However, it attains extreme values around the damage location. For illustration purposes, simulation studies on a shear building have been carried out to show the derivatives of the first few mode shapes to be sensitive to the damage location. An experimental case study involving a shake-table test has also been performed on a miniature model of a 6-story steel frame to investigate the efficiency of the proposed technique in real situations. Therefore, the mathematical formulation followed by the numerical study as well as the experimental investigation shows the competence of the proposed approach in structural damage identification.

Linear elastic fracture mechanics has been widely used for fracture analysis of cracked metals. For ductile materials, it is known that the yielding of a crack front results in the easing of stress intensity at the crack front, which ultimately increases the total fracture toughness of the material. Therefore, to use linear elastic fracture mechanics for prediction of the failure of ductile materials requires the extraction of the elastic portion of the fracture toughness. The intention of this paper is to develop a new theory of fracture toughness for ductile materials. Two methods, namely the elastic-plastic parameter method and the failure assessment diagram method, are proposed to determine the elastic fracture toughness. After verification of derived models, the developed elastic fracture toughness theory is applied to ductile metal pipes. Factors that affect the elastic fracture toughness are also studied in the paper. It is found in this study that the elastic fracture toughness is a function of the geometry of cracked bodies, material properties, loading conditions, and mode mixity. The developed theory of elastic fracture toughness will enable accurate prediction of the fracture conditions for both brittle and ductile metals, which is essential to prevent catastrophic failures of structures made of ductile metals.

This paper presents an active control structure and corresponding active control algorithm to suppress the vibration and reduce the dynamic response of an elastically connected double-beam system subjected to excitation loads. Because the double-beam system consists of two beams with an elastic layer in between, a distributed control structure is proposed, which adopts actuators along the elastic layer and acts on the two beams at the same time. An active control algorithm that synthesizes independent modal space control (IMSC) and a linear quadratic regulator (LQR) is developed for the proposed active control structure. The application of IMSC transfers the coupling equations of motion for the double-beam system with active control to the decoupled equations in modal space and makes the vibration control act on each mode. The adoption of LQR allows calculation of the active control forces in the modal domain, which further determines the applied control force in the physical space. Numerical examples are demonstrated to verify the efficiency of the proposed active control, which has great potential for application in future engineering practices.

This study investigates propagation buckling of subsea pipe-in-pipe (PIP) systems under hydrostatic pressure. Unlike in previous studies, PIP systems consisting of carrier pipes with a diameter-to-thickness ($D_o/t_o$) ratio in the range 26–40 are examined here. Experimental results from ring squash tests (RSTs), confined ring squash tests (CRSTs), and hyperbaric chamber tests are presented and compared with a modified two-dimensional (2D) analytical solution and with numerical results using three-dimensional (3D) finite-element (FE) analysis. The comparison indicates that the proposed modified analytical expression provides a more accurate lower-bound estimate of the propagation buckling pressure of PIP systems compared with the existing equations, especially for higher $D_o/t_o$ ratios. The novel RST and CRST protocols proposed for PIP systems give lower-bound estimates of the propagation pressure. The FE analysis outcomes demonstrate that the lengths of PIP system transition zones are almost twice the corresponding lengths in single pipes. New modes of buckling are discovered in the hyperbaric chamber tests of PIP systems with $D_o/t_o=26$.

This paper presents large eddy simulations (LES) of model-scaled neutrally stratified atmospheric boundary layer (ABL) flows for structural engineering applications and examines their statistical properties. A one-k-equation eddy model is used for the subgrid-scale (SGS) motions, and a wall shear model is applied on the ground. The mean streamwise velocity profile is approximately logarithmic, yet near the ground a mismatch persists because of the limited accuracy of the SGS model. The second moments of the turbulence represent well the underlying physics. The spectra of the velocity components at a point are consistent with commonly accepted expressions. The spatial coherences decay exponentially as functions of reduced frequencies. The results suggest that, except for the mean velocity near the ground, the ABL turbulence statistics can be well represented by large eddy simulations with simple SGS and wall models.

In this paper the influence of the virtual boundary layer on a fractional continuum is under consideration. The virtual boundary layer appears as a consequence of the definition of a both-sided fractional derivative, which is the basic operator in the description. The paper studies the one-dimensional elasticity problem under different boundary conditions, together with a range of length scales applied and different orders of fractional continua.

Two elastostatic approaches are presented in order provide a simple, but technically effective, assessment of shear coefficients in Timoshenko beam theory. First the elasticity solution of Saint-Venant’s flexure problem is used to set forth a unified formulation of Cowper’s formula for shear coefficients. Afterward a novel elasticity-based displacement field for a Timoshenko beam is introduced and an energy-consistent variational scheme is developed using the Reissner principle. The new variational framework is then applied to elliptical, circular, and rectangular cross sections. Validation of the results is given by numerical comparison with the other shear deformation factors over an extended range of Poisson’s and aspect ratios. Unlike previous treatments, the proposed shear coefficients for shallow cross sections do not result in numerical instability.

Insulated sandwich panels consist of two layers of wythe separated by a foam insulation. In recent years, fiber-reinforced polymer (FRP) materials have begun to be incorporated as shear connectors, because they have a lower thermal conductivity than steel and can significantly reduce thermal bridging. Until now, no effective guidelines exist for the design of these panels. Generally, they are treated as rectangular beams, which is not reasonable because the longitudinal stress over the wythe section is nonuniform resulting from the in-plane shear flexibility of the wythe, which is called the shear lag effect. The effective flange width has been used to describe the shear lag effect for a deck-on-girder composite beam system, reducing a three-dimensional behavior of the composite beam system to the analysis of a T-beam section with a reduced width of deck. This paper extends the concept of effective flange width to insulated concrete sandwich panels. A shear lag model is first developed to study the sandwich panel system, in which partial degree of composite action (DCA) owing to a flexible FRP shear connector is considered. The analytical model is then verified through close correlations between finite-element and analytical results for a concrete sandwich panel with FRP shear connectors. Finally, a parametric study was conducted using the analytical model.