Journal of Engineering Mechanics

Due to high demand for the safe operation of structures, structural members with the potential to shift their natural frequencies/specific-stiffness to satisfy design requirements or avoid the occurrence of dynamical instability are of great importance. Hence, the purpose of this study is to present a methodology to evaluate the impact arising from the number of layer and properties of laminas on the natural frequencies of a passive periodic-array beam. The periodic array is assumed to be composed of two different materials, basic and embedded laminas, which are periodically embedded into the beam. The problem is solved by treating the periodic-array beam as a single-phase nonhomogeneous continuum. The variation of material properties in the axial direction is expressed by a Fourier series half-range expansion with a wavelength equal to the average space between the two materials. The Fourier-series-based approach and Newtonian mechanics are employed in the analysis. The result of the study indicates that due to the nonhomogeneity of the periodic array’s materials, the symmetry of the system’s coefficient matrix strongly depends on the quantity of laminas. If there are more than a few periodic layers, the number of off-diagonal entries in the matrix is low and can be neglected when compared with the diagonal elements; the problem reduces to a self-adjoint eigenvalue problem. It shows that the periodic array can be treated as a tuning parameter to vary the natural frequency of the beam; the frequency shifting range depends on the ratio between the mechanical properties of the two materials. This implies that if periodic laminas are integrated into structures, it gives structures the potential to prolong their useful life by adjusting their natural frequencies to reduce the possibility of occurrence of dynamic instability, such as resonance.

Active flow control is applied at different locations over a surface-mounted prism to reduce extreme pressure coefficient and loads. Different control strategies including blowing, suction, and synthetic jets are evaluated. The full unsteady Navier–Stokes equations are solved to determine the pressure coefficients. The extent of reduction when using these three strategies with different flux injections, slot locations, and angles is determined. These strategies are assessed in two flow regimes corresponding to different Reynolds numbers. It is found that for the case of $\mathsf{R}={10}^3$, a reduction of the peak pressure, by nearly 50% is obtained. For the case of $\mathsf{R}={10}^4$, the best reduction is about 25%.

The study uses the material point method (MPM) and dynamic adaptive mesh refinement (AMR) technique to simulate incompressible free surface flows. The MPM can be regarded as a quasi-meshless method in which the background grid acts like a scratch pad while the material point (hereafter referred to as particle) motion overlies it. The states of the particles are updated through the solutions on the background grid. The artificial compressibility coefficient is employed to treat incompressible flows as slightly compressible flows within the MPM framework. Boundary conditions, such as free surfaces and reflective walls (both slip and no-slip conditions), are implemented and tested using the ghost-cell method. A generalized far-field characteristic boundary for wave propagation simulation has been established. Typical water wave propagation and violent wave breaking involving discontinuous free surfaces are simulated as well as compared to the arbitrary Lagrangian-Eulerian (ALE) method. The results indicate that the improved material point method is a promising tool to simulate free surface flows.

This paper presents a semianalytical method to analyze the natural frequencies and mode shapes of an undamped double-beam system, which is composed of two beams joined by a uniformly distributed connecting elastic layer, with arbitrary beam mass, beam flexural rigidity, and arbitrary boundary conditions. The classical modal expansion method is further applied to determine the forced vibration responses in the double-beam system based on the natural frequencies and mode shapes obtained from the free vibration analysis. A specific orthogonality condition for the double-beam system is derived, and then applied to decouple and simplify the motion differential equations. Numerical examples are presented and discussed in detail to verify and illustrate the efficiency of the proposed semianalytical method that can further help characterize the dynamic responses and design work for double-beam structures.

Two finite-element formulations are developed for the general distortional analysis of beams with monosymmetric sections. In the first formulation, cubic and linear Hermitian polynomials are adopted to interpolate the nodal displacements; whereas in the second formulation, shape functions that exactly satisfy the governing field equations were used. Because the distortional lateral-torsional and the longitudinal-transverse responses are fully uncoupled, separate finite elements were developed for both types of behaviors. A comparison with other finite-element solutions and a recently developed distortional theory established the validity of the present formulations. A study was then performed on the stability and convergence characteristics of both elements. The new elements were then adopted to solve linearly static analysis of simple beams and beams with overhangs. The formulation is shown to reliably capture the difference in behavior between stiffened and unstiffened beams.

A two-phase model is introduced that simulates the nonlinear dynamic behavior of a reinforced soil wall, incorporating a generalized plasticity soil model and an elastic perfectly plastic inclusion model. The two-phase model is an extension of homogenization methods developed using the virtual work theorem. It considers composite reinforced soil as the superposition of two mutually interacting continuous phases; the matrix and the reinforcement. The main advantages of the two-phase method are that layer-by-layer modeling is not needed, modifying the arrangement of inclusions is easy, and computation time decreases considerably. The Pastor-Zienkiewicz-Chan model has been specifically modified to improve its prediction of the ratcheting effect during cyclic loading of geosynthetic reinforced soil walls and was implemented for the behavior of the matrix phase. The proposed approach uses finite-difference code and was validated using simulations of reduced-scale reinforced soil walls subjected to seismic loading in shaking tables. Lateral displacement of the wall face from the two-phase model was compared with experimental values at different acceleration amplitudes. Investigation of the deformation patterns and potential failure surfaces in the two-phase models shows overturning deformation mode and formation of a bilinear wedge-shape zone that is consistent with the results of experiments.

This paper presents a study on the applicability of the preview control method for improving the performance of active seismic control systems. The active preview control method is examined as described for its ability to improve vibration suppression as follows: (1) the relation between the number of preview steps and the degree of improvement in control performance is clarified by analysis using predicted earthquake waves, and (2) to evaluate the applicability to an actual structure, predicted surface seismic waves are calculated by an autoregressive model from observed KiK-net data on 100–200-m-deep underground seismic waves and the applicability of the method is confirmed.

Hybrid simulations have shown great potential for economic and reliable assessment of structural seismic performance by combining physical experimentation on part of the structural system and numerical simulation of the remaining structural components. Current hybrid simulation practices often use a fixed numerical model without considering the possible availability of a more-accurate model obtained during hybrid simulation through an online model updating technique. To address this limitation and improve the reliability of numerical models in hybrid simulations, this paper presents a method and an implementation procedure of conducting real-time hybrid simulation (RTHS) with online model updating. The Unscented Kalman Filter (UKF) was adopted as the parameter identification algorithm applied to the Bouc-Wen model that defines the hysteresis of the experimental substructure. The identified parameters are then used to update the models of the numerical substructures during RTHS. A parametric study of the UKF system model parameters is carried out first to determine the optimum values to be used in the verification experiments. Then RTHS of a three-story steel shear building model is conducted and the effectiveness of online model updating in RTHS and the proposed implementation procedure is demonstrated. Guidelines for implementing the UKF for online model updating in RTHS and research needs for further development are discussed.

The paper presents a methodology for identification of localized structural damage using highly incomplete modal information, such as a subset of modal frequencies. The proposed methodology is based on linearized modal sensitivities and ${\ell }_1$-norm minimization of the algebraic difference between identified frequencies in damaged and undamaged states. The method is verified using stochastic simulations and validated using a series of laboratory experiments in which the number of potentially damaged elements is significantly larger than the number of identified modal frequencies.

For consideration of the wide applications of concordance and order information in global sensitivity analysis (SA), a new sensitivity index based on the spearman correlation coefficient (S-CC) is presented in this article. S-CC can reflect the linear order correlation between variables; thus the proposed sensitivity index can be used to measure the influence of input on the linear order of output. Then the main task becomes efficiently estimating the defined index. Here the authors introduce the basic unscented transformation (UT) to compute the index with high efficiency, and high order unscented transformation (HOUT) is also employed to further improve the computational accuracy. Several examples, including the commonly used Ishigami test function and other engineering examples, are used to demonstrate the validity of the proposed sensitivity index and the efficiency of the proposed UT-based methods.

Torsional resistance of a single prestressing tendon was derived on the basis of the theorem of virtual work to control the torsional rotation by nonequal prestressing forces on both sides of the webs of a flexural member. The energy formulation revealed that the vertical component of the prestressing force has a significant role in resisting the torsional rotation, whereas the axial component is responsible for the warping-related stiffness. The most influential location of the prestressing tendon was the point where the value of the warping function is maximized. The resulting finite-element equilibrium equations yielded nodal forces at the degrees of freedom corresponding to torsion and warping. Through numerical applications, it was suggested that the conventional solution method of beam finite-element formulation on the basis of the transformed cross section can be improved by adopting the nodal forces derived in this paper. Further, it was shown that the torsional rotation can be controlled by introducing nonsymmetrical prestressing forces on the right and left sides of the webs of a prestressed thin-walled flexural member.

Recently the authors developed an output-only (or blind) identification technique for the modal identification of structures under ambient/free vibrations. In the present study, this method is extended to incorporate nonstationary unknown inputs—a feature that existing output-only methods are unable to replicate. The method employs a so-called PARAllel FACtor technique to decompose the third-order tensor that is built using the spatial time–frequency matrices of the response signals in order to find the mode shapes and modal coordinates’ auto time–frequency distribution (TFD). The proposed method is first verified using a synthetic data set and then used to extract the modal parameters from vibration data recorded during shaking table tests on the International Institute of Earthquake Engineering and Seismology (IIEES) test structure. The accuracy of the blind identification results is assessed through comparisons with a well-established input–output identification method, namely, a well-known combination of the eigensystem realization algorithm and the observer/Kalman filter identification (ERA/OKID) method. Next, rigidities of the connections of the IIEES Test Structure are identified through a finite-element (FE) model updating procedure. Finally, the proposed method is validated through comparisons between responses predicted using the updated FE model and those directly recorded in additional shaking table tests that were not used in model updating studies.

Bond strength deterioration in corrosion-damaged reinforced concrete structures significantly affects serviceability and load-carrying capacity in their remaining service life. This paper presents a new analytical model for predicting the cracking development in the surrounding concrete and the residual bond strength of rebar in concrete structures due to reinforcement corrosion. The proposed analytical method adopts the thick-walled cylinder model for the cover concrete and considers the realistic properties of the corrosion-induced cracked concrete such as anisotropic behavior, residual tensile strength, and reduced tensile stiffness. As corrosion progresses, three phases for bond strength evolution associated with concrete cracking development are defined and the corresponding corrosion levels in each phase are determined. By using the constructed new governing equation, the crack width growth in the concrete cover and the radial bursting pressure at the bond interface are evaluated. The ultimate bond strength is then estimated from the contributions of adhesion, confinement, and corrosion pressure as a function of corrosion level. Finally, the effectiveness of the proposed analytical model is demonstrated by comparing the predicted results with experimental data available, and the results show that the proposed model is useful for predicting the bond strength evolution of the corroded rebar in concrete structures.

When a beam is subjected to an in-plane linear temperature gradient field, the thermal effects of the temperature gradient field tend to change the curvature of the beam in the transverse direction and to expand the beam in the axial direction. The rotation and expansion of the ends of the beam may be restrained elastically by its supports or by adjacent members such as columns. The restrained thermal actions will produce bending moments and compressive forces in the beam, and when these actions reach critical values the elastically restrained beam may bifurcate from its primary in-plane equilibrium configuration to an out-of-plane buckled equilibrium configuration. This paper investigates the thermoelastic out-of-plane buckling of an elastically restrained beam with a doubly symmetric cross section that is subjected to an in-plane linear temperature gradient field. The analytical solution for the critical temperature gradient for thermoelastic out-of-plane buckling of the beam is derived. It is found that the positions of the effective centroid and shear center of a cross section subjected to a linear temperature field are different from those under mechanical loads. Beams having a doubly symmetric cross section under a linear temperature gradient field behave as beam-columns with a monosymmetric cross section, thereby rendering the thermoelastic out-of-plane buckling of an elastically restrained beam under a linear temperature gradient field more complicated than its counterpart under mechanical loading.

A framework is developed for determining the stochastic response of linear multi-degree-of-freedom (MDOF) structural systems with singular matrices. This system modeling can arise when using more than the minimum number of coordinates, and can be advantageous, for instance, in cases of complex multibody systems whose dynamics satisfy a number of constraints. In such cases the explicit formulation of the equations of motion can be a nontrivial task, whereas the introduction of additional/redundant degrees of freedom can facilitate the formulation of the equations of motion in a less labor-intensive manner. Relying on the generalized matrix inverse theory and on the Moore-Penrose (M-P) matrix inverse, standard concepts, relationships, and equations of the linear random vibration theory are extended and generalized herein to account for systems with singular matrices. Adopting a state-variable formulation, equations governing the system response mean vector and covariance matrix are formed and solved. Further, it is shown that a complex modal analysis treatment, unlike the standard system modeling case, does not lead to decoupling of the equations of motion. However, relying on a singular value decomposition of the system transition matrix significantly facilitates the efficient computation of the system response statistics. A linear structural system with singular matrices is considered as a numerical example for demonstrating the applicability of the methodology and for elucidating certain related numerical aspects.

This paper presents a new interface model to simulate the cyclic bond-slip behavior of steel reinforcing bars embedded in concrete. A multi-surface plasticity formulation is used to model two major inelastic deformation mechanisms occurring in bond slip. One is the crushing and shearing of the concrete between the bar ribs, and the other is the sliding between the concrete and bar surfaces. These two mechanisms are represented by different yield surfaces and nonassociated flow rules. The flow rules account for the shear dilatation of the interface induced by the wedging action of the bar ribs and crushed concrete particles. The interface model has been implemented in a finite element analysis program and has been validated with experimental data. The model is easy to calibrate and is able to reproduce the bond-slip behavior of bars under a wide range of confinement situations, including bar pullout and concrete splitting failures.

Owing to the differences between earthquake excitations and barge impact loads, the modal combination rules [e.g., square root of the sum of the squares (SRSS)] commonly used in seismic analysis are not appropriate for the shock spectrum analysis (SSA) technique of barge-bridge collisions. For this reason, this paper aims to develop a specialized and reasonable combination rule for the SSA method. A parametric study is first carried out to explore the modal response characteristics of bridge structures subjected to barge impact loading. It is found that the time instant ($t_m$) corresponding to the peak value of the combined (total) dynamic response can be approximately predicted by analyzing the limited modal responses. The approximate equations are developed to predict the time instant $t_m$ for four different cases. On the basis of the estimated time instant, a new modal combination rule, called weighted algebraic sum (WAS), is proposed for the SSA method of barge-bridge collisions. The collision-induced peak responses of bridge structures derived from the SSA method with either WAS or SRSS are compared with those determined by the direct dynamic analysis technique. It is demonstrated that the WAS rule is more accurate in the barge-bridge collision spectrum analysis, particularly for the moderate- and high-energy impact events, whereas the SRSS rule is not recommended because of its lower accuracy. Also, the results obtained using the weighted function of cosine are slightly superior to those obtained using sine functions for the WAS rule.

Description of tire model development using the finite element (FE) method is presented. Three-dimensional tire-pavement contact stresses were predicted for braking, traction, and free rolling using the FE method. Measured load-deflection curves, contact area, and contact stresses were used for model outcome validation. Slide-velocity-dependent friction and accurate input regarding geometry and material properties were considered. The developed tire model, which helped in studying contact stresses variation in each direction, was used to explain the various phenomena taking place at the tire-pavement interface during straight-line rolling. The analysis matrix includes nine rolling conditions and various loads, tire inflation pressures, and speeds. Vertical contact stresses were not significantly affected by speed or slip ratio; however, contact stresses were greatly modified along the in-plane directions by rolling conditions. Analytical expressions were introduced to represent vertical and longitudinal contact stresses for full braking and full traction. Formulas are presented for low speed and full braking, which are relevant for roadway intersections design.

The transverse impact of a uniformly translating beam hitting a fixed-fixed column is investigated. Although in-air impact is considered, the study is motivated by water-driven woody debris during flood, storm surge, and tsunami. Hence, the beam (pole) is assumed to be wood, and the column is concrete, steel, or wood. Given the relatively small magnitude of the impact speed in such events, only elastic impact is considered. An analytical solution method is presented, which is also used to verify finite-element results. The results show that the contact force between the pole and the column depends on the local shear deformation in the pole and the column, and hence Timoshenko beam theory is needed. Multiple impacts are considered, and the whole collision event is divided into contact phases and separation phases. It is shown that for all cases the maximum contact force occurs during later contact phases and its value can reach up to 1.5 times the peak force in the first contact phase. The impact duration of the first contact phase depends on the shear wave in the pole or the column according to the mass and wave speed ratios. The total impulse on the pole ranges between 1.5 and 1.8 times the initial momentum of the pole, depending on the stiffness of the column. The energy exchange during the multiple impacts, while it can be complicated, reveals that for relatively stiff columns the sum of the translational kinetic and bending strain energies of the pole constitutes approximately 90% of the total energy. In all cases considered, relatively little net energy has been transmitted to the column at the time of final separation.

The behavior of materials and structures is strongly influenced by the loading rate. Compared with quasi-static loading structures loaded by high loading rate and impact acts in a different way. First, there is a strain-rate influence on strength, stiffness, and ductility, and, second, there are inertia effects activated. Both influences are clearly shown in experiments. Although steel does not exhibit significant strain rate sensitivity, the dynamic fracture of steel is highly sensitive on loading rates. In this paper, the static and dynamic fracture of steel is numerically studied on a compact tension specimen (CTS), which is loaded under loading rates up to $100\mathrm{m}/\mathrm{s}$. First, the proposed microplane model for steel is discussed and verified for monotonic and cyclic quasi-static loading. Subsequently, three-dimensional (3D) finite element dynamic fracture analysis is carried out. It is shown that the resistance of steel (apparent strength and toughness) increases progressively after the critical strain rate (approximately $100/\mathrm{s}$) is reached. Moreover, the crack branching phenomena and significant decrease of ductility are observed. The phenomena that are also well known from experimental evidence are attributed to the effect of structural inertia and inertia related to the high nonlinear behavior of steel at the crack tip and in the plastification zone. The numerical results indicate that maximum crack velocity of steel is much lower than the Rayleigh wave velocity, and for the investigated steel, it reaches approximately $400\mathrm{m}/\mathrm{s}$.

In a deck-on-girder composite beam system, the deck and supporting girders work together to effectively provide loading capacity. This system has been widely used for bridges, buildings, and other structures. Effective flange width is typically used to reduce a three-dimensional behavior of the composite beam system to the analysis of a T-beam section with a reduced width of deck. Current studies, including AASHTO specifications, are mainly focused on concrete decks with full-composite action. This paper presents a closed-form solution to study the composite beam system, which considers different degrees of composite action (DCAs) between the deck and supporting girders and can be applied to decks with orthotropic materials. The analytical model is verified through close correlations among test, finite-element, and analytical results for two T-beams with concrete and fiber-reinforced polymer (FRP) decks, in terms of both deflections and stress distributions. A parametric study is then conducted by using the analytical model to study the effects of DCA, deck stiffness, and aspect ratio on effective flange width. Finally, a simplified method is proposed to analyze the composite beam system with different DCAs, which can be used for design purposes.

In the absence of geometrical constraints, ductile fracture has been identified as the predominant mode of failure for structural elements under extreme loads, the prediction of which still represents considerable challenges. Ductile fracture of metals has only recently been recognized to be dependent on both stress triaxiality and Lode angle parameter. In this study, a new fracture model that is dependent on both stress triaxiality and Lode parameter is proposed. The developed model is proposed for the case of monotonic loading and is applicable to a wide range of stress states. The extension of the model to reverse loading, with complex loading history, is addressed in a parallel paper. The developed criterion is evaluated against data extracted from a series of multistress states monotonic experimental results for various metals, and a strong correlation is evident between the proposed model and experimental results in the entire range of the tested stress states. A detailed parametric study is conducted in order to show the effect of the model’s parameters on the fracture map. Comparative study among popular ductile fracture criteria and the proposed model in their prevailing ranges is also performed. The results show that the newly developed criterion, featuring only three parameters, does not lag behind its counterparts in any stress triaxiality ranges.

Ductile fracture of metals resulting from large amplitude inelastic reverse straining has been the predominant reason for the failure of structural components under extreme loadings. This kind of fracture, characterized by only a few reverse cycles with large precrack plastic strain, is often termed ultra-low cycle fatigue (ULCF). Ductile failure of metals has recently been recognized to be a function of stress triaxiality and Lode angle parameter. In this paper, a new fracture model with full consideration of stress triaxiality and Lode angle parameter as well as the cutoff regions is proposed from the extension of its equivalence for monotonic loading in the parallel paper. The underlying mechanism and determination of the cutoff region boundary is well-defined and discussed. Additionally, the effect of load excursion on shifting the boundary of the cutoff region and the subsequent damage evolution is assessed. The nonlinearity of damage evolution is also studied and well-characterized. The developed criterion is evaluated against data extracted from a series of multistress states cyclic experimental results, and excellent correlations between the proposed model and experimental results are achieved. Comparison between the proposed model and other existing models is made, and favorable results are shown for the proposed model. The presented model can be used for predicting the potential for ULCF failure in alloys.

The translation process theory has widely been used in assessing extreme and fatigue damage of stochastic non-Gaussian response processes. It relates a non-Gaussian process to an underlying Gaussian process through a monotonic translation function. For softening non-Gaussian processes with kurtosis larger than three, the Hermite polynomials model has been used in those situations in which the model coefficients are determined from the skewness and kurtosis of the process with closed-form formulations. This study presents a moment-based translation model for hardening non-Gaussian processes with kurtosis less than three. Closed-form formulations for determining the model coefficients in terms of skewness and kurtosis are presented. The accuracy and limitations of moment-based translation model in representing non-Gaussian processes are also discussed. The proposed moment-based translation model facilitates the analysis of extreme and fatigue of hardening non-Gaussian processes.