Journal of Engineering Mechanics

For concrete beams and slabs strengthened with bonded fiber reinforced plastic (FRP) plates, plate debonding from the concrete substrate is a common failure mode. In this paper, the debonding process is modeled as the propagation of a crack along the concrete/adhesive interface, with frictional shear stress acting behind the crack tip. Crack propagation is taken to occur when the net energy release of the system equals the interfacial fracture energy. The analysis is first performed for the special case with constant shear stress along the debonded interface, and then for the general case with slip softening in the debonded zone. From the results, a direct correspondence between energy-based and strength-based analyses can be established for arbitrary softening behavior along the interface. Specifically, through the proper definition of an effective interfacial shear strength, the conventional strength-based approach can be employed to give the same results as the much more complicated energy-based analysis. Also, based on the relation between the effective shear strength and other material parameters, it is possible to explain the very high interfacial shear stresses observed in experimental measurements. As an application example, distribution of plate stress and interfacial shear stress for the linear softening case is derived. The model results are found to be in good agreement with experimental measurements, showing that the simple linear softening model can describe the debonding process in real material systems.

Current practice in buckling design is based on the ultimate strength of a member such that excessive lateral deflections do not occur. This ultimate strength is often dictated by empirically derived formulae which correspond to postulated element imperfections including residual stresses. In this paper, the postbuckling behavior of columns is considered, and the limit state is considered to be total collapse. The load versus end displacement relationship is derived for a simplified elastic–perfectly plastic column model. Using this curve, the energy absorbed and released in going from one load/deflection state to another can be easily quantified. With this, the energy absorption capacity of an already loaded column is considered to be the critical performance metric. This “energy capacity criterion” is then used to develop alternative design curves for different levels of energy absorption capacity.

This paper deals with the exact solution of the differential equations for the out-of-plane behavior of an arch with varying curvature and cross section. The differential equations include the shear deformation effect. The cross section of the arch is doubly symmetric. Due to the double symmetry, in-plane and out-of-plane behavior will be uncoupled. However, a coupling of the out-of-plane bending and the torsional response will exist and will be discussed in this study. The governing differential equations of planar arches loaded perpendicular to their plane are solved exactly by using the initial value method. The analytical expressions of the fundamental matrix can be obtained for some cases. It is also possible to use these analytical expressions in order to obtain the displacements and the stress resultants for an arch with any loading and boundary conditions. The examples given in the literature are solved and the results are compared. The analytical expressions of the results are given for some examples.

Bouc–Wen class models have been widely used to efficiently describe smooth hysteretic behavior in time history and random vibration analyses. This paper proposes a generalized Bouc–Wen model with sufficient flexibility in shape control to describe highly asymmetric hysteresis loops. Also introduced is a mathematical relation between the shape-control parameters and the slopes of the hysteresis loops, so that the model parameters can be identified systematically in conjunction with available parameter identification methods. For use in nonlinear random vibration analysis by the equivalent linearization method, closed-form expressions are derived for the coefficients of the equivalent linear system in terms of the second moments of the response quantities. As an example application, the proposed model is successfully fitted to the highly asymmetric hysteresis loops obtained in laboratory experiments for flexible connectors used in electrical substations. The model is then employed to investigate the effect of dynamic interaction between interconnected electrical substation equipment by nonlinear time-history and random vibration analyses.

This paper proposes a methodology for simulation of binary random fields with application to the problem of generating sample realizations of two-phase random media. The methodology is based on the concept of nonlinear transformations with memory of Gaussian random fields. The simulation is performed according to the autocorrelation function of the binary field which contains considerable information about the microstructural characteristics of the medium. The determination of the probabilistic characteristics of the underlying Gaussian field is achieved through an iterative procedure that was introduced in a previous paper by the same authors in one dimension and is extended here to multiple dimensions. Limiting cases and alternative mappings are also presented. The capabilities of the methodology are demonstrated in a series of examples.

A variety of hot mix asphalt mixtures are used in highway and runway pavement construction. Each mixture caters to specific needs. Mixtures differ from one another in the type and percentage of aggregates and asphalt used, and their response can be markedly different, and thus there is a need to develop constitutive models that can differentiate between the different kinds of mixtures. In this paper, we outline a general procedure for the constitutive modeling of bituminous mixtures. We illustrate the efficacy of this approach by means of an application to sand asphalt. The governing equations for this special problem reduce to a stiff nonlinear ordinary differential equation and this is solved numerically using Gear’s method. We compare the results of the predictions of the model that we have developed with the compressive creep experiments carried out by Wood and Goetz on a typical sand asphalt mixture and find them to be in good agreement.

When an elastic wave propagates through a rock mass, its amplitude is attenuated and velocity is slowed due to the presence of fractures. During wave propagation, if the shear stress at a fracture interface reaches the fracture shear strength, the fracture will experience a large shear displacement. This paper presents a study of the normal transmission of S-waves across parallel fractures with Coulomb slip behavior. In our theoretical formulation, the method of characteristics combined with the Coulomb slip model is used to develop a set of recurrence equations with respect to particle velocities and shear stress. These equations are then solved numerically. In a comparison with the theoretical study, numerical modeling using the universal distinct element code (UDEC) has been conducted. A general agreement between UDEC modeling and theoretical analysis is achieved. The magnitude of the transmission coefficient is calculated as a function of shear stress ratio, nondimensional fracture spacing, normalized shear stiffness, and number of fractures. The study shows that the shear stress ratio is the most important factor influencing wave transmission, and the influence of other factors becomes more apparent when the shear stress ratio is small.

Localization of damage from changes in flexibility in structures identified from operational or ambient vibration has long been hindered by the fact that the flexibility cannot be extracted exclusively from output signals. This obstacle is substantially removed here by noting that the null space of the flexibility change contains the damage localization information and that vectors in this null space can be estimated from output signals without having explicit flexibility matrices. The central pillar of the contribution is a derivation showing that although the spatial distribution of the input that generates the observed output is unknown, the state-space triplet $\left\{A_c{B}_c{D}_c^{-1}{C}_c\right\}$ connected with a collocated input distribution (for a model order up to twice the number of sensors) can be extracted from output measurements. The fact that vectors in the null space of the change in flexibility can be extracted from this triplet falls from the expression for the flexibility in terms of the state-space matrices and from the fact that the damage is assumed to have no effect on the inertial properties.

The flexibility and low damping of the long-span suspended cables in the suspension bridges make them prone to vibrations due to wind and moving loads, which affect the dynamic response of the suspended cables and the bridge deck. This paper shows the design of two control schemes to control the nonlinear vibrations in the suspended cable and the bridge deck due to a vertical load moving on the bridge deck with a constant speed. The first control scheme is an optimal state feedback controller. The second control scheme is a robust state feedback controller, whose design is based on the design of optimal controllers. The proposed controllers, whose design is based on Lyapunov theory, guarantee the asymptotic stability of the system. A vertical cable between the bridge deck and the suspended cable is used to install a hydraulic actuator able to generate the active control force on the bridge deck. The MATLAB software is used to simulate the performance of the system with the designed controllers. The simulation results indicate that the proposed controllers are capable of significantly reducing the nonlinear oscillations of the system. In addition, the performance of the system with the proposed controllers is compared to the performance of the system controlled with a velocity feedback controller. It is found that the system with the proposed controllers can provide better performance than the system with the velocity feedback controller.

Model calibration and parametric studies of the coupled, complex surge-heave motions of a medium-scale experimental, nonlinear, submerged, moored structural system are presented here. The experimental system excited by periodic wave fields consists of a spherical buoy and attached multipoint mooring lines. Sources of nonlinearity include complex geometric restoring forces and coupled fluid–structure interaction exciting forces. The sphere moves mainly in a two-dimensional fashion [or two degrees of freedom (2DOF)] of surge and heave, with negligible pitch. Characteristic experimental results include harmonic, subharmonic, and superharmonic responses. As an extension of single-degree-of-freedom, independent-flow-field (IFF) models, a 2DOF, IFF model is derived and employed. Good agreement is shown between the analytical predictions and experimental results. Existence of complex nonlinear responses, including chaos and multiple coexisting steady states, are numerically identified when the coupling is strong and damping is light. Degree of complexity and nonlinearity of responses diminish with decreasing coupling and/or increasing damping.

Analyses and simulations of the coupled surge-and-heave motions of a nonlinear, moored, experimental, submerged structure subjected to random waves are presented here. The random wave excitations examined include periodic waves with additive noise and narrow-band random waves. Characteristic experimental results include noisy subharmonic and superharmonic responses, and transition behaviors among multiple coexisting responses. This investigation applies a systematic, stochastic analysis procedure to further the deterministic study presented in Part I. Good agreement between the analytical predictions and experimental results is shown. Effects of random perturbations in waves on nonlinear response phenomena are examined, especially for the cases of multiple responses coexisting with chaos. It is found that chaotic responses are sensitive and of weak strength compared to other coexisting responses, and the system response trajectories mainly stay in the stronger, periodic attracting domains. Numerical results indicate perturbation-induced response transitions leading to very large-amplitude response beyond the experimental model limitations.

In this paper we present and propose a design methodology that uses intentional time delays for the active control of structures. We use here positive velocity-feedback, time-delayed control and show that its performance is, in general, superior to the previously developed methodology of using time delayed, negative velocity-feedback control. A detailed study carried out in this paper of the nonsystem poles and their interaction with the system poles reveals the reasons for this. Analytical results related to performance and stability of the new method are presented. We apply the time delayed positive velocity feedback active control methodology to a multidegree-of-freedom system subjected to the S00E component of ground acceleration recorded during the El Centro 1940 earthquake. The excellent behavior in terms of stability, performance, and control efficiency that is demonstrated by our time-delayed control design as well as its facile implementation makes it attractive for earthquake hazard mitigation in a practical sense.