Journal of Engineering Mechanics

In this paper, a method has been proposed to use artificial neural networks for the modeling of concrete gravity dams with nonlinear hysteretic response under earthquake loading. The main advantage of this method is that it makes it possible to design an analysis tool for a specific dam based on the data obtained from monitoring said dam; hence, it is expected that the analysis tool could provide more precise results than analysis software presently available. This advantage is especially pronounced when the dam is to be analyzed under strong earthquakes where its response is nonlinear and hysteretic. The modeler neural network, referred to here as the neuro-modeler, offers considerable possibilities. For example, the nonlinear analysis of dams under earthquake loading requires considerable time; one advantage of designing neuro-modelers for dams is that they can give practically precise results about the response in a short time. As the first study on the subject to prepare a controlled precise data for the training and testing of the neuro-modeler so that the precision of the method could be evaluated, an analysis software was used to simulate the experiment. The smeared crack model, which has been one of the models used successfully in the literature to model concrete gravity dams, has been used in this study as well. Multilayer feed-forward neural networks have also been used. The first step in this method is to analyze the dam under study as it is subjected to different earthquake simulations to collect large data about its linear and nonlinear response. The second step is to train a neuro-modeler, based on the collected data, to implicitly learn the nonlinear hysteretic response of the dam being subjected to the training earthquakes. The third step is to test the precision and generalization capabilities of the neuro-modeler where it is used for the analysis of the dam under a number of selected earthquakes of different properties including both near- and far-field excitations. After passing the tests successfully, the neuro-modeler is expected to be able to provide reliable and precise results about the response of the dam under any given earthquake. Three concrete gravity dams with differing characteristics and in different geographical locations including the Koyna, Pine Flat, and Sefid-Rud dams, which have been both numerically and experimentally studied because they had experienced considerable damage during earthquakes, have been utilized as examples. A neuro-modeler has been trained for each of the dams and tested. The results are reported in this paper. The dam neuro-modelers have been successful in providing precise results in this numerical simulation of the nonlinear hysteretic behavior of dams.

One of the accepted approaches for postpeak finite-element modeling of RC comprises combining plain concrete, reinforcement, and interaction behaviors. In these, the postpeak strain–softening behavior of plain concrete is incorporated by the use of fracture energy concepts. This study attempts to extend this approach for RC at elevated temperatures. Prior to the extension, the approach is investigated for associated modeling issues and a set of limits of application are formulated. The available models of the behavior of plain concrete at elevated temperatures were used to derive inherent fracture energy variation with temperature. It is found that the currently used tensile elevated temperature model assumes that the fracture energy decays with temperature. The existing models in compression also show significant decay of fracture energy at higher temperatures ($>400°$) and a considerable variation in values. Application of the evaluated fracture energy values shows that these impose severe element size and reinforcement ratio limits. The effect of the limits is illustrated for a RC specimen.

In this study, critical buckling load of an impacted composite laminate is predicted, using the structural similitude method. Because of impact loading, damaged regions have formed in the laminate. To establish similarity conditions between impacted laminates for buckling loading, the idea of sequential similitude method is introduced. According to the sequential similitude method, similarity conditions can be established for a structure subjected to different loading situations, provided that each loading event is simulated independently. On the basis of this method, to develop similarity conditions for buckling loading of impacted composite laminates, similarity conditions are developed first for impact loading and then for buckling loading separately. Afterward, the obtained conditions are implemented in the commercial finite-element software, ABAQUS, to obtain the critical buckling load. Results show that sequential similitude method can be used as a simple and accurate method for prediction of buckling load of impacted laminates.

The lateral stability of imperfect discretely braced steel beams is analyzed using Rayleigh-Ritz approximations for the lateral deflection and the angle of twist. Initially, it is assumed that these degrees of freedom can be represented by functions comprising only single harmonics; this is then compared with the more accurate representation of the displacement functions by full Fourier series. It is confirmed by linear eigenvalue analysis that the beam can realistically buckle into two separate classes of modes: a finite number of node-displacing modes, equal to the number of restraints provided, and an infinite number of single harmonic buckling modes, where the restraint nodes remain undeflected. Closed-form analytical relations are derived for the elastic critical moment of the beam, the forces induced in the restraints, and the minimum stiffness required to enforce the first internodal buckling mode. The position of the restraint above or below the shear center is shown to influence the overall buckling behavior of the beam. The analytical results for the critical moment of the beam are validated by the finite-element program LTBeam, whereas the results for the deflected shape of the beam are validated by the numerical continuation software AUTO-07p, with very close agreement between the analytical and the numerical results.

When thin-walled box beams meet at an angled joint, the joint region exhibits significant flexibilities that cannot be modeled by the Timoshenko or Euler beam theory especially at a joint of multiple box beams. Conventionally, the flexibilities are represented by artificial spring elements when the Timoshenko beam theory is used. On the other hand, this investigation presents a higher-order beam analysis applicable to three thin-walled box beams connected at a joint under out-of-plane bending loads; no artificial spring element will be used. Because the higher-order theory includes the sectional distortion and warping degrees of freedom, it accurately predicts the structural behavior of thin-walled straight box beams. The main issue in joint analysis is how to match all field variables of bending displacement, bending rotation, warping, and distortion at the joint—no investigation applicable to the analysis of a joint of three box beams has been reported so far. The difficulties result from the fact that the standard vector transformation useful for the Timoshenko beam is not applicable, because the higher-order beam theory involves variables producing zero resultant. In this work, a three-beam joint-matching condition using the Lagrange multipliers is proposed where the three-dimensional displacements calculated by the higher-order beam theory are imposed to be continuous along shared edges of interfacing beams. The validity of the developed matching approach is tested with several numerical examples. A special consideration is also discussed to deal with the case when joint angles between two of the three beams are unequal.

Underground structures are sometimes threatened by ground shocks induced by subsurface detonations. This paper proposes one possible method to mitigate the subsurface blasts by attaching a cladding consisting of a face sheet and cellular solid core to the exterior of the structure; the cellular core is foam made from relatively strong materials, such as metal or concrete, rather than typical geofoam made from polymer. A simplified model is established to distinguish three scenarios to delineate the dynamic behavior of a foam cladding subjected to a ground shock. The model compares the velocity time histories of the face sheet and the surrounding soil, in which the foam crushing velocity is not high and the foam is densified uniformly. Further, the governing equations for possible high-velocity foam crushing are established, with progressive collapse as foam crushing mode when alleviating subsurface blasts.

This paper provides a simple relationship to theoretically estimate the wave friction factor in various flow regimes in porous media based on the slip factor formula. The theoretical formula shows that the wave friction factor varies inversely with the relative bed roughness, $A/k_s$, over a rough bed and that it can be conveniently determined if wave conditions and sediment parameters are known without using a specific regression formula deduced from experiments. A laboratory experiment that directly measures the wave-driven bed shear stress dominant in the turbulent regime with a permeable bed is used to examine the newly derived relationship. In the laminar regime, the comparison demonstrates that the theoretical results determined by the proposed formula are in good agreement with existing measurements. In the turbulent-rough regime, the influence of eddy viscosity is considered in the slip factor formula and the zero-equation model is used in estimating the average eddy viscosity. The theoretical wave friction factor is reasonably close to the experimental measurement, and considerably better than that obtained by other existing regressions. It is also found that the wave friction factor in the small $A/k_s$ zone can be described by the present model, with comparisons showing that the slip factor theory can be extended to estimate the wave friction factor in the turbulent-rough regime. Additionally, the proposed relationship is demonstrated to be effectively used in an alternate rough bed. Experimental results further indicate that the wave friction factor in a porous medium is affected by the permeability of the sediment.

A matched asymptotic expansion analysis is used to determine the dependence of shear stress boundary layer thickness on adhesive properties in unbalanced single-lap joints. A uniformly accurate expansion of shear stress, in a small and positive dimensionless parameter $\epsilon$, is shown to contain a pair of adhesive edge boundary layers and an outer zone where the stress is slowly varying between the two layers. An overlap constraint is also found, and if it can be satisfied for $\epsilon \ll 1$, then there is sufficient overlap and a single boundary layer of width the order of ${\epsilon }^{1/2}$ at either adhesive end. The analytic results are presented in a generic format allowing their application and/or extension to similar problems. All results are numerically verified using a finite difference approximation.

Lattice transmission towers are vital components of transmission line systems, which play an important role in the operation of electrical power systems. This paper proposes a new type of tuned mass damper (TMD), the pounding tuned mass damper (PTMD), to upgrade the seismic resistant performance of a transmission tower. In the PTMD, a limiting collar with viscoelastic material laced on the inner rim is installed to restrict the stroke of the TMD and to dissipate energy through collision. The pounding force is modeled based on the Hertz contact law, whereas the pounding stiffness $\beta$ is estimated in a small-scale test. A multimass model of a 55-m tower is established to verify the effectiveness of the PTMD numerically. Harmonic excitation and time-history analysis demonstrate the PTMD’s superiority over the traditional TMD. Finally, a parametric study is performed for the optimal design.

By virtue of a new complete scalar potential function, an analytical formulation is presented to determine displacements, stresses, and temperature in an axisymmetric linear thermoelastic transversely isotropic half-space affected by time harmonic surface axisymmetric vertical traction and/or surface heat flux. With the use of only one scalar potential function in a cylindrical coordinate system, the coupled partial differential equations in thermoelasticity are transformed to a sixth-order partial differential equation governing the potential function. Then, by using the Hankel integral transforms, a sixth-order ordinary differential equation is received, which after solving, results in the displacements, stresses, and temperature fields. To prove the validation of the analytical solution presented in this paper, the solutions are reduced to the case of elastodynamics in transversely isotropic half-space and in a quasi-static thermoelastic isotropic half-space, where exact agreements with the solutions reported in the literature are achieved. Because of complexity of the integrands, numerical evaluations of the integrals involved in this paper are carried out using a suitable quadrature scheme by Mathematica software. To show the accuracy and efficiency of the numerical algorithm, the solution of this study is compared with the results of an existing elastodynamic transversely isotropic half-space, where an excellent agreement is achieved.

In this paper, a new solution method is proposed for investigation of the vibration characteristics of finite-length circular cylindrical shells with a circumferential part-through crack. Four representative sets of boundary conditions are considered: simply supported, clamped-clamped, clamped-simply supported, and clamped-free. The governing equation of the cracked cylindrical shell is derived by integrating the line-spring model with the classical thin shell theory. A computationally efficient numerical solution method for determining the natural frequency of the system of a given mode is proposed. The algorithm calculates the natural frequency from an initial trial through a one-dimensional optimization process. Two initial trial estimation methods are considered: the beam-function method and Soedel’s expression method. On the basis of the case study results, a recommendation is made on the selection of a suitable initial trial calculation method. The verification of the proposed method is divided into two parts. In the first part, the intact cylindrical shell analysis results obtained from the proposed method are compared with those from the literature and from finite-element (FE) analysis using Ansys. Because relevant cracked cylindrical shell analysis results are not available from the literature, the proposed method’s performance in this case is verified using the FE method alone in the second part. The verification results demonstrate that the proposed method provides a fast and efficient way to calculate the time-domain responses of a cracked cylindrical shell. Furthermore, the case study results indicate that the dynamic characteristics of short shells are more sensitive to circumferential surface cracks than those of long shells. This observation makes it possible to extend the proposed cracked shell modeling method to crack detection following the model-based approach, especially for short shell members.

Glass fiber-reinforced polymer (GFRP) concrete reinforcement exhibits high strength, is lightweight, can decrease time of construction, and is corrosion resistant. However, research has shown that chemical reactions deteriorate the GFRP reinforcing bars over time, resulting in a reduced tensile capacity. This paper develops a time-variant probabilistic model to predict the tensile capacity of GFRP bars embedded in concrete. The developed model is probabilistic to properly account for the relevant sources of uncertainties, including the statistical uncertainty in the estimation of the unknown model parameters (because of the finite sample size), the model error associated with the inexact model form (e.g., a linear expression is used when the actual and unknown relations are nonlinear), and missing variables (i.e., the model only includes a subset of the variables that influence the quantity of interest.) The proposed model is based on a general diffusion model, in which water or ions penetrate the GFRP bar matrix and degrade the glass fiber-resin interface. The model indicates that GFRP reinforcement bars with larger diameters exhibit lower rates of capacity loss. The proposed probabilistic model is used to assess the probability of not meeting the tensile strength requirement based on specifications over time and can be used to assess the safety and performance of GFRP reinforced systems. Sensitivity and importance analyses are carried out to explore the effect of the parameters and random variables on the probability estimates.

The nonlinear vibration differential equation and vibration frequency of cable net glazing subject to earthquake loading was determined, and a geometrically nonlinear single-degree-of-freedom model for cable net glazing was developed. The nonlinear response spectra were established, and nonlinear time history analysis with finite element (FE) models was conducted to verify them. The nonlinear vibration differential equation and frequency obtained as described in this paper provide a basis for the nonlinear single-degree-of-freedom model for cable net glazing. The analytical formula for the nonlinear frequency with a simplified expression is highly precise and convenient for use in engineering practice. For larger-amplitude seismic waves, the difference between the linear and nonlinear response spectra are more obvious. As the natural period of cable net glazing is always less than 2 s, the linear response spectra in the Chinese code for the seismic design of buildings can be used in the seismic design of cable net glazing as an approximation rather than the nonlinear response spectra of cable net glazing.

In this paper, an optimal $H_{\infty }$ control algorithm using direct velocity feedback is used for the design of control systems in reducing structural seismic responses. An optimum design strategy was developed for deciding two control parameters, $\gamma$ and $\alpha$, which are introduced in the control algorithm and play important roles in system stability and control performance. $\gamma$ is a positive attenuation constant, which denotes a measure of control performance, and $\alpha$ is a control weighting factor, indicating the relative significance between control force requirement and response reduction. Analytical results show that decreases in $\gamma$ or increases in $\alpha$ yield better control performance but require larger control forces. The selection range of $\gamma$ and $\alpha$ for a controlled system yielding overdamped or unstable responses is found. To assure system stability and better performance than linear quadratic regulator (LQR) control, analytical expressions of the upper and lower bounds of $\gamma$ and $\alpha$ are derived for direct velocity feedback control. Therefore, the seismic responses can be effectively reduced with an appropriate selection of $\gamma$ and $\alpha$. In addition, when a time delay in control force execution exists, explicit formulas to calculate the maximum allowable delay time and critical control parameters of $\gamma$ and $\alpha$ are also derived for the design of a stable time-delayed control system. An optimal design flowchart is also provided. The desired control performance can be guaranteed, even with time delay.

A Green function–based approach is presented to address the nonlinear tensionless contact problem for beams resting on either a Winkler or a Pasternak two-parameter elastic foundation. Unlike the traditional solution procedure, this approach allows determination of the contact locus position independently from the deflection curves. By doing so, a general nonlinear connection between the loading and the contact locus is found, which enlightens the specific features of the loading that affect the position of the contact locus. It is then possible to build load classes sharing the property that their application leads to the same contact locus. Within such load classes, the problem is linear and a superposition principle holds. Several applications of the method are presented, including symmetric and nonsymmetric contact layouts, which can be hardly tackled within the traditional solution procedure. Whenever possible, results are compared with the existing literature.

Vortex-like flow patterns are often observed in experiments on granular media for which uniform strain is expected based on the loading boundary conditions. These deformations become apparent when the motion associated with uniform strain is subtracted from the total particle motion. Besides presenting an interesting phenomenon that begs explanation, these vortex patterns suggest multiscale structure for nonaffine motion as suggested by modern continuum theories. Further, the authors note that the rotational velocity field added to a uniform strain field produces a planar slip field. Thus, these structures are associated with the slip-band fields that eventually form, which are generally associated with bifurcations in the solution path of the governing partial differential equations. The authors present a procedure to extract these motion fields from discrete-element simulations along with conjugate forces associated with these motions. A key finding from the simulations is that the motions that eventually lead to shear band formation develop throughout the loading history rather than arising as a distinct bifurcation. Further, the pattern of rotational fields, and hence the shear banding pattern, are controlled by the boundary conditions. A question, only partly resolved here, is the origin of forces driving the rotational fields.

An analytical method for responses of a class of nonlinear single degree-of-freedom (DOF) systems under nonstationary random excitations (NSREs) is presented. It is based on the transformation of the nonlinear stochastic differential equations that govern the vibrations of nonlinear systems under NSREs into a polynomial of which the exact roots are available, and therefore solutions without approximation of the nonlinear system can be evaluated. For demonstration purposes, the van der Pol-Duffing oscillator under a time-modulated zero mean Gaussian white noise process is considered. Representative solutions are verified by the Monte Carlo simulation (MCS) technique. The main conclusions are as follows. First, a simple and relatively straightforward method has been developed to transform the nonlinear stochastic differential equations of a class of nonlinear single DOF systems into polynomials for which exact solutions are available. The analytical solution developed in this paper is for the deterministic equation of motion for a specific realization of the input excitation function $f\left(t\right)$. The statistics of the displacement response are obtained using the expectation operator applied to the exact solutions computed for every realization of $f\left(t\right)$. Second, for the first time solutions without approximation are obtained for a nonlinear single DOF system with nonlinearities involving nonlinear velocity as well as displacement and under NSRE. Third, for solutions of the van der Pol-Duffing oscillator the computational time required by the present method is much more efficient than that using the MCS technique.