Journal of Engineering Mechanics

This paper is devoted to the limit design of cellular cofferdams that are regarded as mixed structures where the backfill is modeled as a three-dimensional continuum, while the surrounding sheet pile wall is treated as a cylindrical shell. Dealing with this structure from a static point of view, it turns out that the problem under consideration requires the calculation of the ultimate load value of a circular cylindrical shell subjected to a linearly varying pressure distribution representing the thrust of the backfill material. Extending the results of previous works, a complete solution to this problem is developed for different boundary conditions. The corresponding results are discussed, notably the influence of the shell relative thickness. They are applied to the design of a single cellular cofferdam whose stability under gravity forces is examined, with the strength of the granular backfill material being described by a Mohr-Coulomb criterion.

In cold regions, rivers may be partially or completely ice covered during a good part of the year. Under these conditions, heat transfer between the river flow and the atmosphere occurs simultaneously at the ice-air and ice-water interfaces of the ice cover. Heat flux from the water to the ice is the most dominant factor in the growth and decay processes of the river ice. A proper evaluation of the heat transfer coefficient at the ice-water interface is the key for an accurate computation of the heat flux and, consequently, for determining ice-cover melting. A variable heat transfer coefficient for both the entry region and for the fully established flow region was derived. The effects of this coefficient on the computation of ice-cover melting are addressed in this paper through the use of a two-dimensional numerical model. The new approach as well as other constant empirical equations used to evaluate the heat transfer coefficient were respectively used in the model to examine their effects on ice melting. Results of computations using the new approach were in a better overall agreement with experimental observations, including the leading edge region.

This paper presents a rate dependent damage model and its implementation in transient dynamics. The rate dependent model is derived from a rate independent damage model simply by changing the expression of the damage evolution equation. The principle of the model follows the format of Perzyna viscoplasticity whereby the definition of the plastic multiplier is modified compared to a standard rate independent plasticity model. The rate dependent model can reproduce very well the major effects of the rate of loading on the response of concrete; that is, an increase of the material strength and a decrease of the softening tangent modulus with increasing strain rate. The wave propagation problem is assessed. We show that the resulting equations of motion are unconditionally hyperbolic. Well-posedness and mesh objectivity are verified numerically on a simple one-dimensional (1D) problem. As an example of implementation in a finite element calculation, the computation of the response of a reinforced concrete beam subjected to an impact is presented.

A study of the dynamic responses of flexible tanks containing nonuniform liquid under horizontal base excitations is presented. The system considered is an upright, circular cylindrical tank filled with an incompressible and inviscid liquid in which the density increases with the liquid depth. Only the impulsive components of response are considered in this study since the convective components can be computed by considering the tank to be rigid. It is shown in this study that for tanks with height-to-radius ratios between 0.3 and 1.2, the response quantities may be estimated utilizing the rigid tank solutions. Also, it is found that the pressure distribution along the tank wall is not sensitive to the detailed distribution function of the liquid density, and that the base shear and moments for the tank with nonuniform liquid can be estimated conservatively by assuming that the tank is filled with an equivalent uniform liquid density that preserves the total liquid weight. Finally, a simple equation for evaluating the fundamental natural frequency of the system is proposed.

A new model for the determination of fracture-mechanics parameters in concrete is developed. Application of this method requires merely knowledge of peak load and peak crack-mouth–opening displacement (CMOD) values. The interrelationship between the damaged and undamaged sections within the microcracked zone is drawn through an analogous composite beam section. The extent of damage material within the process zone is assumed to vary linearly from its maximum level at the crack tip all the way to the boundary of the undamaged section. Hence, the fracture-process zone is defined as a composite material with a linearly variable modular ratio within its boundary. By using this approach, it is possible to determine a number of important fracture parameters from the knowledge of peak load and CMOD at peak load alone. These parameters include the fracture-process–zone size ( r _p ), critical fracture-energy release rate ( G _IC ), fracture toughness ( K _IC ), and fracture energy ( G _F ). Furthermore, use of the proposed methodology makes it possible to construct the entire load CMOD, deflection diagrams from the peak load, and CMOD data alone. Fracture-mechanics parameters and load-displacement relationships obtained through analysis by the present approach compare very well with a number of available experimental results.

This study compares the performances of a conventional feedforward controller and a neurocontroller in compensating the effects of the actuator dynamics and computational phase delay in a simple digital vibration control system. The model of this system is based on an earlier experimental study where a two-degree-of-freedom dynamic system was constructed in the laboratory. This system consisted of two electrohydraulic, position-controlled actuator-mass systems, mounted one on top of the other. Bode frequency domain plots were used to identify the governing parameters of the system. Based on the identified model of the experimental setup, a conventional feedforward controller and a neurocontroller are designed to compensate for the adverse effects of actuator dynamics and computational phase delay. The identified model is used to generate training information for the neurocontroller in a frequency domain of interest. To accomplish this endeavor, a neural network simulator is developed. This software uses a modified generalized delta rule with an adaptive momentum term for its learning mechanism and has a dynamic network topology capability. Through experiments and numerical simulations, it is shown that the neurocontroller is far more effective in compensating for actuator dynamics and time delay than the conventional feedforward controller. Factors contributing to the superior performance of the neurocontroller are identified and discussed.

This paper represents the first part of a two-part study devoted to the theory and application of $H_{\infty }$ state feedback optimal control to civil structures in the presence of actuator limitations and time varying parametric uncertainties. The primary goals when applying optimal control theory to civil structures is the maintenance of stability and the achievement of specific performance criteria, including control efficiency, in the face of random disturbances. Two important issues in achieving these goals are the consideration of nonlinear actuator saturation effects and unknown, time-varying, parametric uncertainties. Most importantly both of these issues must be addressed concomitantly within the same control design. Robust $H_{\infty }$ state feedback controllers are developed here that achieve the desired $H_{\infty }$ norm bound while accounting for prespecified bounds on the time-varying parametric uncertainties. Stability of these controllers in the presence of nonlinear actuator saturation can be proven through the construction of a Lyapunov function for the saturated control system using a nonlinear state space model and new mathematical programming techniques. Application of these newly developed algorithms to an actively controlled 33‐story structure in Tokyo is discussed in part 2 of this study.

This research applies the robust $H_{\infty }$ state feedback control theory developed in Part 1 to the 33-story Riverside Sumida Central Tower, designed and constructed by Obayashi Corporation and located in Tokyo, Japan. Two active mass dampers (AMDs), located on the roof of this structure, are capable of controlling the vibrations due to mild disturbances. This investigation develops robust $H_{\infty }$ controllers for these AMDs that account for structural uncertainty and actuator saturation. Several $H_{\infty }$ controllers are created and the tradeoffs between robust, worst-case closed-loop system performance and predicted peak actuator effort are illustrated. For the structure/control model used in this investigation, the robust $H_{\infty }$ controllers are more effective than traditionally designed LQR controllers at attenuating transient vibrations of the structure when subjected to small magnitude loadings. However, this effectiveness comes at the expense of larger required control efforts. For large magnitude inputs, and nonlinear time-varying systems the $H_{\infty }$ controllers outperform the LQR design, and are limited only by the actuator capacity in their effectiveness.

A pseudo three-dimensional (3D), time-dependent hydrodynamic flow model is developed to simulate flood flows at the confluence of Buffalo and White Oak Bayous in Houston, Texas. This model solves Reynolds-averaged Navier-Stokes equations in a curvilinear coordinate system. A simplified moving-boundary algorithm was also incorporated in the model to determine the moving-fluid domain. The 3D velocity field and free-surface elevation at this interconnected bayou system were computed. Numerical simulations were conducted for both existing and proposed channel geometries. Evaluation of the velocity change due to the proposed channel improvements was studied. The effects of the bayou bathymetry and existing structures on the flow field are also discussed.

An electrorheological (ER) fluid damper suitable for vibration and seismic protection of civil structures has been designed, constructed, and tested. The damper consists of a main cylinder and a piston rod that pushes an ER fluid through a stationary annular duct. The behavior of the damper can be approximated with Hagen-Poiseille flow theory. Under the presence of electric field, the ER fluid exhibits a finite yield stress of the order of 1.8 kPa at 3 kV/mm and manifests some elastic behavior before yielding. An elastic-viscoplastic law is proposed that predicts satisfactorily the fluid behavior obtained from viscometric tests at different frequencies. The contribution from the elasticity of the fluid is insignificant to the global response of the damper at the flow rates of interest, and it is shown that the damper response can be satisfactorily predicted with a simple rigid-viscoplastic law. Experimental results on the damper response with and without the presence of electric field are presented. As the rate of deformation increases viscous stresses prevail over yield stresses and a smaller fraction of the total damper force can be controlled. Some design recommendations on ER dampers for seismic protection applications are provided.

Model uncertainty, if ignored, can seriously degrade the performance of an otherwise well-designed control system. If the level of this uncertainty is extreme, the system may even be driven to instability. In the context of structural control, performance degradation and instability imply excessive vibration or even structural failure. Robust control has typically been applied to the issue of model uncertainty through worst-case analyses. These traditional methods include the use of the structured singular value, as applied to the small gain condition, to provide estimates of controller robustness. However, this emphasis on the worst-case scenario has not allowed a probabilistic understanding of robust control. In this paper an attempt to view controller robustness as a probability measure is presented. The probability of failure due to parametric uncertainty is estimated using first-order reliability methods (FORM). It is demonstrated that FORM can provide quite accurate results on the probability of failure of actively controlled structures. Moreover, a comparison of FORM to a suitably modified structured singular value robustness analysis in a probabilistic framework is performed. It is shown that FORM is the superior analysis technique when applied to the class of problems discussed. In addition, the robustness qualities of various active control design schemes such as the linear quadratic regulator (LQR), H₂ , H_∞ , and μ-synthesis are discussed in order to provide some design guidelines.

Based on a new expression for the work done due to buckling, a computationally efficient method is presented for the lateral distortional buckling of monosymmetric beams. The method requires a knowledge of the stress distribution in the beam. For a simply supported monosymmetric beam subjected to a concentrated vertical load, a simplified stress distribution is assumed and the Rayleigh-Ritz method is used to analyze the lateral distortional buckling behavior. When distortion of the web is suppressed, the present approach agrees with the classical energy methods. However, for short beams and for concentrated loads, web distortion becomes important and the classical methods seriously overestimate the critical load. Other methods that have allowed for web distortion have been limited to end moments (or a cantilever), whereas this method can deal with any type of load including concentrated loads. The accuracy of the method is verified by results obtained from ABAQUS.