Journal of Engineering Mechanics

A direct continuum approach for shape‐design sensitivity of three‐dimensional elastic components is presented. By analyzing the shape‐design perturbation process, the shape change can be represented by a boundary loading on the design boundary. Therefore, the design sensitivity can be obtained by solving a boundary‐value problem, which has an identical geometry with the original problem, but with different loads. This approach does not involve the perturbed geometry, and is independent of the perturbation step. The total design sensitivity is obtained by using the material derivative concept. The direct continuum approach is implemented using the boundary‐element method, and the terms corresponding to the stress variation on the design boundary are expressed using the boundary information only. Three numerical examples are used to study the accuracy of the approach with respect to different boundary‐element meshes. The numerical results indicate that the direct continuum approach can provide good sensitivity results, and a proper mesh distribution on the design boundary is essential for sensitivity analysis.

An algorithm to calculate optimal direct output feedback gain is developed in a simple fashion such that a certain prescribed performance index is minimized. With the introduction of a special matrix operation, optimal feedback gain is obtained systematically by solving simultaneously linear algebraic equations iteratively. Control forces are then calculated from the multiplication of output measurements by a time‐invariant feedback gain matrix. Numerical verification is illustrated through the control of single‐degree‐of‐freedom and three‐degree‐of‐freedom structures subjected to real earthquake excitation. It is shown that the number of sensors and controllers may be very small compared with the dimension of states. A small number of sensors and controllers, and simple on‐line calculation, make the proposed control algorithm favorable to real implementation. Since the full‐order mathematical model of the structure is considered throughout the derivation, the spillover effect in control and observation due to modal control is eliminated. Hence, if the structure is well described by the mathematical model, system stability is guaranteed. Finally, the optimal allocation pattern of sensor and controller is suggested.

The load carrying capacity of a rectangular section is investigated. Using Hencky's total strain theory, interaction relations between axial force, shear and bending moment are obtained for an elastic‐linear strain hardening material. A unified set of equations are presented which can be reduced for any combination of forces and any simpler modeling of materials, including the elastic‐perfectly plastic material. Although the results are generally limited to proportional loading, the accuracy is quite acceptable in most cases, as long as all the applied loads increase monotonically in a quasi‐proportional manner. As a demonstration of the possible broader usage of the derived equations, beam columns under combined loading are examined using the existing approximate beam‐column theory. The results indicate that strain hardening is important in certain situations, particularly when the beam is bulkier. The same principle can be applied to other types of structural sections such as I‐beams.

Considering the difference in the bond behavior between the ordinary reinforcement and the tendons, which are placed in grouted ducts, first a differential equation is formulated to describe the relationship between slip and strains of steels and concrete in prestressed concrete members. In the second step a numerical method is developed to solve the differential‐equation system for single cracks and stabilized crack patterns. The method is based on the application of Runge‐Kutta method for the numerical integration and on the Newton method for the optimization of the vector function. The method presented here allows the calculation of crack width, the stiffness, and the redistribution of stresses between ordinary reinforcement and tendon in prestressed concrete members. An example is provided demonstrating the practical applicability of the method. The presented method is also suitable for reinforced concrete.

The stability analysis of natural draught cooling tower shell subjected to nonaxisymmetric wind pressure has been carried out using finite ring elements. In this investigation, concept of a local enhancement of wind pressure coefficients at the top—in addition to the usual variation of wind pressures with height—has been newly introduced. Justification for the use of such modified wind pressure coefficients has been presented. By considering the modified distribution of wind pressure coefficients, a parametric study has also been carried out to assess the influence of top ring stiffener, gradual thickening at shell bottom edge, and vertical cracking due to thermal gradient on the buckling behavior of natural draught cooling tower shells. Guidelines are furnished for choosing dimensions of the top ring stiffener to avoid top edge buckling.

A cluster of interconnected plane bodies is treated as a discrete system, and each body is considered as an irregularly shaped disk modeled by a system of circular disks bound together by finite bonding forces. The motion of interconnected bodies is governed by the system of differential and algebraic equations in which the differential part is associated with the topological tree and the algebraic one with the constraints imposed by the loops. For an arbitrary topology explicit expressions for the equations of motion are derived based on the Lagrangian approach. The equations are given in terms of the path matrix characterizing the topological tree. The analytical method of generation of equations of motion makes the computer simulation of the nonsteady motion of the discrete system of plane bodies more efficient in terms of both computer time and accuracy. It is achieved by avoiding operations with large sparse matrices (if the equations are generated numerically) and by canceling out some terms in Lagrange's equations analytically.

A half‐plane flat crack in a transversely isotropic elastic space subjected to arbitrary normal load is considered. An exact closed‐form solution is obtained in terms of elementary functions to the complete field of stresses and displacements in the whole space due to a point force loading. Both transversely isotropic and purely isotropic cases are considered. The solution is based on the results previously reported by the first writer. The transversely isotropic solution does not seem to have been reported in the literature. The isotropic case was considered by Ufliand who used the integral transform approach. A comparison with his results shows exact correspondence. Explicit formulas are also given for the stress intensity factor, as well as for the stresses and displacements in the plane of the crack.

The classical viscoelastic models for aging materials such as concrete, which consist of Volterra history‐integral equations, found only limited applications since they required storing the entire stress or strain history. Although the subsequent introduction of the Dirichlet series expansion of the creep or relaxation function reduces these requirements by leading to a set of linear differential equations equivalent to aging Kelvin or Maxwell chain models, problems arose in the identification of the aging moduli of these models. This paper refines and extends a recent formulation that remedies these problems by considering the aging to result from the progressive solidification of a basic constituent that behaves as a nonaging viscoelastic material. The new possibilities explored involve the alternative use of the relaxation function for characterizing the nonaging constituent, and the expansion of both the compliance and relaxation functions of the constituent into Dirichlet series. In this way, one recovers the rate‐type equations of an aging Kelvin or Maxwell chain in which all the moduli vary proportionally to a single aging function $v\left(t\right)$. Some convenient advantages are the well‐posedness of the problem of moduli identification, with always positive values, and the nonexistence of creep or relaxation reversal upon load removal.

Vortex‐induced response of a spring‐mounted circular cylinder was observed in a low‐speed wind tunnel. Vertical (lift) displacement of the cylinder and velocity fluctuations in the near wake region of the upper shear layer were recorded. The experiments were designed to provide insight into the effects of various control variables upon the evolution of vortex shedding and vortex‐induced vibration. Included in this study are the effects of homogeneous, isotropic turbulence in the incident flow, variation of mechanical damping, artificially fixed separation points on cylinder surface and different initial conditions for cylinder vibration. Also, in addition to the observation of the phenomenon of classical synchronization, manifestations of what may be termed “alternate synchronization” were also observed and recorded. This paper presents some of the new data in detail. The results from the analytical modeling effort are presented in the companion paper.

The analytical work presented in this paper closely follows the data obtained from new experiments on vortex‐induced vibration of circular cylinders in air. The experimental data are presented in the companion paper preceding in the journal. The vortex‐induced vibration of a flexibly supported circular cylinder is modeled by a new single‐degree‐of‐freedom model with velocity‐dependent coefficients. The model is of the ordinary differential equation type with a self‐excited, self‐limiting van der Pol‐type aeroelastic damping pair and an aeroelastic parametric excitation term. The latter term is the innovative addition in the current model. The development of the model equations is outlined, following which it is analyzed and its parameters estimated in conjunction with the data from experiments reported in the companion paper. The model and its parameters have been rendered dimensionless in the analysis, to facilitate universal applicability.

The characterization of the exact response of an acoustic emission sensor is of fundamental importance for the quantitative nondestructive evaluation of engineering components. To effectively determine an acoustic emission source, the influence of the sensor on the measured waveform must be determined. A heterodyne interferometer is developed and tested for the detection of acoustic emission signals. This optical device makes localized absolute measurements of out‐of‐plane surface velocities with very high fidelity. An important feature of this system is that a linear frequency modulation (FM) discriminator is used to demodulate the carrier signal; as a result, the interferometer behaves as a Doppler‐shift detector. A series of experiments was performed to test the response of commercially available, piezoelectric acoustic emission transducers in order to understand their potential influence on a measured acoustic emission waveform.

This paper presents an experimental and analytical study of hybrid control of bridges using sliding bearings, with recentering springs, in parallel with servohydraulic actuators. A new control algorithm with absolute acceleration feedback, based on instantaneous optimal control laws, is developed. The developed control algorithm is implemented in a shake‐table study of an actively controlled sliding‐isolated bridge. The objective of implementing the hybrid system is to evaluate its advantages in addition to those due to the passive sliding system. The experimental system used in the shake‐table test is described and the results of the experiments are presented. It is shown that substantial reduction of response acceleration is possible, using hybrid control, while confining the sliding displacement within an acceptable range, and eliminating almost completely postearthquake permanent offsets. Comparisons of the results of hybrid system with results of passive system are presented. The advantages of hybrid control, in addition to those due to passive control, are discussed.

Methodology is presented for simulating properly correlated earthquake ground motions at an arbitrary set of closely spaced points, compatible with known or prescribed motions at other locations. The input consists of the spectral density function and frequency‐dependent spatial correlation function in several nonoverlapping ground‐motion segments. Linear‐prediction estimators are used to generate a set of statistically independent, frequency‐specific, spatial random processes, based on which ground motions are composed by means of a fast‐Fourier‐transform algorithm. The method's advantage over existing linear‐estimation techniques, known as kriging, is that it correctly reproduces the specified space‐time correlation structure of the ground motion. Examples are given to illustrate the features of the simulation methodology; in particular, response spectra and dynamic response ratios are compared for recorded and simulated motions at the site of the SMART 1 strong‐motion accelerograph array.

This technical note concerns the estimation of the outcrossing rate of nonstationary Gaussian vector processes from a convex polyhedral limit-state surface enclosing the origin. The theoretically most attractive approach for this type of problem in time-dependent structural reliability analysis is to employ the concept of first-passage probability in stochastic-process theory. Because the use of the generalized Rice formula poses some difficulty, the outcrossing problem is formulated in another way; i.e., using the original Rice formula directly. This situation allows the multidimensional integral to be reduced to a one-dimensional integral. This then allows the formulation (which applies also to smooth nonstationary processes) to be extended to time-dependent domain boundaries. An example is given to illustrate the method.