Journal of Engineering Mechanics

A convenient and computationally efficient technique for analyzing the one-dimensional consolidation of periodically layered deposits is developed. This technique involves the use of a Laplace transform and an analytic solution to the governing equations is determined in transformed space. The transform is then inverted numerically. This technique requires minimal computational storage or calculation. The technique is then used to examine the response of periodically layered deposits. Particular emphasis is given to the effects of pumping from an underlying aquifer and to the time required to establish steady state flow from an overlying (possibly polluted) aquifer. The consolidation of deposits with a linear initial excess pore pressure distribution and impermeable or permeable base is also fly examined.

The uncertainty of a continuous variable is estimated by the combination of the objective entropy, which is obtained from the statistics of a countable population, and the fuzzy entropy, which is a measure of imprecision estimated from an engineer's experience and knowledge. This is illustrated by using subjective, imprecise, fuzzy information to update the objective parameters of an initial truncated normal distribution by means of combining Shannon's objective information entropy and fuzzy entropies. The entropies are treated as information measures of uncertainty of both the objective and subjective kinds. Three fuzzy entropy functions are presented and their effects on the altered parameters illustrated.

Recent developments related to the analysis and design of liquid storage tanks are surveyed. Different aspects of the problem are examined. Background for finite element formulation is also outlined. A numerical tank model which accounts for the lateral pressure loading is developed to provide an understanding of this effect on the behavior of liquid storage tanks. This lateral pressure loading is simulated via an equivalent hydrostatic approach in which the follower force effect is accounted. Results show that the tank model collapses at a critical load 20% lower than the classical prediction. It also shows that the axial stress is basically dominated by cos θ mode. Higher order modes, are significant in the hoop stress profile which is nonlinear in character. The observed “elephant-foot buckle” and the “ovalling” response of liquid storage tanks in many tank failures during earthquakes can be predicted with these nonlinear methodologies.

First-passage probabilities are investigated for the absolute value of the zero-start response of 2DF linear oscillators excited by stationary white noise having a normal probability distribution. Only the long-time portion of the response has been studied. Most attention is given to the exponential decay rate of the probability of survival, but some data is also given for the generally less important multiplier of the exponential term. A two-dimensional Markov amplitude model is shown to provide a relatively economical method to supplement and extend the results of a 2DF Monte Carlo simulation. Relatively simple empirical equations are given to approximate the values of the probability of survival for a fairly wide range of situations. These approximations appear to be acceptable when damping is between 1% and 10%, modal frequencies are separated by at least a factor of two, the low frequency mode contributes at least 50% of the response, and the barrier level is at least two times the rms value of the response.

A method of optimal open-loop critical-mode control has been applied to building structures excited by earthquake that is modeled as a nonstationary random process. The time dependent statistics of building response quantities and required active control forces have been presented. Monte Carlo simulations for building response quantities with or without active control systems have been performed to demonstrate the behavior of buildings subject to earthquake excitations. It is shown that a significant reduction for the building response can be achieved by use of active control systems. Furthermore, the required active control forces computed based on the stationary earthquake model are too conservative. A sensitivity study has been carried out to determine the effect of uncertainties involved in estimating structural properties on the results of optimal control. The active tendon control system is not sensitive to the estimation uncertainties for the damping and stiffness of the building. Although the active mass damper system is not sensitive to errors in damping estimation, it is moderately sensitive to the stiffness uncertainty of the building.

Two-parameter elastic foundations are more accurate than a one-parameter (Winkler) foundation and are simpler than semi-infinite elastic continuum foundation models. Two kinds of finite elements are formulated in this paper to analyze beams on one-or two-parameter foundations. Models include Winkler, Filonenko-Borodich, Pasternak, generalized, and Vlasov foundations. One of the two kinds of elements is based on the exact displacement function. The other is based on a cubic displacement function. The stiffness matrix and consistent load vector is derived for each. Numerical tests show that the element based on the exact displacement function can give exact numerical results even if the number of elements is very small. The element based on a cubic function may require a fine mesh to give acceptable results.

The random response of bilinear hysteretic yielding systems subjected to a stationary Gaussian white noise excitation is studied. The responses considered are the root mean square (rms) interfloor displacements of yielding multidegree-of-freedom (MDF) shear beam type building structures. An analytical method to approximate the response levels is presented, as well as fairly extensive simulation results. Nearly elastoplastic 2DF, 4DF, and 10DF systems with small viscous damping are studied. The major trends observed in the simulation results are shown to be basically in agreement with what one would predict from the superposition of a reduction in stiffness of each yielding story and an increase in structural damping. The stiffness reduction varies monotonically with the amount of yielding, while the damping effect is most pronounced at intermediate yield levels. The analytical method used here involves a higher-order linear substitute system and it provides relatively satisfactory approximations of the rms responses. It predicts proper trends, and gives relatively accurate values for the larger distortion values.

Types of aeroelastic and elastic wind tunnel models available for measuring fluctuating wind loads on tall buildings are described together with some of their advantages and limitations. A new technique for using numerous pressure transducers to directly measure these fluctuating wind loads is presented. In this technique, analog circuits are used to sum individual pressure measurements in obtaining records which represent loads over segments of the model or over the entire model. Recent tests using the technique are described and sample results are shown. Forces measured with the transducers on a fixed model are used to predict the response of an aeroelastic model of similar shape, for which response measurements have been published in the literature. It is shown that the predicted and measured response agree within the bounds of expected errors up to values of reduced gradient velocity of approximately 15. At reduced gradient velocities in excess of 15, the fixed model predictions underestimate the aeroelastic model results and the slope of the response curve is quite different because motion of the aeroelastic model alters the aerodynamics.

An eigenvector updating method is proposed to fit modal test data. The calculated eigenvectors are updated by coinciding some of them with the corresponding measured eigenvectors as a result of an orthogonal transformation. The advantage of the method is the applicability to large complex structures without necessity of recomputation of the eigendata.

This paper presents some contributions to the development of the methodology for the evaluation of subjective uncertain factors such as omissions, mistakes, incorrect modeling, construction errors, etc. By using fuzzy sets theory, failure event can be defined in the more flexible form than the usual form. Especially, the concept of fuzzy probability aids to derive a new reliability analysis which includes the subjective assessment of engineers without introducing any additional correction factors. Several numerical examples are presented to illustrate the analytical method developed herein.

The results of experimental investigations comparing the local stability of sandwich plates with variable and constant core densities are presented. The effects of density changes in the cores of the tested sandwich plates are shown. A method of realizing one-directional compression in the plane of the facings is described. Maximal loads carried and light-weight ratios are compared showing that sandwich plates with variable densities through the core thickness are able to carry greater compressive loads, even if they are of the same weight and require the same quantity of material as classical sandwich plates with constant core properties. A comparison of the results of the experimental investigations of sandwich plates having variable core densities with a previously published analytical formula is presented.