Journal of Engineering Mechanics

In the analysis of artificial ground freezing problems, one encounters the domains of interest extending to infinity. A conventional finite element method deals with these problems by extending the mesh to some considerable distance away from the zone of interest and applying a fixed boundary condition there. This method requires a large number of nodal points in modeling the remote region where the perturbation in the variable of interest is virtually zero. Consequently, the cost of numerical analysis increases. The purpose here is to show how the infinite boundary can be treated within the finite element method by developing infinite elements that can be incorporated into standard finite element programs. The proposed method results in appreciable savings in the computer storage and cost of the analysis. The infinite elements employed possess semi‐infinite domain with properly selected decaying shape functions.

Random variation of environmental humidity is characterized by its power spectrum, and random variation of pore humidity and stresses in a half‐space is analyzed under the assumption that the problem is linear (or linearized). The diffusion equation and the superposition integral for stress relaxation are used. The dependence of both the creep properties and the drying diffusivity on age is taken into account. Complex variable expressions for the frequency response functions of humidity and stress are obtained and are evaluated numerically. In contrast to nonaging structures, these functions depend on both the current age of concrete and the age when drying starts. The standard deviations of pore humidity and of stress exhibit oscillations about a drifting mean. For typical diffusivities of concrete, the solution is nonstationary for at least 5O yr, and for environmental fluctuations whose period does not exceed one year, the fluctuations are not felt at depths over 20 cm below the surface. Since, even for aging structures, the spectral densities of input and response are related algebraically, the spectral method is computationally more efficient than the impulse response function method, in which the autocorrelation functions of the input and the response are related by integrals.

A constitutive law for concrete under monotonic biaxial loading up to peak stress is presented in the form of a total, explicit relation between stresses and strains. Explicitness is achieved by expressing the bulk and shear moduli of elasticity as nonlinear functions of the first two invariants of the strain tensor. Since in the plane‐stress states the transversal deformation, which appears as principal strain component in the definition of these invariants, is different from zero, it must be eliminated in order to obtain a biaxial formulation. This, in general, would require the solution of a nonlinear implicit equation; but explicitness has been preserved by finding an empirical, but very accurate, expression of the transversal component of strain as a function of the in‐plane principal components. The resulting stress‐strain relation depends only on three parameters, which characterize the concrete, initial elastic moduli, and compressive strength. Its use is very simple and leads to accurate predictions of the experimental results even close to the peak stress, where inelastic dilatancy occurs.

A finite deformation formulation for dynamic analysis of cable nets is presented. Lagrangian coordinates and Piola‐Kirchhoff stresses are used and elasto‐plastic material behavior is considered. Under assumption of straight cable elements and a displacement field varying linearly along the element, global equations of motion are established by referring the displacements to an initial configuration. These equations are linearized for iterative computation of the equilibrium configuration and for determining the eigenfrequencies and mode shapes of the linear vibration of the net about its equilibrium configuration. This analysis is performed by means of a computer program that can analyze nets anchored in fixed points. Slackness of cable elements is allowed. Three application examples are presented for linear elastic material behavior, showing a good agreement with experimental and computed published data.

A turbulence model is used to study the behavior of plane buoyant jets before the point of neutral buoyancy in stably linear stratified environments. The calculation of the center line velocity, density, turbulent kinetic energy, half‐width of buoyant jets, and the profiles of turbulent kinetic energy, turbulent dissipation function, turbulent shear stress and turbulent heat flux are made for a wide range of exit densimetric Froude numbers and ambient temperature stratifications. A unified scaling law is derived for normalization of these results. The correlation of the predicted results shows that the established zone of buoyant jet in the stably linear stratified environment may be divided into three regions: nonbuoyant region, intermediate region, and plume region. The variation of center line velocity, density and turbulent kinetic energy, and the spread of velocity half‐width along the axial line for both uniform and linearly stratified environments for a given exit densimetric Froude number is found to converge to a single curve under the unified scaling law. The profiles of mean velocity, mean temperature, and turbulent transport properties are given.

Cylindrical web panels of horizontally curved plate girders subjected to pure bending and combined bending and shear are analyzed on the basis of Washizu's nonlinear theory of thin shells. A set of nonlinear differential equations is solved by the use of finite difference method. Nonlinear properties of the deflection and the distributions of various stresses are investigated from the numerical results. Furthermore, the results obtained by this analysis are compared with those given by Culver et al.

The effects of an inclusion on the dynamic response of a shear wall foundation system subjected to plane harmonic SH‐waves are investigated. The inclusion and foundation are modeled as having circular and semicircular cross sections, respectively. A closed form solution for the inclusion‐soil‐foundation interaction problem is obtained by the method of wave functions expansion. The image technique is employed to account for the reflection of waves at the ground surface. The numerical studies carried out indicate that the response of the foundation and the shear wall are influenced by both the size and location of the inclusion, especially in the low frequency range. On the contrary, for any inclusion location, the direction of excitation has greater influence on the response of the system at higher frequencies. It is also observed that the effect of the inclusion on the system response decreases with an increase in the mass of the shear wall.

An open‐loop active control mechanism is proposed to restrain the dynamical effect for machinery foundation. The active control mechanism is presented and the foundation reaction considering the active control mechanism is formulated. The design of the active control mechanism to eliminate the dynamical effect at the foundations is reviewed.

The structural reliability theory encounters the difficult problem of assessing the probability that a random vector process crosses out of a given safe domain within a given time interval. For stationary vector processes, a way of calculating an optimal lower bound is demonstrated. The method is illustrated on examples of scalar Gaussian processes. For small outcrossing probabilities, the lower bounds are quite close to the well‐known upper bounds based on the mean outcrossing rate. The comparison with some general asymptotic results valid for stationary Gaussian processes and the comparison with the only known exact result (due to Slepian) valid for a particular Gaussian process reveal some peculiar problems of evaluating the outcrossing probability for Gaussian processes with an infinite mean outcrossing rate. These types of processes seem questionable as civil engineering models when directly used in a threshold crossing failure criterion without first being passed through a suitable smoothing filter.

Series systems with correlated random safety margins distributed according to the normal distribution play an important role in recent developments of methods of structural reliability theory. These methods require calculation of values of n‐dimensional normal distribution functions. The paper points at a surprisingly accurate rule of thumb calculation method based on a modified second order Taylor expansion in terms of the correlation coefficients and with equicorrelation as expansion point. The equieorrelation coefficient to be used in the method is determined such that the first differential of the distribution function vanishes. The modification is simply to omit the coefficient 1/2 on the second differential in the expansion.

Uncertainties in dynamic soil‐structure interaction are divided into two groups: Model and parameter uncertainties. Modeling uncertainties are associated with the differences between the real world phenomenon and the model, and parameter uncertainties are uncertainties in the parameters which appear in the model definition. A method to evaluate the effect of parameter uncertainties on the dynamic response of a soil‐structure system is described and illustrated. The method is based on the response surface methodology and is fully compatible with current numerical modeling codes (computer programs) used to analyze dynamic soil‐structure interaction. It consists of the development of a graduating function which approximates the true response, based on a limited number of code evaluations. The graduating function, called the response surface, is then used to evaluate the effects of uncertainties in place of the soil‐structure interaction code. The method embodies the traditional parametric or sensitivity analysis techniques and can be considered an extension of the partial derivative method or first‐order, second‐moment method to the numerical realm.