Journal of Engineering Mechanics

Extensive wind‐tunnel tests are performed to investigate the mutual interference between neighboring tall square buildings with different sizes and breadths in a highly turbulent shear layer over an urban area. The effect of turbulence on the interference excitation is also examined, and it is compared to other results under a relatively low turbulence flow. Neither the along‐wind nor the cross‐wind response of the object building is significantly altered by the presence of an upstream building of any size within the highly turbulent flow except when an interfering slender building is located in the immediate upstream of the object building. The relative changes in responses with and without interference, i.e., the buffeting factors in each direction, decrease exponentially with the increase in turbulence, and reduce to around 1 when the turbulence intensities are increased up to 17–18%. That is, the dynamic responses in the downstream building are independent of the mutual interference effect and nearly equal to those in the isolated building.

The computation of multivariate integrals is an important mathematical problem in reliability theory. Various approximation methods have been developed for this task. In the so‐called FORM and SORM methods, it is assumed that all variables have been transformed into independent standard normal ones. Only then can the methods be applied. Here, it is shown that such transformations are not necessary. It is sufficient to maximize the log likelihood function of the probability distribution in the original space, then to approximate the function and limit‐state function near the maximum points by second‐order Taylor expansions to obtain asymptotic approximations. In the same way, asymptotic sensitivity factors for the parameter dependence of the failure probability can be found. The advantages of this method are that the often‐complicated numerical transformation into the normal space is avoided and that the results have a natural interpretation in terms of the parameters of the original random variables and limit‐state function.

An unbounded homogeneous transversely isotropic body of revolution containing two twin spheroidal cavities is subjected to a torsional loading at infinity. The axis of twist coincides with the axis of elastic symmetry of the material and the axis of revolution of the body. The linear elasticity solution is obtained in series form by employing the Lekhnitskii stress function approach, and numerical results are presented for the case of two spherical cavities perturbing the Saint‐Venant torsion field for a circular cylinder. Of particular interest is the influence of cavity spacing and material constants on the degree of stress interference between the two perturbations.

An experimental investigation is conducted to study dynamic load transfer in granular rock media. The granular rock media is modeled as a one‐dimensional chain of disks fabricated from four different types of white Vermont marble. The study focuses on the effect of microstructure on transient pulse propagation. The transient pulse is generated by exploding a small amount of lead azide charge on top of the rock disk assembly. During wave propagation dynamic contact strains are recorded using electrical resistance strain gages. The location of the strain gages is chosen such that the averaging effects are minimized. This information is used to calculate wave velocity and attenuation as a function of the cumulative damage in the disk assembly. The results indicate a considerable influence of the microstructure and prior loading history on the wave propagation process. A correlation exists between the stress wave velocity and the microstructure of the rock material. Also the wave velocity increases initially and then decreases with repeated explosive loading.

The wake characteristics of constrained, cavitating two‐dimensional bluff bodies are studied over a large range of blockage. Prismatic sources with fixed separating points are chosen to reduce or eliminate Reynolds number effects. The effect of blockage on the geometrical characteristics of the wake such as the length and width of cavity are obtained. The frequency of cavity pressure pulsations, the pressure histograms, and the mean static pressure distributions along the wake axis are also determined at various cavitating conditions. Efforts are made to obtain the proper velocity and length scales to form the Strouhal numbers to absorb blockage effects. At very large blockages, the generation of small eddies in the shear layers accompanied by a reduction or elimination of Karman vortex street is noticed. Limited studies related to the wake characteristics of a circular source at a moderate blockage of 33% are also reported.

A procedure is presented for analysis of earthquake response of concrete arch dams to nonuniform motion of the canyon walls. A dam is modeled by the finite‐element method. The nonuniform, free‐field motion of canyon walls is obtained by solving the two‐dimensional wave equation. The transient, upstream‐downstream (antiplane) motions of the canyon walls induced by plane SH‐waves are illustrated. The response of an idealized arch dam is investigated neglecting the dam‐canyon interaction, and the effects caused by the wave propagation across the canyon. The dam response to the nonuniform canyon accelerations decreases by about 25–30% with respect to the case of excitation by the uniform canyon motion.

The cross‐stream and vertical nonuniform motions of canyon walls caused by body SV‐, P‐, and surface Rayleigh waves are studied. Using a two‐dimensional wave equation, the motion of an irregularly shaped canyon is computed. To illustrate only the basic physical phenomena in the dam response assocated with “closing,” “opening,” and “out of phase” motions of canyon walls, examples of the responses of an idealized arch dam (see companion paper) type 5 to transient SV‐, P‐, and Rayleigh waves are presented. Accelerations and displacements along the canyon walls depend on the frequency and the incidence angle (for SV‐ and P‐waves) of the arriving motions. Many components of the quasi‐static stresses caused by nonuniform canyon displacements are larger than the dynamic stresses induced by nonuniform canyon accelerations. The dynamic stresses can be larger and distributed differently than those caused by the corresponding uniform canyon accelerations.

A new technique for modeling localized deformations within a softening band is described, where softening is attributed to a displacement discontinuity within an element. Concepts such as fracture strain are not included in the formulation of the model, and consequently nonlocal parameters such as internal length measures are not needed. It is shown that the shape functions within the element provide the necessary information normally given with internal length. In this manner, objectivity with regard to element configuration seems to be automatically satisfied, which is demonstrated by numerical studies in which Rankine failure criterion is employed. It is also noted that the displacement field rather than the strain field is additively decomposed into elastic and inelastic parts. This additivity is valid independently of the magnitude of displacement continuity in the softening band, which implies that the technique can be extended in a straight‐forward fashion to finite displacements.

The dynamic response of an orthotropic elastic half plane subjected to a set of time‐harmonic buried loadings is investigated. The governing differential equations are established in terms of displacements and a general solution is derived using Fourier integral transforms with respect to the x‐coordinate. The boundary‐value problems corresponding to time‐harmonic vertical and horizontal loads acting in the interior of the half plane are solved. Explicit analytical solutions are presented for displacements and stresses due to buried uniformly distributed and concentrated loadings. Some characteristics of the analytical solution are investigated, and its numerical evaluation is also discussed. Selected numerical results for displacements and stresses of isotropic, ice, layered soil, and cadmium half‐plane regions are presented. A discussion of these numerical solutions is presented to investigate the influence of the degree of material anisotropy, frequency of excitation, and the type of loading on the response of the elastic half plane.

In this paper, we consider the stress distribution in adhesive‐bonded, single‐lap joints under tension, for which the two adherends could have different thicknesses and lengths and consist of different materials. Hence, we consider herein an analysis that is more general than those in the literature. Two‐dimensional elasticity theory, in conjunction with the variational principle of complementary energy, is used in determining the stresses in the joint. All boundary stress conditions of the joint are strictly satisfied. Since high stress intensities occur in the end zones of the joint, the satisfaction of stress‐free end conditions of the joint is important. By means of the present approach, closed‐form solutions—which are adaptable for any possible adhesive‐layer conditions, flexible, inflexible, and a medium range of flexibility—are obtained. Numerical examples are provided to illustrate the effects of nonidentical adherends on the distributions and intensities of stresses in the joint. With a given ratio of material properties of the adherends and adhesive, there ought to be a thickness ratio of nonidentical adherends that yields the least stress intensities in the joint.

An anisotropic creep model is formulated for metallic composites with strong fibers and low to moderate fiber volume percent $(<40\%)\text{.}$ The idealization admits no creep in the local fiber direction and assumes equal creep strength in longitudinal and transverse shear. Identification of the matrix behavior with that of the isotropic limit of the theory permits characterization of the composite through uniaxial creep tests on the matrix material. Constant and stepwise creep tests are required as a data base. The model provides an upper bound on the transverse creep strength of a composite having strong fibers embedded in a particular matrix material. Comparison of the measured transverse strength with the upper bound gives an assessment of the integrity of the composite. Application is made to a Kanthal composite, a model high‐temperature composite system. Predictions are made of the creep response of fiber reinforced Kanthal tubes under interior pressure.

The assumption of probabilistic independence is commonly made in engineering analysis to gain mathematical tractability. Although the criteria of the independence of random variables have been presented in many different ways, such as in terms of probability‐distribution functions, mathematical expectations, etc., a criterion in terms of joint cumulants has not yet been properly described. This paper presents the relationship between probabilistic independence and the joint cumulants (i.e. semi‐invariants) of random variables. When a random variable is a linear or nonlinear combination of a number of independent random variables, the calculation for the statistics of this random sum is more convenient using cumulants than central moments or moments. Examples that show the convenience of applying cumulants are presented, including a simple proof for the central limit theorem, the calculation of statistics for the Morison wave force, and the statistics of wave profiles using second‐order stochastic Stake's wave theory. In addition, an example related to the response statistics of linear systems subjected to quadratic Gaussian excitations is presented.

The propagation of microcracks in concrete under compression is studied by the finite element method. To this end, concrete is modeled as a two‐phase composite, consisting of a mortar matrix and aggregate inclusions. Two distinct types of microcrack (mortar crack and bond crack) are considered. To reflect the current stage of development, the principle of nonlinear fracture mechanics and the joint finite elements coupled with the generalized plasticity concept are incorporated into the present analyses. The numerical results thus obtained indicate that the stress state has a very significant influence on the development of mortar cracks; much less influence on the propagation of bond cracks is seen. Combined with well‐known experimental results then, the present study concludes that the deformation of a concrete specimen before peak load should be more uniform than its postpeak deformation and that the hardening behavior of a concrete specimen should be less influenced by loading conditions than the softening behavior. These conclusions provide an explanation of the cause of the characteristic observed behavior of concrete.

A semiexact solution approach is presented to study the static deflection and stability of a general, elastically end‐restrained, nonuniform beam under combined loads. The governing equation is a nonhomogeneous fourth‐order ordinary differential equation with variable coefficients. The Green's function for the static deflection and the characteristic equation for the stability problem are concisely expressed in terms of the four fundamental solutions of the governing equation. These fundamental solutions can be obtained approximately through a simple and efficient numerical algorithm. Of the four typical boundary conditions, when placed under the same distributed axial loads, the critical buckling load of the beam with clamped‐clamped boundary condition increases most rapidly, and the load of the beam with clamped‐free boundary condition increases most slowly. Under the same boundary condition and among the axial loads discussed, the critical buckling load of the beam subjected to linearly distributed follower forces $g_0[1-(x/l\left)\right]$ increases more rapidly than that of the beam subjected to the other types of distributed follower forces, as the breadth taper ratio is increased.

A simple theory using the stiffness concept is presented for linkage-motion analysis. The nonlinear incremental mechanism equations are established and their solution procedure is proposed. The kinematic system is first regarded as an instable elastic structure. The tangent stiffness equations are updated for current mechanism configurations. The obtained singular stiffness matrix is then used to predict incremental nodal displacements. The stress-associated deformation is designated as numerical error. The proposed stiffness method follows successively the mechanism motion in an incremental-iterative manner. Computed numerical examples show that the elastic deformation can easily be removed with a few iterations. The proposed stiffness approach to kinematics may be incorporated into existing finite-element computer program systems and can be applied to general three-dimensional mechanisms.

As the height of a tall building increases, the lateral deflection of the structure caused by lateral loading is amplified by gravity loads, since the latter becomes eccentric. The second-order effect may become significant in slender structures. In recent years, the research on stability of tall buildings has become an important area of study. An ``exact'' analysis for the effect can be made by suitably modified first-order procedures. However, these techniques are a complication for preliminary analysis in the earlier stages of design, where only an approximation of the second-order effect is required.

An elasto-viscoplastic constitutive equation is derived for a lead-tin alloy used in the microelectronics industry. This crystalline material exhibits nonlinear characteristics, such as strain hardening and saturation phenomena, if the applied load is cyclic. The constitutive equations govern the microdeformations undergone by a representative volume of the material during mechanical loading. The model is based on an averaging procedure from the microlevel (grains and grain boundaries) to the overall level, followed by an evolution equation that determines the orientation and extension of the characteristic slip-crack system. The averaging process introduces two fundamental functions related to the current damage and hardening recovery of the material. Properties of the material that are seen on the microlevel (such as microcracks, slip bands, and voids) are incorporated into the analysis by a simple rheological model, made of spring, dashpot, and slider, which allows the overall response of the material to be rate-dependent and to match the experimental data for both tensile and cyclic loadings obtained at different strain rates.