Journal of Engineering Mechanics

A comprehensive analysis is presented for the galloping of an oscillator that may vibrate both transversely and torsionally. Explicit solutions are given for the conditions needed to initiate galloping and also for the ensuing nonlinear periodic responses. Internal resonance as well as previously considered nonresonance responses are treated consistently by employing an averaging method. The usefulness and advantages of the analytical formulation are demonstrated by using square prismatic and bluff structural angle sections. Analytical predictions are verified by their close agreement with numerically integrated data from the original equations of motion. A variety of responses is shown to be possible for certain parameters. Moreover, it is demonstrated that the twist can be instrumental to galloping in plunge.

The stiffness of shallow foundations on homogeneous soil layers can be predicted by means of an in‐situ model test and a scaling rule. In this paper, the existing scaling rules are reviewed first. Then a scaling rule is developed on the basis of a constitutive model for frictional materials. The material behavior is categorized by two characteristic stiffnesses: deviatoric loading and isotropic compression. The parameter in the scaling rule can be determined on the basis of either a series of drained triaxial tests or a series of in‐situ‐plate‐loading tests. Both approaches are verified experimentally. The practical relevance of the scaling rule is illustrated by an example. For a scale factor of 10, the dependence of both characteristic stiffnesses on the magnitude of the isotropic stress can cause errors in the predicted settlement of a factor of two. For an accurate determination of the foundation stiffness at small load levels, a large‐diameter model plate is required, and special attention must be given to the contact between the plate and the soil.

A method is developed for estimating and bounding the probability of failure of Daniels systems with brittle fibers of random resistances that are subject to quasistatic or dynamic nonstationary Gaussian load processes. A simple local load‐sharing rule is considered in the analysis to model stress concentrations occurring in the vicinity of failed fibers. The system can have numerous failure paths, depending on the number of fibers, probabilistic characteristics of fiber resistances, and the local load‐sharing rule. Concepts of system reliability are employed to develop bounds of various degrees of accuracy on the reliability of Daniels systems. Random vibration techniques, results of the extreme theory of stochastic processes, and a generalized Slepian model are also used in the developments of the paper. Theoretical findings are illustrated by reliability analysis of Daniels systems with three and four fibers subjected to quasi‐static nonstationary Gaussian loads. Results sugggest that even the simplest bounds can provide a conservative estimate for the reliability of Daniels systems.

This paper presents a unified solution procedure to analyze the load transfer from a partially embedded long (finite) cylindrical elastic bar into a transversely isotropic elastic half‐space. The bar may be subjected to a torque, an axial force, a horizontal force, or a bending moment at the top end. The solution approach is different from that proposed by Muki and Sternberg (1970). It is based on the interaction between a one‐dimensional elastic bar and a three‐dimensional elastic half‐space with a cylindrical cavity. The displacement compatibility is achieved along the contact surface between the bar and the half‐space. A variational technique coupled with a boundary integral equation scheme based on a set of exact Green's functions is used in the analysis. The boundary conditions at the top end of the bar are incorporated into the variational formulation through a set of Lagrange multipliers. Selected numerical results are presented for elastic bars embedded in some representative transversely isotropic media.

An adjoint approach for the shape design sensitivity analysis of plane elasticity problems with a direct boundary integral equation formulation is presented. The objective function or the constraint function is expressed in an integral form and augmented by incorporating the elasticity equations via adjoint functions. The variation of the augmented function is taken by performing its material derivative to obtain the sensitivity of the objective function or the constraint function. The adjoint functions are obtained through the solution of the adjoint problem resulting from setting the local variations of the displacement, velocity, and traction fields equal to zero. An approximate procedure for the application of concentrated adjoint load in the boundary element framework is suggested. This allows the computation of displacement, traction, and stress sensitivities at discrete nodal points. The requirement of choosing an averaging characteristic function in earlier formulations is obviated by this development. The present formulation includes the treatment of body forces in sensitivity calculations. A series of numerical examples is solved to demonstrate the validity of the present approach.

The ovaling behavior of a ring‐stiffened thin‐walled cylinder subjected to a static circumferentially varying pressure load is explained, and some useful approximate solutions are obtained. The important effects due to the presence of ring stiffeners are: (1) The load transferred to the stiffeners by the shell; and (2) the ovaling‐induced membrane axial and shear stresses in the shell. The load transfer to the ring stiffeners is expressed in terms of a tributary load width. The membrane axial stress is expressed by means of an ovaling stress ratio that compares the axial stress to the circumferential flexural stress that would exist in the absence of the stiffeners. A single parameter, $C_{n}L/a\sqrt{h/a}\text{,}$ classifies the ovaling behavior as that of a short, intermediate, or long shell, where $C_n$ is a number that depends on load harmonic n, and $L/a\sqrt{h/a}$ is a nondimensional shell length. The limiting values of tributary load width and ovaling stress ratio that are approached in the short and long shell limits are functions of an additional parameter, the nondimensional ring flexibility F. Simple analytical approximations are derived for these limiting cases. The axial ovaling stress has added significance when the shell has lower strength in the axial direction than in the hoop direction, such as in filament‐wound composite shells. The results presented are for elastically isotropic shells, but they can be easily extended to orfhotropic elastic properties.

Granular material perceived as a collection of particles is modeled as a macrocontinuum. The model takes into account the effects of microdiscreteness and the interparticle contact properties in the system. With consideration of particle rotation, the continuum model for granular solid is found to be of micropolar type. The derived constitutive law of the material includes variables of Cauchy stress, polar stress, deformation strain, and polar strain. Considering the effect of particle interaction, the stresses are defined in terms of interparticle contact forces and contact couples. The constitutive coefficients are derived explicitly in terms of the interparticle contact stiffness. Using the derived stress‐strain relationships, a solution procedure based on variational principle is applied to obtain solutions for boundary value problems. Examples of boundary value problems are shown for particle assemblies with elastic contact interaction. The results are compared with those obtained from a discrete element method to demonstrate the applicability of this method.

A solution is derived for the elastic problem of two bonded dissimilar planes. The bonded planes are symmetric with respect to the interface, which is straight. A rational mapping function and complex stress functions are used for the analysis. The problem is reduced to a Riemann‐Hilbert problem. Elastic constants of the solution is expressed by Dundur's parameters. The first derivative of the loading term is obtained as a closed form, which does not include an integral term. Therefore, there is no need of a numerical integration to obtain components of stress. As an example, the analysis is carried out for bonded half‐planes subjected to concentrated couples at infinities and with cracks at an end of the finite interface. Stress distributions before and after initiation of the crack are investigated. Stress‐intensity factors are investigated for some elastic constants. In particularly stress‐intensity factors for short cracks are obtained, and it is also investigated that a crack initiates at either material.

The results of experiments in open channels and closed pipelines show two kinds of patterns for the vertical distribution of particle concentration (i.e., pattern I and pattern II). The former shows a pattern of maximum concentration at some location above the bottom and the downward decay of the concentration below the location. The latter always shows an increase of the particle concentration downward over the whole vertical, with the maximum value at the bottom. Many investigations were made on the pattern II, but few were made on pattern I. In this paper, a particle velocity distribution function is first obtained in the equilibrium state or in dilute steady state for the particle in two‐phase flows, then a theoretical model for the particle concentration distribution is derived from the kinetic theory. More attention is paid to the predictions of the concentration distribution of pattern I and comparisons of the present model are made with the data measured by means of laser doppler anemometry (LDA). Very good agreements are obtained between the measured and calculated results.

An analytical model is proposed to describe the interfacial sliding characteristics of Teflon and stainless steel based on experimentally observed quasi‐static and dynamic sliding characteristics. The effects of normal pressure, sliding distance, normal pressure history, sliding velocity, sliding velocity history, normal pressure rate, sliding work, etc., are included. The dependence of the dynamic friction force on both the normal pressure and the sliding velocity is uncoupled in this formulation. The dynamic friction force is determined by multiplying the quasi‐static friction force by an amplification factor. The amplification factor is a pure function of sliding velocity. The proposed model is validated by a quasi‐static test and a dynamic sliding test. In the quasi‐static verification test, the applied normal contact pressures are changing during sliding. For the dynamic validation test, the Teflon‐stainless‐steel interfaces are subjected to varied normal pressures and sliding velocities. Very good agreement between the predicted and the experimental results is obtained.

The present work analyzes the implication and limitation of some scalar damage models. In particular, the elastic‐damage thermodynamic potential and the effective stress concept are reexamined. It is demonstrated that isotropic damage does not necessarily imply scalar damage representation in general. The notion of isotropic and anisotropic damage variables in continuum damage mechanics is then discussed. In addition, some results from micromechanical analyses are applied to show the direct relationship between the fourth‐order damage tensor and the damage‐induced compliance tensor characteristic of microcrack‐weakened brittle materials. It is shown that even for isotropic damage one should employ an isotropic fourth‐order damage tensor (not a scalar damage variable) to characterize the state of damage in materials, in accordance with the effective stress concept. In general, however, a damage tensor is anisotropic and should be derived from micromechanical analysis when possible.

Elastic-plastic foams are commonly used in engineering practice in the core of structural sandwich members and in energy absorption devices dissipating the kinetic energy of an impact without generating high stresses. Due to complexities involved in both the geometry and the loads, the analysis often requires a complete material constitutive model. Studies of the postyield constitutive modeling of foams under multiaxial stresses do not exist. A failure criterion describing the failure surface at the onset of plasticity for open-cell, isotropic foams idealized as linearly elastic–perfectly plastic is employed here in a plasticity-based formulation to obtain the postyield constitutive matrix. The model is valid when the material experiences zero hardening and deforms according to the associated flow rule. The first assumption appears realistic for open-cell foams at small to moderate strains, while the second needs further investigation.

This note shows that the strain energy of a plate suffers a finite jump when the boundary contour of the plate is subject to a change, however small, from a smooth curve to a piecewise linear curve, if either the displacement or the slope, both of which are prescribed, is homogeneous at every point along the plate boundary. The proof is based on an observation that the plate strain energy depends linearly on Poisson's ratio when the lateral load, the boundary displacement and slope are specified. It also makes use of a previous result that the Gaussian curvature term in plate strain energy is a discontinuous functional of the boundary contour, and extends the theorem to that of the plate strain energy itself. This note suggests that this singular behavior may result from a discontinuous dependency of the solution to plate equation on small changes of the domain of existence.

A modification is proposed for the widely used Baz˘ant age-adjusted effective modulus method (AEMM) based on the generalized Baz˘ant theorem. The modified method is a numerical approximation procedure for calculating stresses and deformations in structures subject to creep, which accounts for the loading history of the structure. By applying this method to the case of time-dependent loads, it is possible to obtain exact solutions for homogeneous structures and approximate solutins for nonhomogeneous structures. The modified AEMM reduces to the usual AEMM for the case of instantaneously applied time-independent loads.