Journal of Engineering Mechanics

A numerical analysis using the 3D distinct element method (DEM) is conducted in order to examine the performance of screw conveyors. In particular, the simulation of horizontal and vertical types is studied. The results are compared with previous work and empirical equations. As a result, it is determined that this method is sufficiently well developed and useful to analyze the performance of screw conveyors.

Composites exhibit a considerable amount of variation in their material properties because their fabrication/manufacturing process involves a large number of parameters that cannot be controlled effectively. In the present study, the material properties have been modeled as random variables for better prediction of the system behavior. The classical laminate theory and first-order and higher-order shear deformation theories have been employed in deriving the governing equations for buckling of laminated rectangular plates. A mean-centered first-order perturbation technique has been used to find the second-order statistics of the buckling load. The approach has been validated by comparison with results of Monte Carlo simulation. Typical results have been presented for a plate with all edges simply supported. The effectiveness of the theories in predicting the buckling load dispersions has been examined. The sensitivity of buckling loads to change in the standard deviation of random material properties and to system parameters—side-to-thickness ratio and aspect ratio—has been examined for cross-ply symmetric and antisymmetric laminates.

In engineering practice, rectangular holes (openings) are often encountered. The presence of rectangular holes increases the complexity of the analysis of engineering media (e.g., soils around a diaphragm wall panel) and structural members (e.g., floor slabs). However, there is currently no simple but sufficiently accurate solution readily available for engineers to obtain stress and displacement distributions around an artificial rectangular hole in an elastic plate. This paper presents a simple approximate solution to the problem for an infinite elastic and isotropic plate subjected to uniaxial stress at infinity. A linear elastic plane stress analysis is carried out using complex variables. By introducing a correction factor, simplified and explicitly expressed, a general conformal transformation function that transforms the area outside an arbitrary rectangular hole into the region inside a unit circle is created and used to obtain a solution. The solution is verified by comparing the calculated results using a finite-element method. Displacements caused by the formation of a rectangular hole are investigated. The ease of implementation of the solution is illustrated.

Hysteretic rate-independent constitutive laws are introduced within the framework of continuum thermodynamics with internal variables and revisited using concepts and arguments related to dynamical system theory. The evolution of internal variables is formulated either by a system of differential equations or by the associated phase flow. The restrictions implied by rate independence and thermodynamics are pointed out. Within this framework, the class of models with Masing hysteretic rules and Bouc endochronic relations are reviewed, and notions such as irreversibility, noninvertibility, and memory effects are discussed having recourse to different choices of internal variables. By introducing plastic strain as the internal variable, thermodynamic admissibility is proved for both models. However, while the processes with Masing rules exhibit a limited memory and are therefore noninvertible, the processes based on Bouc models are shown to have full memory and to be invertible though irreversible.

The deformation and pore-water pressure responses of clayey soils are of great interest to civil engineers. In this paper, displacements and pore-water pressures of a clay subjected to the loading of a strip footing are simulated using a fully coupled finite-element (FE) consolidation method incorporated with a newly developed 3D elastic viscoplastic (EVP) model for the clay. A brief introduction to the 3D EVP model and its implementation in the FE analysis is presented. The 3D EVP model can describe the time-dependent stress-strain behavior of clayey soils, including volumetric creep. The main objective of this paper is to examine how the viscosity (or creep parameter ψ/V) of the clay affects the deformation and pore-water pressure responses of the clay. For this, the value of the creep parameter ψ/V is varied in the FE analysis. When viscous nature is taken into account, the pore-water pressure in the soil is higher than that without consideration of the viscous nature. The phenomenon of pore-water pressure increase due to creep is studied in this paper. It is found that larger creep parameter ψ/V results in higher pore-water pressure and larger deformation in the soil. The difference of the pore-water pressure due to the Mandel-Cryer effects and the creep is investigated using the FE model and discussed in this paper. In addition, a few other parameters (Poisson's ratio ν, permeability k, clay layer thickness h, and thickness h to a half footing width a ratio h/a) are also varied to investigate their influence on deformation and pore-water pressure of the soil with creep. It is found that, the lower the permeability of soil, the higher is the pore-water pressure and the larger is the local deformation. The thickness of the soil layer also has a great influence on the pore-water pressure induced by the viscous effect. All these increased pore-water pressures result from a balance of the pore-water pressures induced by creep (and the Mandel-Cryer effects or both) and dissipated because of drainage.

Determination of sensitivity gradient is a major prerequisite for structural optimization, reliability assessment, and parameter identification. As the conventional deterministic sensitivity analysis cannot provide complete information, stochastic analysis is needed to tackle the uncertainties in structural parameters. This study focuses on the utility of the stochastic finite-element method for random response sensitivity analysis. The stochastic modeling of a random parameter is based on a commonly used 2D local averaging method generalized for a 3D case. The Choleski decomposition technique is then employed for digital simulation. The Neumann expansion based finite-element simulation method is extended for stochastic sensitivity analysis. This technique leads to a considerable saving of computational time. Example problems are used to compare the accuracy of this method to the direct Monte Carlo simulation and perturbation method in terms of varying stochasticity and efficiency in CPU time.

A systematic presentation of the concept of a well-defined stochastic damage accumulation model for fatigue calculation is attempted; the model is applicable for both organic and ceramic matrix composites. Stationary and nonstationary, with one or more blocks, discrete time and finite state Markov chain models are employed. They are found appropriate for yielding fatigue life probability distributions and damage evolution information at different stress levels. The structure, applicability, flexibility, and limitations of the model are examined in detail. The theoretical concepts are elucidated by the incorporation of data from a comprehensive testing program.

The generalized bending of a large plate with a circular elastic inclusion is discussed here. The solution for a hole or a rigid inclusion, which is the limiting case of an elastic inclusion, has been discussed frequently, but there is little work on an inclusion with arbitrary rigidity. Early investigators solved the problem of a large thin plate with a circular elastic inclusion, subjected to uniaxial bending, balanced biaxial bending, pure twisting, and transverse shear. This work was recently generalized to arbitrary bending loading, and explicit formulas were presented for dimensionless maximum circumferential bending moments in the plate and in the inclusion. This paper solves the analogous problem with Reissner's shear-deformable plate theory. Arbitrary bending loading is considered. A general solution is derived for the governing differential equations. Explicit formulas are developed for the maximum circumferential and radial moments in the plate and the inclusion. The results for four typical loadings are illustrated graphically, and two limiting forms of the solution are obtained.

The stochastic response of the Santa Felicia earth dam, in southern California, to spatially varying earthquake ground motion (SVEGM) is analyzed. An SVEGM model that accounts for both incoherence and propagation of seismic waves is used, the results are compared with those for various simplified excitations, and the sensitivity of the responses to coherency models proposed by different researchers is investigated. A 3D inhomogeneous finite-element model is used to represent the dam. Finite element-based random vibration analysis is performed and the statistical moments of Cartesian displacement, stress, and strain responses are computed. Statistical moments of the maximum shear stress are computed using Monte Carlo simulation that utilizes results from the random vibration analysis. The results indicate that the stress response of stiff material near the base of the dam can be significantly increased due to SVEGM, and that the increase is sensitive to the low-frequency variation of ground motion coherency.

The principles of continuum damage mechanics are reviewed first for the case of uniaxial tension. The damage variable is then decomposed into two variables called crack damage variables and void damage variables. A consistent mathematical formulation is presented to decompose the damage tensor into two parts: one caused by voids and the other caused by cracks. In the first part of this work, isotropic damage in the uniaxial tension case is assumed. However, the generalization to three-dimensional states of damage is presented in the second part of this work, using tensorial damage variables. It is shown that the components of tensorial crack damage variables and void damage variables are not independent of each other, implying a coupling between the two damage mechanisms. This coupling may be obvious based on the physics of the problem, but a rigorous mathematical proof is given for it. Also, explicit relations governing the components of the crack and void damage variables are derived.

In this paper a boundary element method is developed for the nonuniform torsion of composite bars of arbitrary constant cross section. The composite bar consists of a matrix surrounding a finite number of inclusions. The materials have different elasticity and shear moduli and are firmly bonded together. The bar is subjected to an arbitrarily concentrated or distributed twisting moment while its edges are restrained by the most general linear torsional boundary conditions. Because warping is prevented, besides the Saint-Venant torsional shear stresses, the warping normal stresses are also computed. Two boundary-value problems with respect to the variable along the beam angle of twist and to the warping function at the shear center are formulated and solved employing a boundary element method approach. Both the warping and the torsion constants are computed by employing an effective Gaussian integration over domains of arbitrary shape. Numerical results are presented to illustrate the method and demonstrate its efficiency and accuracy. The contribution of the normal stresses caused by restrained warping is investigated.

A kinematic method is developed to determine the shakedown limits of elastic-perfectly plastic steel-reinforced concrete beams under quasi-static and dynamic cyclic loads. This procedure, like the respective kinematic approach of plastic limit analysis, is visual and easy to use in engineering applications. The load parameters (amplitudes, frequency) versus yield moment diagrams, constructed from possible collapse modes, should assist in choosing the reinforcement scheme and amounts of reinforcement to meet the load bearing requirements for the structures.

Experimental procedures for the determination of physical properties of viscoelastic materials are discussed in this paper. Two well-known methods—a standard ASTM method and the other based on indirect measures—are compared to the method proposed here that uses direct measures of forces and response in terms of displacements or accelerations. Two kinds of materials were tested using these three methods; some conclusions, stressing the advantages of the suggested methodology, are presented at the end of the paper.

Geosynthetic reinforcements are manufactured from polymers such as polyester, polypropylene, and high-density polyethylene. Compared to metals, they exhibit large plastic strains, and highly nonlinear and hysteretic behaviors under cyclic loading. Most geosynthetic reinforcements do not sustain compression load. Traditional cyclic models with the Masing rule fail to simulate such unique behavior. A 1D bounding surface concept is used to develop a model that considers these unique properties of geogrids. The unique features of the model include nonparallel bounding lines and different loading and unloading hardening parameters. The model was calibrated and compared with the experimental results of two geogrids under monotonic and cyclic loadings with different load amplitudes.