In this study, we present theoretical derivation of seepage flow in unsaturated and static soil using Homogenization theory. The derivation started in the microscopic scale in the soil. The representative elementary volume (REV) in the soil is set to be one order larger than the scale of characteristic length of pore. Solids in the REV are assumed to be rigid and cohesionless. The liquid velocity in the pore is slow. By no-slip boundary condition on the solid boundary in REV, we could obtain the microscopic flow conditions. Using spatial ensemble average under the microscopic scale, we obtain the relation between water content, pressure head and velocities in macroscopic scale. This macroscopic averaged equation is validated to be equal to Richards' equation.

This research takes the resistance formula of spherical cavity expansion theory as its foundation. It establishes a predictive model of the residual velocity, ballistic limit velocity, and penetration depth of ogival nose projectiles striking metal target plates at high speed. They are aimed at 6061-T651 aluminum plates of different thicknesses using the iterative algorithm of the numerical method, thereby investigating the theoretical calculation of the residual velocity, penetration depth, ballistic limit velocity, and changes in resistance of ogival nose projectiles when making a normal impact target. In addition to analyzing the resistance undergone by the projectile nose section, this predictive model also considers the effects of friction resistance of the projectile shank section. In this research, we also used the finite element software LS-DYNA to perform a simulated analysis on the penetration depth of the aluminum plate after normal perforation by ogival nose projectiles. Ballistic test experiments were then performed using 0.30” AP (armor piercing) bullets. Finally, a comparative analysis was performed based on the theoretical model, experiments, and numerical simulation results.

This work integrates the Taylor theorem and the method of fundamental solutions to develop a numerical tool for estimating the added mass coefficient tensor for a solid object of any convex shape moving in potential flow. In potential flow theory, the Taylor theorem calculates the added mass coefficient tensor for a Rankine body with algebraic manipulations of the properties of the internal singularities employed to generate the corresponding flow. To apply this theorem for objects in other shapes, the singularity strength and locations are required information which is facilitated numerically in this work by the method of fundamental solutions (MFS). The developed scheme is tested on a circle, an ellipse, a square, and a rhombus and the numerical results are in good agreement with the corresponding analytical values. A final example of a Cassini oval is also considered to show the potential applications on bio-engineering problems.

This study performs parametric analyses on the displacement ductility capacity of a fixed-head reinforced concrete pile in homogeneous clay, considering the spread of plasticity in the pile. The parametric study regards the pile as a limited ductility structure, which conditionally allows the pile to have inelastic response during large loading. The variables considered include the pile section parameters and p-y model parameters. A large number of pushover analyses are conducted to examine the displacement ductility capacity of the pile. The results show that the plastic hinging will occur at the pile head region for a fixed-head pile, and the displacement ductility capacity of the pile is mainly influenced by the over-strength ratio of the pile section. Furthermore, the second plastic region may occur in ground when the axial force is in high tension. Based on the design concept of limited ductility structures, the high tensile force in pile should be avoided in pile design. A quantitative relationship between the displacement ductility capacity and over-strength ratio is suggested for engineering applications.

Impulsive loading by the ground reaction force (GRF) around heelstrike during walking is closely related to joint degeneration and might be affected by joint movement of the locomotor system. Fifteen healthy males (age: 25.5 ±3 years) were studied to investigate the association between the quantitative joint angles, angular velocities and accelerations of the lower-limb joints, and the loading rates of the GRF. Apart from the gait speed, both the ipsilateral kinematics during the swing phase, and the contralateral kinematics around the beginning of the terminal double limb stance (DLS), may significantly contribute to the heelstrike and maximum loading rates of the GRF. The magnitude of the heelstrike impulsive GRF was particularly affected by the peak ankle dorsiflexion velocity during the swing phase of the ipsilateral limb. However, for generating the maximum loading rate of nearly eight times the magnitude of that of the heelstrike one needed more kinematic variables to be modulated in advance, especially the knee flexion velocities around the beginning of the terminal DLS of the contralateral limb. Knowledge of the joint mechanics of the locomotor system for controlling the magnitude of the impulsive GRF during normal walking might be helpful for gait retraining for the elderly or patients who might have excessive impulsive GRF and a high risk of joint degeneration.

The present study is concerned with a theoretical analysis of the photophoresis of a microsized long cylinder in a perpendicular optical field. Different from previous studies of photophoresis, thermal stress slip usually neglected is taken into account in the analysis. The gaseous fluid relative to the microparticle in photophoretic motion falls into slip-flow regime. Asymmetric distribution of the absorbed heat energy within the particle becomes the driving force for photophoretic motion of the cylinder-shaped particle. By evaluating heat source function distributions at various conditions, the study focuses on the effects of particle size and optical properties on the energy distribution and the resultant influences on the photophoresis. The photophoretic mobility is developed by the slip flow model with consideration of thermal stress slip. The results reveal that the photophoretic mobility decreases with the increase of particle thermal conductivity (k*) and increases with Knudsen number (Kn). The thermal stress slip effect on photophoretic velocity is more noticeable at high Kn, but disappears at the continuum limit. A long cylinder-shaped particle has higher photophoretic velocity than a spherical particle at low k*, while the situation reverses at high k*. With thermal stress slip considered, the critical condition for crossing of the photophoretic velocity curves of cylindrical and spherical particles is mildly influenced by Kn.

Cavity expansion theory has been widely adopted by many researches in predicting penetration depth of objects under impact. The main purpose of this paper is to construct two models, each comprising different damaged zones based on the cavity expansion theory, to predict the target resistance when regarding the dual-layer ceramic/aluminum panel with finite thickness under high velocity impact. Once the target resistance obtained, the modified Bernoulli equation T-A model was adopted to predict the residual velocities of the projectile after penetrating targets with different thickness combination. The residual velocities predicted by the two models were compared with the results from ballistic test using .30” AP projectile. It was found that the accuracy of the models depends mainly on the thickness of ceramic material, that is, different model is suitable to predict different thickness combination of dual layer target considered. The damaged phenomenon after test was also investigated and analyzed. Therefore, it is suggested that the damaged models constructed in this study could be applied to predict the energy absorption of dual layer panel with different combination and thickness, as long as consideration of the cavity expansion zones is adjusted.

The reliability of the impeller-spindle with respect to the effects of abnormal vibrations and noises is relative to the whirl rotation in notebook (NB) computers, all-in-one (AIO) desktop systems, and tablet PCs. This study experimentally investigates the stability of a herringbone-microgrooved journal bearing in an impeller-spindle under static radial forces.The experimental device operated at 2700, 3600, 4200, and 4900rpm, with a static load ranging from 0.4, 0.8, and 1.6N. The experiment obtained the stiffness and damping coefficients, and the study involved analyzing the stability. Results show that the dimensionless threshold speed of rotation decreased as the Sommerfeld number increased. The proposed impeller-spindle is stable when the Sommerfeld number is less than 59, indicating that the impeller-spindle should not operate at an eccentricity ratio below 0.18.

In this paper, a model has been presented for generating a special ring vortex by applying a nonconservative force with specific distribution through the Navier-Stokes equations. Moreover, the ring's vortical pattern has been compared with the analytical and experimental results. In continuation, the diffusion, dissipation, and dispersion errors of four basic convection term interpolation schemes for the velocity and vorticity field of the vortex ring have been investigated. The simulations are performed for both the small and large time steps. Next, an appropriate discretization scheme for the convection term, and a proper order of time steps for simulating flows that contain ring vortices have been proposed. Finally, the ring vortexes generated by non-conservative force are added to the turbulent channel flow as a bubble induced vortex on carrier flow in two-phase flows, and the drag reduction due to the interaction between ring vortexes and flow vorticity field is observed.

This study uses the nanoindentation technique to evaluate the mechanical properties of thin copper films at indentation depths measured in the order of nanometers. Copper films with various thicknesses are deposited on a single crystal silicon wafer with a (100) orientation and on a polymethylmethacrylate (PMMA) substrate, respectively. The experimental results show that for soft thin films on a hard substrate, the substrate effect is negligible when the indentation depth is less than 20% of the film thickness. However, the results suggest that hard films on a soft substrate should be treated as a composite system in indentation because the substrate effect is significant. Finally, the results reveal that a significant indentation size effect exists for thin films with a thickness of less than 100nm. A number of possible reasons for the depth dependence of the hardness properties at ultra-shallow indentation depths are proposed and discussed.

A solution based on an advancing model for the content of diffusion material in a cube of medium is derived. The cube is assumed to be surrounded by diffusion material, and the diffusion material penetrates through all six surfaces and diffuses toward the center of the cube. The model accounts for the interaction between the diffusions in the three principle coordinates of the Cartesian coordinate system. For the first time, an exact solution of the content of the diffusion material based on the advancing model is derived in a clean form for a three-dimensional case.

The problem of rotating annular disk subjected to a uniformly distributed load is treated in two ways. Stress is divided into a rotating part because of the angular velocity and a bending part due to force loading. New set of equilibrium equations with small deflections is developed. Solutions for radial displacement, deflection, forces and moment resultants, and the rotating and bending stresses of the first-order theory are presented in terms of corresponding quantities of annular disks based on the classical theory. The boundary conditions at the edges of the annular disk are roller supported, clamped or free. Several examples are presented to illustrate the use and accuracy of these relationships. The effects of several parameters on the radial and vertical displacements and rotating and bending stresses are studied. It is observed that the classical theory is sufficient to study the problem of rotating annular disks. However, the inclusion of the effect of shear deformation is necessary to study precisely the curvature of moderately thick annular disks.

This paper deals with the optimal design for a twin die stacked package. Firstly, the numerical model is built up in terms of a three-dimensional slice model along the diagonal direction of the package. The material behavior of the solder balls is a consequence of the viscoplastic property which can be described by the Anand's model. Secondly, the Darveaux model is applied to predict the solder ball reliability of the stacked die package under a cyclic temperature loading. Since simulation analysis found an obvious relation is found between the fatigue life of the solder ball and the distribution of the accumulated strain energy density (SED) on the critical solder ball of the package through the simulation analysis, the average value of the strain energy density for all solder balls is adopted as the optimization indicator of reliability. With such a viewpoint, the critical solder ball position can be ignored, and accordingly an efficient analysis can be obtained. Finally, the Box-Behnken regression model is adopted to construct all the experiments. Each experiment analyzes the reliability of the package under varying parameters. Subsequently, the pattern search algorithm is applied to search for optimal factors.

Through optimal analysis with the fatigue reliability indicator of an average SED, the fatigue life is found to be 59% lower than that of the original design. The fatigue life had clearly improved and the lowest ball fatigue life is found to be 2.859 times longer than the original one.

This study investigates the effects of disk position nonlinearities on the nonlinear dynamic behavior of a rotating flexible shaft-disk system. Displacement of the disk on the shaft causes certain nonlinear terms which appears in the equations of motion, which can in turn affect the dynamic behavior of the system. The system is modeled as a continuous shaft with a rigid disk in different locations. Also, the disk gyroscopic moment is considered. The partial differential equations of motion are extracted under the Rayleigh beam theory. The assumed modes method is used to discretize partial differential equations and the resulting equations are solved via numerical methods. The analytical methods used in this work are inclusive of time series, phase plane portrait, power spectrum, Poincaré map, bifurcation diagrams, and Lyapunov exponents. The effect of disk nonlinearities is studied for some disk positions. The results confirm that when the disk is located at mid-span of the shaft, only the regular motion (period one) is observed. However, periodic, sub-harmonic, quasi-periodic, and chaotic states can be observed for situations in which the disk is located at places other than the middle of the shaft. The results show nonlinear effects are negligible in some cases.

In this paper a system of depth-integrated equations for over-saturated debris flows on three-dimensional topography is derived. The lower layer is a saturated mixture of density preserving solid and fluid constituents, where the pore fluid is in excess, so that an upper fluid layer develops above the mixture layer. At the layer interface fluid mass exchange may exist and for this a parameterization is needed. The emphasis is on the description of the influence on the flow by the curvature of the basal surface, and not on proposing rheological models of the avalanching mass. To this end, a coordinate system fitted to the topography has been used to properly account for the geometry of the basal surface. Thus, the modeling equations have been written in terms of these coordinates, and then simplified by using (1) the depth-averaging technique and (2) ordering approximations in terms of an aspect ratio ϵ which accounts for the scale of the flowing mass. The ensuing equations have been complemented by closure relations, but any other such relations can be postulated. For a shallow two-layer debris with clean water in the upper layer, flowing on a slightly curved surface, the equilibrium free surface is shown to be horizontal.

This research alters the traditional single inlet/outlet opening of the pin type flow channel of direct methanol fuel cells (DMFCs). Multi-inlet/outlet openings are designed with the aim to distribute the methanol solution evenly and effectively remove CO2 bubbles and to improve the cell performance. The CO2 bubble dynamics in anode flow channels and the cell performance are investigated. Results show that the newly designed flow channels can overcome restrictions resulting from fuel and effectively remove CO2 bubbles, thereby enhancing the performance of the pin type DMFC. The “three-inlet and three-outlet” design increases the current density output by 19%.

Complex method and Green's function method are used here to investigate the dynamic analysis for circular inclusion near interfacial crack impacted by SH-wave in bi-material half-space. Firstly, the displacement expression of the scattering wave was constructed which satisfied the free boundary conditions, then Green's function could be constructed, which was an essential solution to the displacement field for an elastic right-angle space with a circular inclusion impacted by out-plane harmonic line source loading at vertical surface. Secondly, crack was made out with “crack-division” technique. Meanwhile, the bi-material media was divided into two parts along the bi-material interface based on the idea of interface “conjunction”, and then the vertical surfaces of the two right-angle spaces were loaded with undetermined anti-plane forces in order to satisfy displacement continuity and stress continuity conditions at linking section. So a series of algebraic equations for determining the unknown forces could be set up through continuity conditions and the Green's function. Finally, some examples and results for dynamic stress concentration factor of the circular elastic inclusion were given. Numerical results show that they are influenced by interfacial crack, the incident wave number and the free boundary in some degree.