To model the viscous effect, the core area of particles in Leonard's core spreading vortex method must grow linearly in time, which however results in growing convective errors and consequently causes the failure of a correct convergence of the method to the Navier-Stokes equations. The so-called diffusion vortex method was proposed and claimed to have smaller core-area growth rates because part of the viscous effect is modeled into the movement of particles. The growth rates however are non-uniform and an additional diffusion error arises due to the nonzero divergence of the diffusion velocity. The goal of this work is to analyze the associated errors of several existing versions of the diffusion vortex method and compare them with that of Leonard's. Simulations of two axisymmetric flows are performed to measure the involved diffusion errors and consequently distinguish these diffusion vortex methods. The results show that the circulation conservation is important, besides a small core-area growth rate, in obtaining a good accuracy. Under the consideration of both efficiency and accuracy, the diffusion vortex method in which each vortex particle conserves its own circulation on its core area alone is recommended.

Bulk migration of particles towards regions of lower shear occurs in suspensions of neutrally buoyant spheres in Newtonian fluids undergoing creeping flow in the annular region between two rotating, coaxial cylinders (a wide-gap Couette). For a monomodal suspension of spheres in a viscous fluid, dimensional analysis indicates that the rate of migration at a given concentration should scale with the square of the sphere radius. However, a previous experimental study [12] showed that the rate of migration of spherical particles at 50% volume concentration actually scaled with the sphere radius to approximately the 2.9 power. In the current study, a series of experiments is performed to extend the previous study to two new concentrations, namely, 35% and 42.5%. The new study indicates that the power scaling decreases with concentration.

This paper uses three lubrication models to explore the differential phenomenon in the status of thin film lubrication (TFL). According to the viscous adsorption theory, the modified Reynolds equation for thin film elastohydrodynamic lubrication (TFEHL) is derived. In this theory, the film thickness between lubricated surfaces is simplified as three fixed layers across the film, and the viscosity and density of the lubricant vary with pressure in each layer. Under certain conditions, such as a rough or concentrated contact of a nominally flat surface, films may be of nanometer scale. The thin film elastohydrodynamic lubrication (EHL) analysis is performed on a surface forces (SF) model which includes van der waals and solvation forces. The results show that the proposed TFEHL model can reasonably calculate the film thickness and the average relative viscosity under thin film EHL. The adsorption layer thickness and the viscosity influence significantly the lubrication characteristics of the contact conjunction. The differences in pressure distribution and film shape between surface forces model and classical EHL model were obvious, especially in the Hertzian contact area. The solvation force has the greatest influence on pressure distribution.

In the framework of the finite volume method, a robust and easily implemented hybrid flux-splitting finite-volume (HFF) scheme is proposed for simulating hydraulic shock waves in shallow water flows. The hybrid flux-splitting algorithm without Jacobian matrix operation is established by applying the advection upstream splitting method to estimate the cell-interface fluxes. The scheme is extended to be second-order accurate in space and time using the predictor-corrector approach with monotonic upstream scheme for conservation laws. The proposed HFF scheme and its second-order extension are verified through simulations of the 1D idealized dam-break problem, the 2D oblique hydraulic shock-wave problem, and the 2D dam-break experiments with channel contraction as well as wet/dry beds. Comparisons of the HFF and several well-known first-order upwind schemes are made to evaluate numerical performances. It is demonstrated that the HFF scheme captures the discontinuities accurately and produces no entropy-violating solutions. The HFF scheme and its second-order extension are proven to achieve the numerical benefits combining the efficiency of flux-vector splitting scheme and the accuracy of flux-difference splitting scheme for the simulation of hydraulic shock waves.

An analysis is presented for wave propagation in infinite homogeneous elastic plates of piezoelectric materials. The analysis is an extension to the work by Shuvalov [1] on wave propagation in general anisotropic elastic plates. A real form of dispersion equation is provided for a piezoelectric plate subjected to different boundary conditions on the plate surfaces. Perturbation theory [2] is exploited to obtain long-wavelength low-frequency approximation for physical quantities of wave propagation, including wave amplitude, stress, electric potential, electric displacement and velocity.

The elastic fields of a torsional dislocation loop in a homogeneous material are first derived. The solution is based on torsional symmetry. The stress and displacement solutions are then extended to the case of a torsional loop in a bi-material. A main utility of basic dislocation solutions is in fracture mechanics. In particular, circular loop solutions can be used in the modeling of both cylindrical and penny-shaped cracks. In the present study we use them to model a Mode III cylindrical crack via the application of a “distributed-dislocation technique”. Stress intensity factors at the crack tips are presented. The influences of crack radius and material pair on the stress intensity factor of interfacial cracks are investigated.

For performance-based seismic engineering of buildings, the direct displacement-based seismic design method is different from the coefficient method used in FEMA-273 and the capacity spectrum method adopted in ATC-40. The method not only is a linear static procedure but also is applied to the design of new constructions. This paper concerns with experimental studies on the accuracy of the direct displacement-based design procedure. Experimental results of three reinforced concrete (RC) columns designed by the displacement procedure are presented and discussed through pseudo-dynamic tests and cyclic loading tests. From the tests, it is shown that the stiffness degrading factor of RC columns plays a key role. The direct displacement-based seismic design method can reliably capture the maximum displacement demand of the test RC columns if the stiffness degrading factor adopted in the displacement design method for RC material is adequate.

Element-free Galerkin method (EFGM) based on moving least-square curve fitting concept is presented and applied to elastic fracture problems. Because no element connectivity data are needed, EFGM is very convenient and effective numerical method for crack growth analysis. This paper is intended as an investigation of crack trajectory for different notch locations under three-point bending test. The initial crack growth angles obtained by element-free Galerkin method in comparison with those obtained by lab test reveal that both results are very close. However, numerical results also show that the location of an original notch can stronger affect the variation of crack path for different increment. The stress intensity factors (SIF) of cracks under three-point bending test with different increment are also investigated by EFGM.