A modified error indicator is developed to study the supersonic turbulent flow over a backward-facing step. In the Cartesian coordinate system, the unsteady Navier-Stokes equations with a low-Reynolds-number k−ε turbulence model are solved. The modified error indicator, in which the unified magnitude of substantial derivative of pressure and unified magnitude of substantial derivative of weighted vorticity magnitude are incorporated, is applied to treat the mesh refining. To assess the present approach, the transonic turbulent flow around an NACA 0012 airfoil is performed. Based on the comparison with the experimental data, the accuracy of the present approach is confirmed. According to the high-resolutional result on the adaptive mesh, the structure of backstep corner vortex, expansion wave and oblique shock wave is distinctly captured.

A series solution is presented for a spherical inclusion embedded in an infinite matrix under a remotely applied uniform intensity. Particularly, the interface between the inclusion and the matrix is considered to be inhomegeneously bonded. We examine the axisymmetric case in which the interface parameter varies with the cone angle θ. Two kinds of imperfect interfaces are considered: an imperfect interface which models a thin interphase of low conductivity and an imperfect interface which models a thin interphase of high conductivity. We show that, by expanding the solutions of terms of Legendre polynomials, the field solution is governed by a linear set of algebraic equations with an infinite number of unknowns. The key step of the formulation relies on algebraic identities between coefficients of products of Legendre series. Some numerical illustrations are presented to show the correctness of the presented procedures. Further, solutions of the boundary-value problem are employed to estimate the effective conductivity tensor of a composite consisting of dispersions of spherical inclusions with equal size. The effective conductivity solely depends on one particular constant among an infinite number of unknowns.

Cycloid drives are widely used in the industries because of their excellent characteristics, namely, high gear ratio, smooth transmission, compact size, high efficiency, low noise and long service life. In this paper, a mathematical model of an epitrochoid gear for a cycloid drive with a small tooth number difference has been proposed. Computerized simulation of the generated epitrochoid gear has also been developed. In this paper, the pressure angle, which has an important role in the analysis of cycloid drives as it influences the direction and magnitude of force transmission in gears, is derived based on the theory of differential geometry. The rack cutter profile, which is the fundamental tooth profile of a hob cutter, which in turn is the main manufacturing process of epitrochoid gear, has been obtained based on the theory of gearing. It is anticipated that the results from this paper will be beneficial to the design, analysis and manufacture of cycloid drives.

The dynamic response of a homogeneous, isotropic and elastic circular plate on an elastic foundation subjected to axisymmetric time dependent loads is investigated both analytically and numerically in thisv paper. First, the Extended Finite Hankel Transform (EFHT) is derived. After applying the technique of the EFHT to the governing equation of the vibrating circular plate, the governing partial differential equation (PDE) is transformed into the governing ordinary differential equation (ODE). Therefore, the analytical solution of the plate problem can be found completely. Once the dynamic response of the plate is solved, the internal forces of the plate, including shear force, bending moment and torsion, can be obtained subsequently. Under the particular case that elastic springs do not exist under the foundation, the dynamic response of the circular plate by the method of EFHT matches exactly with that by the method of modal analysis. By comparing the methods of EFHT, Boundary Element Method (BEM) and Finite Element Method (FEM), the results indicate that the proposed method of EFHT is accurate, systematic and convenient.

The thermal stress for a penny-shaped crack contained in an infinite isotropic elastic solid initially subjected to an axisymmetrical tension of any amount at infinity is investigated using the techniques of Hankel transforms and multiplying factors. The effect that the lateral normal stress has on the thermal stresses is studied on the basis of the theory of small deformations superposed on finite deformation. Symmetrical thermal loadings are applied over the crack surfaces. For the case of constant temperature over the crack surfaces, expressions for the crack shape and thermal stresses in the crack plane are obtained in closed forms. The stress intensity factor is also obtained and shown to be dependent on the lateral stress.

This paper presents the nonlinear finite element modeling of the global behavior for RC beam strengthened by externally epoxy bonded steel plates up to failure. In addition to the consideration of nonlinear behavior and cracking of concrete, the model involves interface element to capture not only the shear and normal stress concentration at the plate curtailment, but also the separation due to the exceeded peak shear and normal stress. The internal steel bar using truss element and the external steel plate using deformation theory of plastic have been confirmed by compare finite element solution with plastic theory. The proposed finite element solutions result in close correlation with experimental data available for RC beams strengthened by epoxy bonded steel plates with different thickness.

In this paper viscous boundary layer flows above and inside a permeable wavy bed are studied. The flow motions are driven by an oscillatory horizontal velocity just outside the Stokes boundary layer above the bed. Analytical and numerical solutions are obtained for both the oscillatory velocity component and the steady streaming inside the permeable bed, the Stokes boundary layer and the outer boundary layer. Two specific situations are examined: (1)Weak oscillatory motions over a wavy bed with finite slope and (2) strong oscillatory motions over a small wavy slope. In both situations, the slip (tangential) velocity and the normal velocity do not vanish on the wavy surface because of the permeability. The magnitude of the bed shear stress decreases as the permeability increases. The permeability can also affect significantly the steady streaming patterns; they could change from having two pairs of recirculating cells above an impervious wavy bed to one pair of recirculating cells above a wavy permeable bed.

Electrochemical experiments in microgravity are essential for the optimum design of advanced life support systems and power storage systems in space. In the absence of gravity, the evolved gas bubbles will clog the electrode and slow the reaction. Here, a rotating cell concept is introduced as a plan for improving mass transfer and bubble removal in a microgravity environment. A primary experimental study of bubble behavior in rotating water electrolysis cells has been done in reduced gravity through KC-135 parabolic flight. The results show that the cell resistance decreases with increasing rotation rate. Without rotation, the bubbles stick on the electrode surface during reduced gravity period, thus, the cell efficiency degrades. Mass transfer enhanced by bubble generation is investigated in ground-based work at high rotation rate of test cells, so that gravitational effects are minimized.

This paper aims to investigate the failure probability of short high-strength concrete tied columns using the Monte Carlo technique. The random variables considered in this study are the strength of concrete, the strength of steels, the cross-section dimensions, the location of the steel reinforcement, the variability of strength model and the loads. The results show that the failure probabilities of high-strength concrete columns designed according to the ACI Code are relatively high. The current ACI Code may not be conservative for design of short high-strength concrete tied columns.

A new acoustic transducer and measurement method have been developed for precise measurements of surface wave velocity. This technique is used to investigate the acoustoelastic effect of surface waves in polymethylmethacrylate (PMMA). The transducer utilizes two miniature conical PZT elements for surface wave transmitter and receiver, and hence can be viewed as a point-source/point-receiver (PS/PR) surface wave transducer. Surface waves are excited and detected with the PZT elements and the surface wave velocity can be accurately determined over a small measurement area. Improvement has been made so that the transducer can be used for both conductive and non-conductive materials. The transducer is then applied to measure the acoustoelastic effect of surface wave in a PMMA specimen. The acoustoelastic coefficients are experimental determined.

Traditionally, the yield displacement of a nonlinear structure was calculated by using the direct displacement-based seismic design method which usually requires a repeatedly iterative procedure no matter whether the substitute structure or inelastic design spectra has been adopted in the procedure. This will sometimes result in inefficiency if too many iterative cycles need to be produced in a design case for convergency. To avoid this disadvantage, this paper presents a non-iterative direct displacement-based design procedure for SDOF steel columns using the substitute structure approach. By combining the yielding property with the stiffness property of the designed steel columns, the procedure can immediately obtain the column's cross-section via the chosen target displacement and ductility ratio.

The general approximate solutions for the two-dimensional thermoelastic problems with a nearly circular hole are provided in this study. Based on Stroh formalism and the method of conformal mapping, the boundary perturbation analysis is applied to solve the problems of a hole with arbitrary shape. The radius of the hole considered here is represented as a sum of a reference constant and a perturbation magnitude that is expanded into a Fourier series. In order to illustrate the applicability and efficiency of the present approach, special examples associated with polygonal hole problems are solved explicitly and discussed in detail. Since the general solutions have not been found in the literature, comparison is made with some special cases for which the analytical solutions exist, which shows that our proposed method is effective and general.

This research is focused in the measurement and modelling of the dispersion relations of Lamb waves propagating in a piezoelectric plate. A theoretical model based on a partial wave analysis is used to provide numerical calculations for the dispersion relations of Lamb waves propagating in an LiNbO3 plate with different propagating directions. The dispersion relations are presented in an innovative image format. A non-contact laser ultrasound technique operated in B-scan mode with the aid of double Fast Fourier transform signal-processing scheme is used to measured multi-mode dispersion realtions. Among all the propagation angles, the measured dispersion curves show good agreement with the theoretical calculations. The Rayleigh wave speeds are extracted from the measured and calculated dispersion curves, showing favorable comparison with classical theory by Campbell.

A newly developed point-source/point-receiver (PS/PR) acoustic transducer is used for measuring the depth of surface-breaking cracks. The transducer consists of two miniature conical PZT elements which form a transmitter/receiver pair for generating and detecting surface waves. A tone-burst measurement system operates the PS/PR transducer at a fixed frequency. When a surface-breaking crack is present in between the transmitter and receiver, the change in time-of-flight of surface wave propagation caused by the crack is measured and used to estimate the crack depth. To verify the feasibility of this method, machined slots on a carbon steel sample are tested by the PS/PR transducer for crack depth determination. Good experimental results are obtained. Future applications and improvements on the PS/PR transducer system are addressed.

An approximate anisotropic yield function is presented for anisotropic sheet metals containing spherical voids. Hill's quadratic anisotropic yield function is used to describe the anisotropy of the matrix. The proposed yield function is validated using a three-dimensional finite element analysis of a unit cell model under different straining paths. The results of the finite element computations are shown in good agreement with those based on the yield function with three fitting parameters. For demonstration of applicability, the anisotropic Gurson yield function is adopted in a combined necking and shear localization analysis to model the failure of AA6111 aluminum sheets under biaxial stretching conditions.

A state space approach to heat conduction in a cylindrically anisotropic circular tube of functionally graded materials (FGM) is presented. A power-law type of the radial inhomogeneity for the FGM is considered. By means of eigenfunction expansion and matrix algebra, analytic solutions for transient and steady-state heat conduction in the FGM tube under general thermal boundary conditions are derived.

The evolutionary structural optimization method is improved and extended to elastic-plastic topology optimization for the first time. An adaptive rejection ratio is proposed to control the number of removal elements without destroying the symmetric pattern in each evolution. Two performance indices suitable for elastic-plastic topology optimization are also proposed and examined. The performance indices can be used to investigate the material efficiency of structures in different evolutionary stages, and to serve as stop criteria in the evolutionary process. Moreover, an interactive special purpose computer analysis and graphics system is developed to visualize the topology in the evolutionary process. Finally, the effects of yield stress, Young's modulus, and the prescribed displacement in an elastic-plastic analysis on the obtained topology are discussed.

In this paper, spline collocation method (SCM) is successfully extended to solve the generalized problems of beam structures. The spline functions in SCM are re-formulated by finite difference method in a systematical way that is easily understood by engineers. The manipulation of SCM is further simplified by the introduction of quintic table so that the matrix-vector governing equation can be easily formulated to solve the weighting coefficients. SCM is first examined by the problems of a generalized single-span beam undergoing various types of loadings and boundary conditions, and it is then extended to the problems of continuous beam with multiple spans. By comparing with available analytical results, differential quadrature method (DQM), if any, excellent accuracy in deflection is achieved.

In this paper, the analysis of the responses of the pseudo dynamic test of two rectangular reinforced concrete (RC) bridge columns using the Hilbert-Huang transform (HHT) is introduced. Firstly, two 40%-scaled rectangular RC bridge columns are subjected to the pseudo dynamic test. The input of the pseudo dynamic test is set as the near-fault ground accelerations of the Chi-Chi Earthquake, which happened in 1999 in central Taiwan. After damage occurs to the bridge columns, we use non-shrinkage mortar to repair the columns, and then use 3 layers of CFRP to rehabilitate their plastic zone. The repaired bridge columns are again tested. Then we use the HHT to analyze the responses of the as-built and repaired bridge columns. The merit of applying the HHT to the responses of bridge columns is that it can transfer the displacement-time responses into instantaneous frequency responses, while the spectra are a function of both frequency and time. We can observe from the Hilbert spectra of the bridge columns that, at the instant when the frequency changes, the structural behavior changes from elastic to inelastic. The HHT can therefore be used to obtain the instantaneous natural frequencies of the bridge columns and to understand the relationship between the frequency changes and stiffness condition of the bridge columns.

In this paper, a discrete system model and its equation of motion for beams with arbitrary supports at two ends are established. These supports include elastic, rigid and free supports in translation and rotation directions. Based on theory of oscillatory matrices, a series of qualitative properties of frequencies and modes of this system are derived. The basic properties include: non-zero frequencies are distinct; the ith displacement mode has i - 1 nodes; nodes of ith mode and (i + 1)th mode interlace.

Some additional important qualitative properties owned by rotation modes and strain modes are given as well.