• Journal of applied mathematics & informatics
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• 제36권3_4호
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• pp.181-203
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• 2018

In this paper, we have constructed an overlapping Schwarz method for singularly perturbed second order convection-diffusion equations. The method splits the original domain into two overlapping subdomains. A hybrid difference scheme is proposed in which on the boundary layer region we use the central finite difference scheme on a uniform mesh while on the non-layer region we use the mid-point difference scheme on a uniform mesh. It is shown that the numerical approximations which converge in the maximum norm to the exact solution. When appropriate subdomains are used, the numerical approximations generated from the method are shown to be first order convergent. Furthermore it is shown that, two iterations are sufficient to achieve the expected accuracy. Numerical examples are presented to support the theoretical results. The main advantages of this method used with the proposed scheme is it reduces iteration counts very much and easily identifies in which iteration the Schwarz iterate terminates.

• 한국기계가공학회지
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• 제13권5호
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• pp.35-42
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• 2014

The influence of sine wave striated surface roughness on load carrying capacity of a bearing is studied for thin film effect of slider bearing. A Reynolds equation appropriate for slider bearing is used in this paper for analysis and it is discussed using finite difference method of central difference scheme. For a slider bearing with sine wave simple roughness form, several parameters such as pressure, load capacity and shear stress of the bearing can be obtained and also this results can be stored in sequential data file for latter analysis. After all, their distribution can be displayed and analyzed easily by using the matlab GUI technique. The parameters such as amplitude, number of waviness and slope of the surface are used for discussing the load carrying capacity of the rectangular bearing. The results reported in this paper should be applied to the other slider bearing such as rectangular or round embossed surface of slider bearing.

• Tribology and Lubricants
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• 제30권5호
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• pp.284-290
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• 2014

The influence of round embossed surface on slider bearing characteristics and its load carrying capacity is discussed for thin film effect of embossed slider bearing. For the numerical computation of lubrication parameters such as pressure, load capacity and shear stress that are normalized and a Reynolds equation is used for the analysis of embossed slider bearing characteristics. For this purpose, the finite difference method of central difference scheme is used in this study. In a slider bearing with embossed form, several simulation parameters such as pressure, load capacity and shear stress of the bearing can be obtained according to independent parameters such as the slope of the slider bearing and number of embossing in the upper slider. Also this results can be summarized and be stored in sequential data file for latter analysis. After all, their distribution of the pressure and shear stress parameters can be displayed and be analyzed easily by using the developed program with matlab GUI technique. The independent parameters such as a number of embossing and a slope of the embossed surface slider are used for discussing simulation parameters of pressure distribution, shear stress and load carrying capacity of the round embossing. These study results reported in this paper should be applied to the other shaped slider bearing with a rectangular embossed surface or rectangular waved surface.

• Geomechanics and Engineering
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• 제16권1호
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• pp.59-69
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• 2018

This study focused on the mechanical and hydraulic characteristics of underwater tunnels based on Mohr-Coulomb (M-C), Hoek-Brown (H-B) and generalized H-B failure criteria. An improved approach for calculating stress, displacement and plastic radius of the circular tunnel considering hydraulic-mechanical coupling was developed. The innovation of this study was that the radius-incremental-approach was reconstructed (i.e., the whole plastic zone is divided into a finite number of concentric annuli by radius), stress and displacement of each annulus were determined in terms of numerical method and Terzaghi's effective stress principle. The validation of the proposed approach was conducted by comparing with the results in Brown and Bray (1982) and Park and Kim (2006). In addition, the Rp-pin curve (plastic radius-internal supporting pressure curve) was obtained using the numerical iterative method, and the plastic radius of the deep-buried tunnel could be obtained by interpolation method in terms of the known value of internal supporting pressure pin. Combining with the theories in Carranza and Fairhurst (2000), the improved technique for assessing the reliability of the tunnel support was proposed.

• Structural Monitoring and Maintenance
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• 제2권4호
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• pp.399-418
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• 2015

Automated damage detection through Structural Health Monitoring (SHM) techniques has become an active area of research in the bridge engineering community but widespread implementation on in-service infrastructure still presents some challenges. In the meantime, visual inspection remains as the most common method for condition assessment even though collected information is highly subjective and certain types of damage can be overlooked by the inspector. In this article, a Frequency Response Functions-based model updating algorithm is evaluated using experimentally collected data from the University of Central Florida (UCF)-Benchmark Structure. A protocol for measurement selection and a regularization technique are presented in this work in order to provide the most well-conditioned model updating scenario for the target structure. The proposed technique is composed of two main stages. First, the initial finite element model (FEM) is calibrated through model updating so that it captures the dynamic signature of the UCF Benchmark Structure in its healthy condition. Second, based upon collected data from the damaged condition, the updating process is repeated on the baseline (healthy) FEM. The difference between the updated parameters from subsequent stages revealed both location and extent of damage in a "blind" scenario, without any previous information about type and location of damage.

• Geomechanics and Engineering
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• 제16권6호
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• pp.619-626
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• 2018

A simple prediction procedure was investigated for calculating the stresses and displacements of a circular opening. Unlike existed approaches, the proposed approach starts each step with a radius increment. The stress for each annulus could be obtained analytically, while strain increments for each step can be determinate numerically from the compatility equation by finite difference approximation, flow rule and Hooke's law. In the successive manner, the distributions of stresses and displacements could be found. It should be noted that the finial radial stress and displacement were equal to the internal supporting pressure and deformation at the tunnel wall, respectively. By assuming different plastic radii, GRC and the evolution curve of plastic radii and internal supporting pressures could be obtained conveniently. Then the real plastic radius can be calculated by using linear interpolation in the evolution curve. Some numerical and engineering examples were performed to demonstrate the accuracy and validity for the proposed procedure. The comparisons results show that the proposed procedure was faster than that in Lee and Pietrucszczak (2008). The influence of annulus number and dilation on the accuracy of solutions was also investigated. Results show that the larger the annulus number was, the more accurate the solutions were. Solutions in Park et al. (2008) were significantly influenced by dilation.

• 한국윤활학회:학술대회논문집
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• 한국윤활학회 1999년도 제29회 춘계학술대회
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• pp.182-188
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• 1999

A theoretical study of elastohydrodynamic lubrication of elliptical contacts with both rolling and spin has been carried out. A finite difference method and the Newton-Raphson method are applied to solve the problem. The velocity vectors resulting from combined spin and rolling/sliding motion lead to asymmetric pressure distributions and film shapes. Film contours and variations of the minimum and central film thicknesses are compared with various spin-roll ratios. At high spin-roll ratios the minimum film thickness is considerably reduced, whereas the central film thickness decreases less dramatically, The present numerical scheme can be used in the analysis of general elliptical contact problems.

• Tribology and Lubricants
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• 제23권2호
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• pp.49-55
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• 2007

A numerical analysis of elastohydrodynamic lubrication of elliptical contacts with both rolling and spinning has been carried out. A finite difference method with non-uniform grid systems and the Newton-Raphson method are applied to solve the problems. The velocity vectors resulting from combined spinning and rolling/sliding motion lead to asymmetric pressure distributions and film shapes. Pressure distributions, film contours and variations of the minimum and central film thicknesses are compared with various spin-roll ratios. Reduction of the minimum film thickness under spinning is remarkable whereas the central film thickness is relatively less. The spin motion have large effect on variations of the minimum film thickness with load parameter which are small in pure rolling/sliding cases. Therefore present numerical scheme can be used in the analysis of general elliptical contact EHL problems and further studies are required.

• Tribology and Lubricants
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• 제24권6호
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• pp.355-361
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• 2008

In highly stressed machine elements such as angular contact ball bearings and toroidal type traction drives, the elastohydrodynamic lubrication of elliptical contacts with both rolling and spinning motion are occur. In this paper, a finite difference method with non-uniform grid systems and the Newton-Raphson method are applied to solve the problems. Pressure distributions, film contours and variations of the minimum and central film thicknesses are compared with various ellipticity parameter, dimensionless speed and load parameter. The results showed that the spinning motion has significant influence especially on the film shapes. Reduction of the minimum film thickness under spinning is remarkable whereas the central film thickness is relatively less. Especially variations of the minimum film thicknesses with rolling velocity, load and ellipticity ratio are a great different from those of pure rolling. Therefore present numerical scheme can be used in the analysis of general elliptical contact EHL problems and further studies are required.

• 제어로봇시스템학회논문지
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• 제12궈1호
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• pp.85-92
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• 2006

A new silicon micro flow sensor with multiple temperature sensing elements was proposed and fabricated in considering wide range flow velocity measuring device. Thermal mass flow sensor measures the asymmetry of temperature profile around the heater which is modulated by the fluid flow. A micro mass flow sensor was normally composed of a central heater and a pair of temperature sensing elements around it. A new 2-D wide range micro flow sensor structure with three pairs of temperature sensing elements and a central heater was proposed and numerically simulated by Finite Difference Formulation to confirm the feasibility of the wide flow range sensor structure. To confirm the simulation result, the new flow sensor was fabricated on silicon substrate and the basic flow sensing properties of the sensor were measured.