• Journal of Korean Association for Spatial Structures
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• v.4 no.4 s.14
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• pp.113-128
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• 2004

A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies and mode shapes of solid paraboloidal and complete (that is, without a top opening) paraboloidal shells of revolution with variable wall thickness. Unlike conventional shell theories, which are mathematically two-dimensional (2-D), the present method is based upon the 3-D dynamic equations of elasticity. The ends of the shell may be free or may be subjected to any degree of constraint. Displacement components $u_r,\;u_{\theta},\;and\;u_z$ in the radial, circumferential, and axial directions, respectively, are taken to be sinusoidal in time, periodic in ${\theta}$, and algebraic polynomials in the r and z directions. Potential (strain) and kinetic energies of the paraboloidal shells of revolution are formulated, and the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four digit exactitude is demonstrated for the first five frequencies of the complete, shallow and deep paraboloidal shells of revolution with variable thickness. Numerical results are presented for a variety of paraboloidal shells having uniform or variable thickness, and being either shallow or deep. Frequencies for five solid paraboloids of different depth are also given. Comparisons are made between the frequencies from the present 3-D Ritz method and a 2-D thin shell theory.

• Smart Structures and Systems
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• v.25 no.6
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• pp.693-705
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• 2020

In the current investigation, large amplitude free vibration behavior of shallow curved pipes (tubes) made of functionally graded materials is investigated. Properties of the tube are distributed across the radius of the tube and are obtained by means of a power law function. It is also assumed that all thermo-mechanical properties are temperature dependent. The governing equations of the tube are obtained using a higher order shear deformation tube theory, where the traction free boundary conditions are satisfied on the top and bottom surfaces of the tube. The von Kármán type of geometrical non-linearity is included into the formulation to consider the large displacements and small strains. Uniform temperature elevation of the tube is also included into the formulation. For the case of tubes which are simply supported in flexure and axially immovable, the governing equations are solved using the two-step perturbation technique. Closed form expressions are provided to obtain the small and large amplitude fundamental natural frequencies of the FGM shallow curved tubes in thermal environment. Numerical results are given to explore the effects of thermal environment, radius ratio, and length to thickness ratio of the tube on the fundamental linear and non-linear frequencies.

• Geophysics and Geophysical Exploration
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• v.10 no.1
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• pp.77-88
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• 2007

Following a successful bathymetric mapping demonstration in a previous study, the potential of airborne EM for seafloor characterisation has been investigated. The sediment thickness inferred from 1D inversion of helicopter-borne time-domain electromagnetic (TEM) data has been compared with estimates based on marine seismic studies. Generally, the two estimates of sediment thickness, and hence depth to resistive bedrock, were in reasonable agreement when the seawater was ${\sim}20\;m$ deep and the sediment was less than ${\sim}40\;m$ thick. Inversion of noisy synthetic data showed that recovered models closely resemble the true models, even when the starting model is dissimilar to the true model, in keeping with the uniqueness theorem for EM soundings. The standard deviations associated with shallow seawater depths inferred from noisy synthetic data are about ${\pm}5\;%$ of depth, comparable with the errors of approximately ${\pm}1\;m$ arising during inversion of real data. The corresponding uncertainty in depth-to-bedrock estimates, based on synthetic data inversion, is of order of ${\pm}10\;%$. The mean inverted depths of both seawater and sediment inferred from noisy synthetic data are accurate to ${\sim}1\;m$, illustrating the improvement in accuracy resulting from stacking. It is concluded that a carefully calibrated airborne TEM system has potential for surveying sediment thickness and bedrock topography, and for characterising seafloor resistivity in shallow coastal waters.

• Journal of the Microelectronics and Packaging Society
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• v.9 no.4
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• pp.17-23
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• 2002

The more productive and stable fabrication can be obtained by applying chemical mechanical polishing (CMP) process to shallow trench isolation (STI) structure in 0.18 $\mu\textrm{m}$ semiconductor device. However, STI-CMP process became more complex, and some kinds of defect such as nitride residue, tern oxide defect were seriously increased. Defects like nitride residue and silicon damage after STI-CMP process were discussed to accomplish its optimum process condition. In this paper, we studied how to reduce torn oxide defects and nitride residue after STI-CMP process. To understand its optimum process condition, We studied overall STI-related processes including trench depth, STI-fill thickness and post-CMP thickness. As an experimental result showed that as the STI-fill thickness becomes thinner, and trench depth gets deeper, more tern oxide were found in the CMP process. Also, we could conclude that low trench depth whereas high CMP thickness can cause nitride residue, and high trench depth and over-polishing can cause silicon damage.

• Geomechanics and Engineering
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• v.21 no.1
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• pp.11-21
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• 2020

The traditional formulations for estimation of bearing capacity in rock mechanics assume a homogeneous and isotropic rock mass. However, it is common that the rock mass consists of different layers of different rock properties or of the same rock matrix with distinct geotechnical quality levels. The bearing capacity of a heterogeneous rock is estimated traditionally through the weighted average. In this paper, the solution of the weighted average is compared to the finite difference method applied to a bilayer rock mass. The influence of different parameters such as the thickness of the layers, the rock type, the uniaxial compressive strength and the overall geotechnical quality of the rock mass on the bearing capacity of a bilayer rock mass is analyzed. A parametric study by finite difference method is carried out to develop a bearing capacity factor in function of the layer thickness and the rock mass quality expressed in terms of the geological strength index, which is presented in a form of a chart. Therefore, this correlation factor allows estimating the bearing capacity of a rock mass that is formed by two layers with distinct GSI, depending on the bearing capacity of the rock mass formed only by the upper layer and considered by that way as homogenous and isotropic rock mass.

• Proceedings of the KIEE Conference
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• 1987.07a
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• pp.465-468
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• 1987

This paper describes a model to calculate the equilibrium electron density of MODFET at the interface that takes into account the simultaneous shallow and deep level in the Al-GaAs layer. In the present study we have made an investigation of the interface electron density with different values of the AlGaAs doping density and spacer layer thickness, considering simultaneously two doner levels. In this case, the ratio of the shallow to the deep donor concentraction is considered. From the comparison with early experimental results we could find the deep level and that the deep donor concentration is about 50% with the Al mole fraction X ${\sim}0.3$, activation energy Edx=65meV, temperature $77^{\circ}K$ and spacer thickness range $50A{\sim}100A$. Also we have investigated the effect of the temperature. As temperature increase, at critical mole fraction X the nature of the donor concentration changes from $\Gamma$ to L and X.

• Structural Engineering and Mechanics
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• v.89 no.1
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• pp.33-46
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• 2024

The present research delves into the analysis of nonlinear free and forced vibrations of porous functionally graded (FG) shallow shells reinforced with oblique stiffeners, which are embedded in a nonlinear elastic foundation (NEF) subjected to external excitation. Two distinct types of PFG shallow shells, characterized by even and uneven porosity distribution along the thickness direction, are considered in the research. In order to model the stiffeners, Lekhnitskii's smeared stiffeners technique is implemented. With the stress function and first-order shear deformation theory (FSDT), the nonlinear model of the oblique stiffened shallow shells is established. The strain-displacement relationships for the system are derived via the FSDT and utilization of the von-Kármán's geometric assumptions. To discretize the nonlinear governing equations, the Galerkin method is employed. The model such developed allows analysis of the effects of the stiffeners with various angles as desired, in addition to the quantitative investigation on the influence of the surrounding nonlinear elastic foundations. To numerically solve the problem of vibrations, the 4th-order P-T method is used, as this method, known for its enhanced accuracy and reliability, proves to be an effective choice. The validation of the present research findings includes a comprehensive comparison with outcomes documented in existing literature. Additionally, a comparative analysis of the numerical results against those obtained using the 4th Runge-Kutta method is performed. The impact of stiffeners with varying angles and material parameters on the vibration characteristics of the present system is also explored. The researchers and engineers working in this field may use the results of this study as benchmarks in their design and research for the considered shell systems.

• Journal of Korean Association for Spatial Structures
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• v.1 no.2 s.2
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• pp.85-92
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• 2001

The structural behaviors of anisotropic laminated shells are quite different from that of isotropic shells, Also, the classical theory of shells based on neglecting transverse shear deformation is invalid for laminated shells. Thus, to obtain the more exact behavior of laminated shells, effects of shear deformation should be considered in the analysis. As the length of x-axis or y-axis is increase, the effects of transverse shear deformation are decrease because the stiffness for the axis according to the increasing of length is large gradually. In this paper, the governing equations for anisotropic laminated shallow shell including the effects of shear deformation are derived. And then, by using Navier's solutions for shallow shells having simple supported boundary, extensive numerical studies for anisotropic laminated shallow shells were made to investigate the effects of shear deformation for 3 typical shells. Also, static analysis is carried out for cross-ply laminated shells considering the effects of various geometrical parameters, e,g., the shallowness ratio, the thickness ratio and the ratio of a(length of x-axis)-to-b(length of y-axis). The results are compared with existed one and show good agreement.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 2002.10b
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• pp.443-444
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• 2002

The uniformity of field oxide is critical to isolation property of device in STI, so the control of field oxide thickness in STI-CMP becomes enormously important. The loss of field oxide in shallow trench isolation comes mainly from dishing and erosion in STI-CMP. In this paper, the effect of slurries on the dishing was investigated with both blanket and patterned wafers were selected to measure the removal rate, selectivity and dishing amount. Dishing was a strong function of pattern spacing and types of slurries. Dishing was significantly decreased with decreasing pattern spacing for both slurries. Significantly lower dishing with ceria based slurry than with silica based slurry were achieved when narrow pattern spacing were used. Possible dishing mechanism with two different slurries were discussed based on the observed experimental results.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.40 no.9
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• pp.638-643
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• 2003

Channel width dependence of hot-carrier effect in nMOSFET with shallow trench isolation is analyzed. $I_{sub}$- $V_{G}$ and $\Delta$ $I_{ㅇ}$ measurement data show that MOSFETs with narrow channel-width are more susceptible to the hot-carrier degradation than MOSFETs with wide channel-width. By analysing $I_{sub}$/ $I_{D}$, linear $I_{D}$- $V_{G}$ characteristics, thicker oxide-thickness at the STI edge is identified as the reason for the channel-width dependent hot-carrier degradation. Using the charge-pumping method, $N_{it}$ generation due to the drain avalanche hot-carrier (DAHC) and channel hot-electron (CHE) stress are compared. are compared.