• Structural Engineering and Mechanics
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• v.60 no.2
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• pp.313-335
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• 2016

In this article, a four-variable refined plate theory is presented for buckling analysis of functionally graded plates subjected to uniform, linear and non-linear temperature rises across the thickness direction. The theory accounts for parabolic distribution of the transverse shear strains, and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. Young's modulus and Poisson ratio of the FGM plates are assumed to remain constant throughout the entire plate. However, the coefficient of thermal expansion of the FGM plate varies according to a power law form through the thickness coordinate. Equilibrium and stability equations are derived based on the present theory. The influences of many plate parameters on buckling temperature difference such ratio of thermal expansion, aspect ratio, side-to-thickness ratio and gradient index will be investigated.

• Journal of electromagnetic engineering and science
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• v.12 no.1
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• pp.128-134
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• 2012

In this manuscript, we consider electromagnetic imaging of perfectly conducting cracks completely hidden in a homogeneous material via boundary measurements. For this purpose, we carefully derive a topological derivative formula based on the asymptotic expansion formula for the existence of a perfectly conducting inclusion with a small radius. With this, we introduce a topological derivative based imaging algorithm and discuss its properties. Various numerical examples with noisy data show the effectiveness and limitations of the imaging algorithm.

• 전기의세계
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• v.29 no.4
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• pp.256-259
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• 1980

A singular pertubation theory is applied to obtain an approximate solution for suboptimal control of nuclear reactors with spatially distributed parameters. The inverse of the neutron velocity is regarded as a small perturbing parameter, and the model, adopted for simplicity, is a cylindrically symmetrical reactor whose dynamics are described by the one group diffusion equation with one delayed neutron group. The Helmholtz mode expansion is used for the application of the optimal theory for lumped parameter systems to the spatially distributed parameter systems. An asymptotic expansion of the feedback gain matrix is obtained with construction of the boundary layer correction up to the first order.

• Journal of electromagnetic engineering and science
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• v.11 no.1
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• pp.56-61
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• 2011

In this paper, we consider the topological derivative concept for developing a fast imaging algorithm of thin inclusions with dielectric contrast with respect to an embedding homogeneous domain with a smooth boundary. The topological derivative is evaluated by applying asymptotic expansion formulas in the presence of small, perfectly conducting cracks. Through the careful derivation, we can design a one-iteration imaging algorithm by solving an adjoint problem. Numerical experiments verify that this algorithm is fast, effective, and stable.

• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.389-400
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• 2023

In this paper, some estimations will be given for the analytic functions belonging to the class 𝓡(α). In these estimations, an upper bound and a lower bound will be determined for the first coefficient of the expansion of the analytic function h(z) and the modulus of the angular derivative of the function ${\frac{zh^{\prime}(z)}{h(z)}}$, respectively. Also, the relationship between the coefficients of the analytical function h(z) and the derivative mentioned above will be shown.

• Journal of Mechanical Science and Technology
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• v.20 no.1
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• pp.158-166
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• 2006

Extended Graetz problem in microtube is analyzed by using eigenfunction expansion to solve the energy equation. For the eigenvalue problem we applied the shooting method and Galerkin method. The hydrodynamically isothermal developed flow is assumed to enter the microtube with uniform temperature or uniform heat flux boundary condition. The effects of velocity and temperature jump boundary condition on the microtube wall, axial conduction and viscous dissipation are included. From the temperature field obtained, the local Nusselt number distributions on the tube wall are obtained as the dimensionless parameters (Peclet number, Knudsen number, Brinkman number) vary. The fully developed Nusselt number for each boundary condition is obtained also in terms of these parameters.

• Journal of Computational Design and Engineering
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• v.2 no.4
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• pp.268-275
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• 2015

Blisk is an essential component in aero engines. To maintain good aero-dynamic performance, one critical machining requirement for blades on blisk is that the generated five-axis tool path should be boundary-conformed. For a blade discretely modeled as a point cloud or mesh, most existing popular tool path generation methods are unable to meet this requirement. To address this issue, a novel five-axis tool path generation method for a discretized blade on blisk is presented in this paper. An idea called Linear Morphing Cone (LMC) is first proposed, which sets the boundary of the blade as the constraint. Based on this LMC, a CC curve generation and expansion method is then proposed with the specified machining accuracy upheld. Using the proposed tool path generation method, experiments on discretized blades are carried out, whose results show that the generated tool paths are both uniform and boundary-conformed.

• The Bulletin of The Korean Astronomical Society
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• v.40 no.1
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• pp.58.3-59
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• 2015

Dynamical expansion of H II regions plays a key role in dispersing surrounding gas and therefore in limiting the efficiency of star formation in molecular clouds. We use analytic methods and numerical simulations to explore expansions of spherical dusty H II regions, taking into account the effects of direct radiation pressure, gas pressure, and total gravity of the gas and stars. Simulations show that the structure of the ionized zone closely follows Draine (2011)'s static equilibrium model in which radiation pressure acting on gas and dust grains balances the gas pressure gradient. Strong radiation pressure creates a central cavity and a compressed shell at the ionized boundary. We analytically solve for the temporal evolution of a thin shell, finding a good agreement with the numerical experiments. We estimate the minimum star formation efficiency required for a cloud of given mass and size to be destroyed by an HII region expansion. We find that typical giant molecular clouds in the Milky Way can be destroyed by the gas-pressure driven expansion of an H II region, requiring an efficiency of less than a few percent. On the other hand, more dense cluster-forming clouds in starburst environments can be destroyed by the radiation pressure driven expansion, with an efficiency of more than ~30 percent that increases with the mean surface density, independent of the total (gas+stars) mass. The time scale of the expansion is always smaller than the dynamical time scale of the cloud, suggesting that H II regions are likely to be a dominant feedback process in protoclusters before supernova explosions occurs.

• Proceedings of the KSME Conference
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• 2007.05a
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• pp.1581-1584
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• 2007

The safety valve is the important equipment used to protect the pressure vessel and pressure facilities from overpressure by discharging the operation medium when the pressure of system is reaching the design pressure of the system. Some materials for a safety valve disk are studied in this paper. A studied safety valve has to resist sulfurous acid and nitric acid. etc. Furthermore teflon which is a general material of the valve easily sticks to a disk and a sliding part of the valve by thermal expansion. Therefore both teflon and stainless-steel are used to improve these problems. The analysis of the thermal expansion is conducted with commercial FEM software to improve the problems. Boundary conditions were temperature and load in this study. From the analysis, the thermal expansion of by teflon/stainless steel-made valve is lower than that of teflon-made valve under high temperature. Thus, teflon/stainless steel-made valve is safe and no malfunction by thermal expansion.

• Structural Engineering and Mechanics
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• v.58 no.6
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• pp.949-966
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• 2016

The second order analysis taking place due to non-linear behavior of the structures under the mechanical and geometric factors through implementing exact and approximate methods is an indispensible issue in the analysis of such structures. Among the exact methods is the slope-deflection method that due to its simplicity and efficiency of its relationships has always been in consideration. By solving the differential equations of the modified slope-deflection method in which the effect of axial compressive force is considered, the stiffness matrix including trigonometric entries would be obtained. The complexity of computations with trigonometric functions causes replacement with their Maclaurin expansion. In most cases only the first two terms of this expansion are used but to obtain more accurate results, more elements are needed. In this paper, the effect of utilizing higher order terms of Maclaurin expansion on reducing the number of required elements and attaining more rapid convergence with less error is investigated for the Bernoulli beam with various boundary conditions. The results indicate that when using only one element along the beam length, utilizing higher order terms in Maclaurin expansion would reduce the relative error in determining the critical buckling load and kinematic parameters in the second order analysis.