• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 1998.03a
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• pp.239-244
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• 1998

ESP(Electronic Speckle Pattern Interferometry) is an optical technique to measure deforamtion of engineering components and materials in industrial areas. ESPI, a non-contact and non-destructive measuring method, is capable of providing full-field results with high spatial resolution and high speed. One of important application aspects using electronic speckle pattern interferometry is to generate contours of a diffuse object in order to provide data for 3-D shape analysis and topography measurement. The electronic speckle contouring is suitable for providing measurement range from millimeters to several centimeters. In this study, we introduce the contouring method by modified dual-beam speckle pattern interferometer and a shift of the two illumination beams through optical fiber in order to obtain the contour fringe patterns. Before the experiments, we performed the geometric analysis for dual-beam-shifted ESPI contouring. And by this geometric analysis, we performed the electronic speckle contouring experiment. We used 4-frame phase shifting method with PZT for quantitative analysis of contour fringes. Finally, we showed good agreements between the geometric analysis and experimental results.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.11a
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• pp.319-324
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• 2001

Free non-linear vibration of a rotating thin ring with a constant speed is analyzed when the ring has both the in-plane and out-of-plane motions. The geometric non-linearity of displacements is considered by adopting the Lagrange strain theory for the circumferential strain. By using Hamilton's principle, the coupled non-linear partial differential equations are derived, which describe the out-of-plane and in-plane bending, extensional and torsional motions. The natural frequencies are calculated from the linearized equations at various rotational speeds. Finally, the computation results from three non-linear models are compared with those from a linear model. Based on the comparison, this study recommends which model is appropriate to describe the non- linear behavior more precisely.

• Kyungpook Mathematical Journal
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• v.50 no.2
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• pp.213-228
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• 2010

A weighted version of the geometric mean of k ($\geq\;3$) positive invertible operators is given. For operators $A_1,{\ldots},A_k$ and for nonnegative numbers ${\alpha}_1,\ldots,{\alpha}_k$ such that $\sum_\limits_{i=1}^k\;\alpha_i=1$, we define weighted geometric means of two types, the first type by a direct construction through symmetrization procedure, and the second type by an indirect construction through the non-weighted (or uniformly weighted) geometric mean. Both of them reduce to $A_1^{\alpha_1}{\cdots}A_k^{{\alpha}_k}$ if $A_1,{\ldots},A_k$ commute with each other. The first type does not have the property of permutation invariance, but satisfies a weaker one with respect to permutation invariance. The second type has the property of permutation invariance. We also show a reverse inequality for the arithmetic-geometric mean inequality of the weighted version.

• Korean Journal of Computational Design and Engineering
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• v.3 no.1
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• pp.1-14
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• 1998

This paper introduces non-manifold offsetting operations, which add or remove a uniform thickness from a given non-manifold model. Since these operations can be applied to not only solids but also wireframe or sheet objects, they are potentially useful for pipeline modeling, sheet metal and plastic part modeling, tolerance analysis, clearance checking, constant-radius rounding and filleting of solids, converting of abstracted models to solids, HC too1 path generation and so on. This paper describes mathematical properties and algorithms for non-manifold offsetting. In this algorithm, a sufficient set of tentative faces are generated first by offsetting all or a subset of the vertices, edges and faces of the non-manifold model. And then they are merged into a model using the Boolean operations. Finally topological entities which are within offset distance are removed. The partially modified offsetting algorithms for wireframes or sheets are also discussed in order to provide more practical offset models.

• Steel and Composite Structures
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• v.45 no.5
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• pp.621-640
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• 2022

In the present article, the vibration response of a geometrically imperfect bi-directional functionally graded plate (2D-FGP) with geometric discontinuities and micro-structural defects (porosities) has been investigated. A porosity model has been developed to incorporate the effective material properties of the bi-directional FGP which varies in two directions i.e. along the axial and transverse direction. The geometric discontinuity is also introduced in the plate in the form of a circular cut-out at the center of the plate. The structural kinematic formulation is based on the non-polynomial trigonometric higher-order shear deformation theory (HSDT). Finite element formulation is done using C° continuous Lagrangian quadrilateral four-noded element with seven degrees of freedom per node. The equations of motion have been derived using a variational approach. Convergence and validation studies have been documented to confirm the accuracy and efficiency of the present formulation. A detailed investigation study has been done to evaluate the influence of the circular cut-out, geometric imperfection, porosity inclusions, partial supports, volume fraction indexes (along with the thickness and length), and geometrical configurations on the vibration response of 2D-FGP. It is concluded that after a particular cut-out dimension, the vibration response of the 2D FGP exhibits non-monotonic behavior.

• Journal of Korean Society of Transportation
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• v.32 no.2
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• pp.170-178
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• 2014

Until now, several research on the relationship of traffic crash occurrences and geometric had been conducted and revealed that projects of road alignment, geometric improvement and hazardous segment selection reduced the number of accidents and accident severities. However, such variables did not consider the non-homogeneous characteristics of roadway segments due to the difficulty of data collection, which results in under-estimation of the standard error affecting the overall modeling goodness-of-fit. This study highlights the importance of non-homogeneity by looking at the effect of the non-homogeneous geometric variables through the modeling process. The model delivers meaningful results when using some geometric variables without relevant geometrics' variables.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.725-733
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• 2011

The characteristic connection is a good substitute for the Levi-Civita connection, especially in studying non-integrable geometries. Unfortunately, not every geometric structure has the characteristic connection. In this paper we consider the space $U(3)/(U(1){\times}U(1){\times}U(1))$ with an almost Hermitian structure and prove that it has a geometric structure admitting the characteristic connection.

• The Journal of Korean Association of Computer Education
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• v.8 no.1
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• pp.73-80
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• 2005

To achieve a natural and plausible interaction with deformable objects and to setup the desirable initial conditions of simulation, user should be able to define and control the geometric constraints intuitively. In addition, user should be able to utilize the simulation as a problem solving platform by experimenting various simulation situations without major modification of the simulator. The proposed physically based geometric constraint simulation system solves the problem using a non-linear finite element method approach to represent deformable objects and constraint forces are generated by defining geometric constraints on the nodes of the object to maintain the restriction. It allows user to define and modify geometric constraints and an algorithm converts these geometric constraints into constraint forces which seamlessly integrate controllability to the simulation system. Simulator can handle linear, angular, inequality based geometric constraints on the objects. Our experimental results show that constraints are maintained in the tight error bound and preserve desired shape of deformable object during the entire simulation.

• Journal of the Korean Mathematical Society
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• v.46 no.4
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• pp.859-893
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• 2009

In this article, we will characterize structures of geometric quotient orbifolds of G-manifold of genus two where G is a finite group of orientation preserving diffeomorphisms using the idea of handlebody orbifolds. By using the characterization, we will deduce the candidates of possible non-hyperbolic geometric quotient orbifolds case by case using W. Dunbar's work. In addition, if the G-manifold is compact, closed and the quotient orbifold's geometry is hyperbolic then we can show that the fundamental group of the quotient orbifold cannot be in the class D.

• Structural Engineering and Mechanics
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• v.88 no.4
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• pp.355-368
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• 2023

Employing the non-local strain gradient theory (NSGT), this paper investigates the nonlinear resonance characteristics of functionally graded material (FGM) nanoshells with initial geometric imperfection for the first time. The effective material properties of the porous FGM nanoshells with even distribution of porosities are estimated by a modified power-law model. With the guidance of Love's thin shell theory and considering initial geometric imperfection, the strain equations of the shells are obtained. In order to characterize the small-scale effect of the nanoshells, the nonlocal parameter and strain gradient parameter are introduced. Subsequently, the Euler-Lagrange principle was used to derive the motion equations. Considering three boundary conditions, the Galerkin principle combined with the modified Lindstedt Poincare (MLP) method are employed to discretize and solve the motion equations. Finally, the effects of initial geometric imperfection, functional gradient index, strain gradient parameters, non-local parameters and porosity volume fraction on the nonlinear resonance of the porous FGM nanoshells are examined.