• Journal of the Korean Society for Precision Engineering
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• v.27 no.11
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• pp.98-105
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• 2010

In this paper, double ball-bar is used to estimate the geometric errors of a rotary table, which includes one-axial motion, two-radial motions and two-tilt motions, except the angular positioning error. To simplify the measurement procedures, three measurement steps have been designed and developed. At each measurement step, one end of the double ball-bar is fixed at the nose of spindle and the other end is located on the rotary table. And specific circular test path is planned to keep the distance between two balls as constant at ideal case. The relationship including the geometric errors of a rotary table and the measured distance between two balls which is distorted by the geometric errors is defined by using ball-bar equation. Each geometric error is modeled as $4^{th}$ order polynomial considering $C^1$-continuity. Finally the coefficients of polynomial are calculated by least-square method. Simulation is done to check the validation of the suggested method considering set-up errors and measurement noise. Suggested method is applied to estimate geometric errors of a rotary table of a 5-axis machine tool.

• The Transactions of the Korea Information Processing Society
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• v.7 no.4
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• pp.1271-1278
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• 2000

A general curve and surface is a basic method to generate Free-form object using the fundamental properties of blending function. In typical method, there is an overhead of calculating to present Free-form object with the line segments and interpolation algorithm, In this paper, for resolving this problem efficiently, it will propose the flexible Free-form curves/surfaces using Ball curve shape-preserving property. This method includes Geometric Continuity that is needed to design Free-form Surface of high degree consisted with many curves. Also, when lots of data are reduced using Geometric Property of Free-form curves, the shape-preserving property of resulting object can be maintained, then it can represent any Free-form object with less calculating .

• Journal of the Korean Society for Precision Engineering
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• v.16 no.5 s.98
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• pp.160-168
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• 1999

This paper describes one method of reverse engineering that machines a free form shape without descriptive model. A portable five-axes 3D CMM was used to digitize point data from physical model. After approximation by rational B-spline curve from digitized point data of a geometric shape, a surface was constructed by the skinning method of the cross-sectional design technique. Since a surface patch was segmented by fifteen part, surface merging was also implemented to assure the surface boundary continuity. Finally, composite surface was transferred to commercial CAD/CAM system through IFES translation in order to machine the modeled geometric shape.

• Honam Mathematical Journal
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• v.30 no.2
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• pp.207-217
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• 2008

Digital geometry has strongly contributed to the study of a discrete topological space $X{\subset}{\mathbf{Z}}^n$ with k-adjacency of ${\mathbf{Z}}^n$. As a survey-type article, we review various utilities of digital geometry.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.4
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• pp.257-265
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• 2009

In this paper we find an explicit form of upper bound of Hausdorff distance between given cubic spline curve and its quadratic spline approximation. As an application the approximation of offset curve of cubic spline curve is presented using our explicit error analysis. The offset curve of quadratic spline curve is exact rational spline curve of degree six, which is also an approximation of the offset curve of cubic spline curve.

• Communications of the Korean Mathematical Society
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• v.22 no.4
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• pp.641-648
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• 2007

In this paper, we present the exact Hausdorff distance between the offset curve of quadratic $B\'{e}zier$ curve and its quadratic $GC^1$ approximation. To illustrate the formula for the Hausdorff distance, we give an example of the quadratic $GC^1$ approximation of the offset curve of a quadratic $B\'{e}zier$ curve.

• Structural Engineering and Mechanics
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• v.62 no.3
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• pp.345-355
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• 2017

The aim of the present study is to develop an elemental approach based on the differential quadrature method for free vibration analysis of cracked thin plate structures. For this purpose, the equations of motion are established using the classical plate theory. The well-known Generalized Differential Quadrature Method (GDQM) is utilized to discretize the governing equations on each computational subdomain or element. In this method, the differential terms of a quantity field at a specific computational point should be expressed in a series form of the related quantity at all other sampling points along the domain. However, the existence of any geometric discontinuity, such as a crack, in a computational domain causes some problems in the calculation of differential terms. In order to resolve this problem, the multi-block or elemental strategy is implemented to divide such geometry into several subdomains. By constructing the appropriate continuity conditions at each interface between adjacent elements and a crack tip, the whole discretized governing equations of the structure can be established. Therefore, the free vibration analysis of a cracked thin plate will be provided via the achieved eigenvalue problem. The obtained results show a good agreement in comparison with those found by finite element method.

• Steel and Composite Structures
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• v.43 no.5
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• pp.603-623
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• 2022

This article is dedicated to predict the natural frequencies of joined conical shell structures made of Functionally Graded Material (FGM). The structure includes two conical segments. The equivalent material properties are found by using the rule of mixture based on Voigt model. In addition, three well-known patterns are employed for distribution of material properties throughout the thickness of the structure. The main objective of the present research is to propose a novel exponential pattern and obtain the related equivalent material properties. Furthermore, the Donnell type shell theory is used to obtain the governing equations of motion. Note that these equations are obtained by employing First-order Shear Deformation Theory (FSDT). In order to discretize the governing system of differential equations, well-known and efficient semi-analytical scheme, namely Generalized Differential Quadrature Method (GDQM), is utilized. Different boundary conditions are considered for various types of single and joined conical shell structures. Moreover, an applicable modification is considered for the continuity conditions at intersection position. In the first step, the proposed formulation is verified by solving some well-known benchmark problems. Besides, some new numerical examples are analyzed to show the accuracy and high capability of the suggested technique. Additionally, several geometric and material parameters are studied numerically.

• Journal of Ocean Engineering and Technology
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• v.22 no.2
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• pp.78-84
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• 2008

As a preliminary step to build a complete superyacht hull design program, the development of superyacht profile design system is introduced. The two-dimensional hull profile is decomposed into four local zones depending upon the functionality and connecting continuity of the profile. Characteristics of each zone are investigated and used to generate the model describing the geometric shape of zone using freeform curves. A set of design parameters is derived from the established geometric model. Generation and modification of a model are is by manipulating the chosen parameters. Four zones designed are integrated to form a final profile. An interactive design system performing all the modeling and modification processes is implemented using the graphic user interface system based an Microsoft Foundation Class and OpenCASCADE, a open graphic library. The shapes of the profiles generated by the developed design system are verified with those of built superyachts. The developed design system will be used for the construction of three-dimensional superyacht hull modeling system.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.577-582
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• 2007

A variational formulation for plane elasticity problems is derived based on an isogeometric approach. The isogeometric analysis is an emerging methodology such that the basis functions in analysis domain arc generated directly from NURBS (Non-Uniform Rational B-Splines) geometry. Thus. the solution space can be represented in terms of the same functions to represent the geometry. The coefficients of basis functions or the control variables play the role of degrees-of-freedom. Furthermore, due to h-. p-, and k-refinement schemes, the high order geometric features can be described exactly and easily without tedious re-meshing process. The isogeometric sensitivity analysis method enables us to analyze arbitrarily shaped structures without re-meshing. Also, it provides a precise construction method of finite element model to exactly represent geometry using B-spline base functions in CAD geometric modeling. To obtain precise shape sensitivity, the normal and curvature of boundary should be taken into account in the shape sensitivity expressions. However, in conventional finite element methods, the normal information is inaccurate and the curvature is generally missing due to the use of linear interpolation functions. A continuum-based adjoint sensitivity analysis method using the isogeometric approach is derived for the plane elasticity problems. The conventional shape optimization using the finite element method has some difficulties in the parameterization of boundary. In isogeometric analysis, however, the geometric properties arc already embedded in the B-spline shape functions and control points. The perturbation of control points in isogeometric analysis automatically results in shape changes. Using the conventional finite clement method, the inter-element continuity of the design space is not guaranteed so that the normal vector and curvature arc not accurate enough. On tile other hand, in isogeometric analysis, these values arc continuous over the whole design space so that accurate shape sensitivity can be obtained. Through numerical examples, the developed isogeometric sensitivity analysis method is verified to show excellent agreement with finite difference sensitivity.