• Computational Structural Engineering
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• v.11 no.4
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• pp.187-196
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• 1998

불연속 갤러킨 정식화에 기초를 둔 시간적분법에 대하여 시간을 변수로 한 유한요소적 접근법을 시도하였다. 단일 형상함수와 두 형상함수 정식화에 대해 각각 선형, 이차 형상함수를 적용하여 모두 네 종류의 시간적분법을 유도하였으며, 각 방법에 대하여 시간시텝의 증가에 따른 변위와 속도의 관계를 나타내는 증폭행렬을 계산하였다. 유도된 방법들의 성능을 평가하기 위하여 부하가 갑자기 변화는 진동 문제를 해석하고 변위의 오차를 비교하였다. 네 가지의 방법에 대하여 국부 오차 추정치를 개발하였으며, 오차 추정치의 정확도를 수치예를 이용하여 평가하였다. 단일 형상함수 정식화에서 이차 형상함수를 이용한 오차 추정치가 실제 국부오차를 잘 나타내었으며 유도된 오차 추정치는 시간간격제어 기법에서 시간간격의 크기를 결정하는 척도로 이용 가능하다.

• The Journal of Korean Institute for Practical Engineering Education
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• v.2 no.2
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• pp.49-54
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• 2010

The functions and their graphs are very important parts in mathematical educations. But there seems be a lot of students studying the functions and their graphs without grasping the meaning of them and without interest with them. We present a learning method of how to match functions and their graphs with outlines of various shapes. That is, outlines of the shapes are assumed to be the graphs of the functions and the graphs will be plotted on the screen of a computer with help of the computer algebra system.

• Computational Structural Engineering
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• v.7 no.3
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• pp.16-23
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• 1994

본 고에서는 형상최적설계에 대한 기초이론이 소개되었다. 재료도함수와 변분법 및 보조변수법에 기초한 형상설계민감도해석 절차는 까다로우며 함수론 등 많은 수학적인 배경을 필요로 한다. 설계민감도가 구해지면 이 정보를 필요로 하는 최적화 알고리즘을 사용하여 형상에 대한 최적해를 구할 수 있으며 그 과정은 재래식 최적설계시와 같다. 구조물 형상최적설게에 있어 형상(영역)변화의 효과는 대부분 경계에서 수직이동의 형태로 나타난다. 따라서 경계면에서 변위나 응력값 등에 대한 정확한 수치해는 성공적인 형상최적화의 중요한 관건이 된다. 따라서 구조해석을 위한 정확한 유한요소해석방법과 형상함수 그리고 경계를 나타내는 적절한 함수들을 지속적으로 개선할 필요가 있다. 반복설계과정 중에서 영역과 경계가 계속 바뀌므로 설계민감도 수치해의 정확도를 높이기 위해 경계요소법과 유한요소법에 기초를 둔 영역법 등을 사용하기도 한다.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.6 no.1
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• pp.61-68
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• 1986

A set of the shape functions which perfectly satisfy the homogeneous Euler Equations has been proposed for deep beam problems. A finite element beam model using the proposed shape functions has been derived by the Galerkin weighted residual method and used to analyze the numerical examples without reduced shear integration, to show the accuracy and efficiency of the proposed shape functions. The result shows that the finite element model using the proposed shape functions gives very accurate solutions for both static and free vibration analyses. The concept of the proposed shape functions is thought to be applied for the finite element analysis of the elasto-static problems.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.22 no.1
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• pp.117-124
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• 2009

The p-convergent boundary element method has been proposed to analyze two-dimensional potential problem on the basis of high order Legendre shape functions that have different property comparing with the shape functions in conventional boundary element method. The location of nodes corresponding to high order shape function are not defined along the boundary, called by nodeless node, similar to the p-convergent finite element method. As the order of shape function increases, the collocation point method is used to solve linear simultaneous equations. The collocation patterns of p-convergent boundary element method consist of non-symmetric hierarchial or symmetric non-hierarchical. As the order of shape function increases, the number of collocation point increases. The singular integral that appears in p-convergent boundary element has been calculated by special numeric quadrature technique and semi-analytical integration technique. The L-shape domain problem including singularity in the vicinity of reentrant comer is analyzed and the numerical results show that the relative error is smaller than $10^{-2}%$ range as compared with other results in literatures. In case of same condition, the symmetric p-collocation point pattern shows high accuracy of solution.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.27 no.3
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• pp.183-189
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• 2014

In this paper, a polyhedral element is presented to solve three-dimensional problems by developing shape functions based on Wachspress coordinates and moving least square approximation. A subdivision of polyhedrons into tetrahedral domains is performed for the construction of shape functions of polyhedral elements, and numerical integration of the weak form is carried out consistently over the tetrahedral domains. The weight functions for moving least square approximation are defined by solving Laplace equation with boundary values based on Wachspress coordinates on polyhedral element faces. Polyhedral elements presented in this paper have similar properties to conventional finite element regarding the continuity, the completeness, the node-element connectivity and the inter-element compatibility. Numerical examples show the effectiveness of the present method for solving three-dimensional problems using polyhedral elements.

• Journal of the Korea Concrete Institute
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• v.14 no.4
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• pp.474-482
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• 2002

The purpose of the study is to establish an optimum geometry and optimum geometry factor through bond test of a structural synthetic fiber, which fully utilizes matrix anchoring without fiber fracturing with the maximum pullout resistance. Seven deformed structural synthetic fibers with widely different geometries were investigated and pullout test was conducted. Included parameters are seven different types of fiber and two of mortar matrixes. The test result shows that the crimped type structural synthetic fiber is significant improvement in the interface toughness(pullout energy) and pullout load. The pullout test was performed with various size of crimped type structural synthetic fiber in order to invest optimum geometry factor, In the basis of the test results, optimum geometry factor is established such as D=b$^{{\alpha}0{\alpha}}$h$^{λ{\beta}}$.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.37 no.3
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• pp.345-352
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• 2013

In this research, a study on stress shape functions was conducted to analyze the contact stress problem by using a hybrid photoelasticity. Because the contact stress problem is generally solved as a half-plane problem, the relationship between two analytical stress functions, which are compositions of the Airy stress function, was similar to one of the crack problem. However, this relationship in itself could not be used to solve the contact stress problem (especially one with singular points). Therefore, to analyze the contact stress problem more correctly, stress shape functions based on the condition of two contact end points had to be considered in the form of these two analytical stress functions. The four types of stress shape functions were related to the stress singularities at the two contact end points. Among them, the primary two types used for the analysis of an O-ring were selected, and their validities were verified in this work.

• Journal of the Korean Society for Railway
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• v.18 no.4
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• pp.279-288
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• 2015

Using the Vehicle Modeling Function, which can model various 3D nose shapes, nose shape optimization is performed to reduce the aerodynamic drag of the KTX Sancheon. 2D characteristic shapes of the KTX Sancheon nose were extracted and a base model of the KTX Sancheon was constructed for design optimization using the Vehicle Modeling Function. The design space was constructed with the base model and does not violate the shape constraints of commercial trains. Through nose shape optimization with the Broyden-Fletcher-Goldfarb-Shanno algorithm, the aerodynamic drag of the optimized shape was reduced by 6% compared to that of the base model. The longer nose and sharper edge of the optimized shape weaken the vortices behind the last car and can reduce the aerodynamic drag.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2011.04a
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• pp.565-568
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• 2011

NURBS는 매개변수를 이용하여 3차원에서 곡면을 표현한 방법으로서 노트벡터, 조정점, 가중치로 구성된다. 레벨셋은 공간을 음함수로 정의된 장으로 형성하여 음함수의 일정한 값을 추적하여 곡면을 표현한 방법이다. 본 논문에서는 스캔 데이터를 NURBS 형태로 추출한 뒤 이를 정밀한 레벨셋 모델로 변환하였다. 레벨셋 모델을 구성하기 위해서 형성된 음함수는 부호를 갖는 거리함수를 사용하였고, 거리함수를 정밀하게 나타내기 위해 Newton 순환법을 이용하였다. 변환된 레벨셋 모델을 이용하여 형상의 몰핑을 수행하였다. 몰핑은 초기 형상을 목표 형상으로 변화시켜 나가는 과정으로서 레벨셋 모델을 이용한 몰핑은 용이성과 질적인 측면에서 우수하다. 수치 예제에서는 스캔 데이터의 레벨셋 모델 변환과 변환된 형상이 자연스럽게 목표형상으로 변화하는지를 확인한다.