• 한국소성가공학회:학술대회논문집
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• 한국소성가공학회 2003년도 춘계학술대회논문집
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• pp.339-342
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• 2003

This paper newly proposes a mesh regularization method for the enhancement of the efficiency in sheet metal forming analysis. The regularization method searches for distorted elements with appropriate searching criteria and constructs patches including the elements to be modified. Each patch is then extended to a three-dimensional surface in order to obtain the information of the continuous coordinates. In constructing the surface enclosing each patch, NURBS(Non-Uniform Rational B-Spline) surface is employed to describe a three-dimensional free surface. On the basis of the constructed surface, each node is properly arranged to form unit elements as close as to a square. The analysis results with the proposed method are compared to the results from the direct forming analysis without mesh regularization in order to confirm the validity of the method.

• Structural Engineering and Mechanics
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• 제30권2호
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• pp.225-245
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• 2008

T-splines are recently proposed mathematical tools for geometric modeling, which are generalizations of B-splines. Local refinement can be performed effectively using T-splines while it is not the case when B-splines or NURBS are used. Using T-splines, patches with unmatched boundaries can be combined easily without special techniques. In the present study, an analysis framework using T-splines is proposed. In this framework, T-splines are used both for description of geometries and for approximation of solution spaces. This analysis framework can be a basis of a CAD/CAE integrated approach. In this approach, CAD models are directly imported as the analysis models without additional finite element modeling. Some numerical examples are presented to illustrate the effectiveness of the current analysis framework.

• 소성∙가공
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• 제12권4호
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• pp.401-407
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• 2003

This paper newly proposes a mesh regularization method for the enhancement of the efficiency in sheet metal forming analysis. The regularization method searches for distorted elements with appropriate searching criteria and constructs patches including the elements to be modified. Each patch is then extended to a three-dimensional surface in order to obtain the information of the continuous coordinates. In constructing the surface enclosing each patch, NURBS(Non-Uniform Rational B-Spline) surface is employed to describe a three-dimensional free surface. On the basis of the constructed surface, each node is properly arranged to form unit elements as close as to a square. The state variables calculated from its original mesh geometry are mapped into the new mesh geometry for the next stage or incremental step of a forming analysis. The analysis results with the proposed method are compared to the results from the direct forming analysis without mesh regularization in order to confirm the validity of the method.

• 대한건축학회논문집:구조계
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• 제35권9호
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• pp.171-182
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• 2019

Isogeometric concept is introduced to carry out free vibration analysis of plane structures. The geometry of structures is represented by using non-uniform rational B-spline surface (NURBS) and its basis function is consistently used in the formulation of plane stress element. In addition, multi-patch strategy is introduced to deal with the openings in building. The performance of the present isogeometric plane stress element is investigated by using five numerical examples. From numerical results, it is found to be that the isogeometric concept can successfully identify reliable natural frequencies and associated mode shapes of plane structures with/without openings in efficient way.

• 한국전산구조공학회논문집
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• 제25권6호
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• pp.497-504
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• 2012

유한요소 해석법에서는 CAD 모델을 유한요소 모델로 이산화하기 때문에 CAD와 해석 모델의 차이로 인해 형상 설계민감도 및 최적설계에서 설계영역 매개 변수화에 어려움이 있다. 반면에 아이소-지오메트릭 해석법은 CAD 모델과 동일한 NURBS 기저함수와 조정점을 해석에 이용함으로써 설계의 기하학적 변화를 해석모델에 직접적으로 표현할 수 있기 때문에 전술된 여러 어려움들을 개선할 수 있다. 본 연구에서는 일반 곡면 좌표계에서 아이소-지오메트릭 해석 모델을 정식화하여 곡면 부재에 대한 구조해석과 형상 설계민감도 해석을 수행하였다. 아이소-지오메트릭 해석에서는 법선, 접선, 곡률 등과 같은 고차의 기하학적 정보들이 엄밀하게 표현될 수 있기 때문에 주어진 CAD 모델에 적합한 일반 곡면 좌표계를 생성해 낼 수 있다. 기존의 아이소-지오메트릭 구조해석 및 설계민감도 해석 결과와 비교하여 제안된 해석방법론이 더 정확한 해와 더 빠른 수렴성을 보이는 것을 확인하였다.

• 한국전산구조공학회논문집
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• 제27권3호
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• pp.155-162
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• 2014

본 논문에서는 아이소-지오메트릭 해석법을 이용하여 고주파수를 가지는 파워흐름 문제에 대하여 연속체 기반 형상 최적 설계를 수행하였다. 아이소-지오메트릭 기법을 형상 최적설계에 적용하면, CAD 기하 모델링에서 쓰이던 NURBS 기저 함수가 직접 쓸 수 있기에 정확한 기하학 정보가 수치계산에서 고려되고, 이에 따라 형상 최적설계 관점에서 볼 때, 전통적인 유한요소법에 비해 향상되고 부드러운 설계 섭동량을 가지는 설계 매개화가 가능하게 된다. 즉, 정확한 기하 모델이 응답 해석과 설계민감도 해석에 쓰이게 되고, 이에 따라 설계영역 전체에서 법선 벡터와 곡률이 연속적으로 되게 된다. 결과적으로 정밀한 민감도 해석이 가능하게 된다. 몇 가지 수치예제를 통하여 개발된 아이소-지오메트릭 설계민감도가 유한차분 설계민감도와 비교하여 정확성을 확인할 수 있었으며, 형상 최적설계 문제를 통해서 본 방법론을 적용하여 검증하였다.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1994년도 추계학술대회 논문집
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• pp.866-871
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• 1994

B-spline curves and surfaces are effective solutions for design and modelling of the freeform models. The control methods of these are using with control points, knot vectors and weight of NURBS. Using control point is easy and resonable for representation of general models. But the movement of control points bring out the reformation of original convex hull. The B-splines with nonuniform knot vector provide good result of the shape modification without convex hull reforming. B-splines are constructed with control points and basis functions. Nonuniform knot vectors effect on the basis functions. And the blending curves describe the prorities of knot vectors. Applying of these, users will forecast of the reformed curves after modifying controllabler primitives.

• Structural Engineering and Mechanics
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• 제88권1호
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• pp.83-94
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• 2023

An accurate and highly efficient inverse element labelled iPCB is developed based on the inverse finite element method (iFEM) for real-time shape estimation of plane-curved structures (such as arch bridges) utilizing onboard strain data. This inverse problem, named shape sensing, is vital for the design of smart structures and structural health monitoring (SHM) procedures. The iPCB formulation is defined based on a least-squares variational principle that employs curved Timoshenko beam theory as its baseline. The accurate strain-displacement relationship considering tension-bending coupling is used to establish theoretical and measured section strains. The displacement fields of the isoparametric element iPCB are interpolated utilizing nonuniform rational B-spline (NURBS) basis functions, enabling exact geometric modelling even with a very coarse mesh density. The present formulation is completely free from membrane and shear locking. Numerical validation examples for different curved structures subjected to different loading conditions have been performed and have demonstrated the excellent prediction capability of iPCBs. The present formulation has also been shown to be practical and robust since relatively accurate predictions can be obtained even omitting the shear deformation contributions and considering polluted strain measures. The current element offers a promising tool for real-time shape estimation of plane-curved structures.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2007년도 정기 학술대회 논문집
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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.

• 한국전산구조공학회논문집
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• 제24권1호
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• pp.61-67
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• 2011

본 연구는 구조 시스템에서 중요 부위, 즉 응력이 집중되는 영역에서의 형상 최적화를 다룬 것이다. 등기하 해석은 기하학적 모델링(CAD)과 수치적 해석(CAE)을 통합하는 효율적인 방법으로 잘 알려져 있다. 이는 NURBS에 의한 기하학적 모델링을 직접 이용함으로써 이루어 질 수 있다. 본 연구에서는 등기하 개념을 도입한 효율적인 구조해석 컴퓨터 코드를 개발하였다. 여기에서는 CAD에 대한 정보를 유한요소 모델링에 직접 이용할 수 있다. 본 연구에서 개발한 코드의 타당성을 보이기 위해, 본 연구에서 개발한 코드에 의한 구조해석 결과를 유한요소해석 상용 패키지인 MSC/NASTRAN에 의한 결과와 비교하였다. 구조역학적인 문제에서 최적화를 다룰 수 있도록 본 연구의 등기하 해석 과정을 최적화 과정과 통합하였다. 본 시스템을 브라켓이 있는 외팔 구조의 형상 최적화에 성공적으로 적용하였다. 본 연구를 통해 개발한 시스템의 타당성을 검증하였다. 이 논문의 끝 부분에서는 본 연구방법의 실용적 적용성과 추후 연구에 대해 언급하였다.