• 대한전기학회논문지:전기기기및에너지변환시스템부문B
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• 제53권8호
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• pp.469-476
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• 2004

In this paper, a 3D shape optimization algorithm which guarantees a smooth optimal shape is presented using parameterized sensitivity analysis. The design surface is parameterized using Bezier spline and B-spline, and the control points of the spline are taken as the design variables. The parameterized sensitivity for the control points are found from that for nodal points. The design sensitivity and adjoint variable formulae are also derived for the 3D non-linear problems. Through an application to the shape optimization of 3D electromagnet to get a uniform magnetic field, the effectiveness of the proposed algorithm is shown.

• Journal of Mechanical Science and Technology
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• 제18권1호
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• pp.82-91
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• 2004

This article deals with a minimum energy control law of S-CVT connected to a dc motor. The S-CVT can smoothly transit between the forward, neutral, and reverse states without any brakes or clutches, and its compact and simple design and its relatively simple control make it particularly effective for mechanical systems in which excessively large torques are not required. And such an S-CVT equipped power transmission has the advantage of being able to operate the power sources in their regions of maximum efficiency, thereby improving the energy efficiency of the transmission system. The S-CVT was intended to primarily for use in small power capacity transmissions, thus a dc motor was considered here as the power source. We first review the structure and operating principles of the S-CVT, including experimental results of its performance. And then we describe a minimum energy control law of S-CVT connected to a do motor. To do this, we describe the results of an analysis of the dynamics of an S-CVT equipped power transmission and the power efficiency of a DC motor. The minimum energy control design is carried out via B-spline parameterization. And we show numerical results obtained from simulations illustrate the validity of our minimum energy control design, benchmarked with a computed torque control algorithm for S-CVT.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1998년도 하계학술대회 논문집 A
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• pp.146-148
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• 1998

For the shape design of electromagnetic devices using the FEM, the choice of design parameters influence to the success of the optimization process. If the design parameter distribution has a one to one corespondence with finite element model, we can encounter not only serious accuracy problem but also obtain a zigzag shape along the interface. The nodes between those design parameters can be parameterized by interpolating using one among many interpolation methods. The conventional parameterization of design parameters has a limit of application for shape, because design parameters and movable nodes are linearly intepolated. In this paper, using the B-spline curve that use to present any interfaces in computer graphics, the curvilinear parameterization between design parameters and node points is compared with the linear parameterization.

• 한국멀티미디어학회논문지
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• 제6권7호
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• pp.1302-1311
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• 2003

본 논문에서는 삼각 메쉬에 관한 보다 안정되고 직관적인 새로운 다중해상도 메쉬 편집 기술을 제안한다. 본 논문의 기본 아이디어는 3차원 메쉬 상에서 편집 영역을 선택하여 2차원 영역으로 임베딩을 하는 과정과 사용자에 의해서 정의되는 편집 정보를 보간하는 곡면을 생성하는 과정으로 이루어지며, 이를 통해 편집 영역 안에 있는 다른 꼭지점의 변위 정보를 곡면 함수값으로부터 생성한다. 본 논문에서 사용되는 임베딩 방법은 확장 볼록 조합 매개변수화 방법으로서 임베딩된 2차원 메쉬의 삼각형들은 자기 교차를 하지 않으며 또한 볼록 조합 계수를 정의할 때 모양 유지 방법을 사용하기 때문에 3차원 삼각형의 모양을 제대로 유지할 수 있다. 또한 편집 결과의 영역을 조절할 수 있도록 하기 위하여 다단계 B-스플라인 곡면을 이용하여, 상호작용적이며 직관적이어서 보다 안정되고 효율적인 메쉬 편집 결과를 얻을 수 있다.

• 한국전산구조공학회논문집
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• 제20권3호
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• pp.339-345
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• 2007

본 논문에서는 등기하 해석법을 이용하여 평면 탄성문제의 변분식을 유도하였다. 등기하 해석법은 새로이 부각되고 있는 해석법으로서 기저 함수가 NURBS(Non-Uniform Rational B-Splines) 로부터 직접 생성되므로 해 공간은 CAD 모델을 구성하는 함수로써 표현된다. 또한 CAD 모델의 B-Spline 기저 함수를 직접 사용하므로 기하학적으로 엄밀한 형상을 표현할 수 있고 요소망의 재구성 없이 해석모델을 정밀화(Refinement)할 수 있는 강점이 있다. 본 논문에서는 이를 확장하여 연속체 기반의 애드조인트 설계 민감도 해석법을 사용하는 등기하 설계민감도 해석법을 유도하였다. 기존의 유한요소 기반형상 최적설계는 형상의 매개화에 어려움을 겪었으나 등기하 기반 최적설계에서는 기하학적 정보가 이미 B-spline 기저함수와 조정점에 포함되어 있으므로 이러한 어려움을 피할 수 있는 잠재력을 가지고 있다. 몇몇 수치 예제를 통해서 등기하 해석법을 사용한 설계 민감도 해석을 수행하였으며 유한차분 민감도와 비교하여 정확성을 확인하였다.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2004년도 추계학술대회 논문집 전기기기 및 에너지변환시스템부문
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• pp.70-72
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• 2004

The ferromagnetic pole piece of permanent magnet assembly for magnetic resonance imaging(MRI) is optimally designed to get high homogenious magnetic field, taking into account the non-linearity of the magnetic materials. In the design, the pole face is kept smooth and axis-symmetric by using B-spline parameterization, and nonlinear design sensitivity analysis is used for search direction.

• 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.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2008년도 정기 학술대회
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• pp.216-221
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• 2008

Shape design optimization for linear elasticity problem is performed using isogeometric analysis method. In many design optimization problems for real engineering models, initial raw data usually comes from CAD modeler. Then designer should convert this CAD data into finite element mesh data because conventional design optimization tools are generally based on finite element analysis. During this conversion there is some numerical error due to a geometry approximation, which causes accuracy problems in not only response analysis but also design sensitivity analysis. As a remedy of this phenomenon, the isogeometric analysis method is one of the promising approaches of shape design optimization. The main idea of isogeometric analysis is that the basis functions used in analysis is exactly same as ones which represent the geometry, and this geometrically exact model can be used shape sensitivity analysis and design optimization as well. In shape design sensitivity point of view, precise shape sensitivity is very essential for gradient-based optimization. In conventional finite element based optimization, higher order information such as normal vector and curvature term is inaccurate or even missing due to the use of linear interpolation functions. On the other hands, B-spline basis functions have sufficient continuity and their derivatives are smooth enough. Therefore normal vector and curvature terms can be exactly evaluated, which eventually yields precise optimal shapes. In this article, isogeometric analysis method is utilized for the shape design optimization. By virtue of B-spline basis function, an exact geometry can be handled without finite element meshes. Moreover, initial CAD data are used throughout the optimization process, including response analysis, shape sensitivity analysis, design parameterization and shape optimization, without subsequent communication with CAD description.

• Steel and Composite Structures
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• 제37권6호
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• pp.663-678
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• 2020

This paper proposes a novel topology optimization method generating multiple materials for external linear plane crack structures based on the combination of IsoGeometric Analysis (IGA) and eXtended Finite Element Method (X-FEM). A so-called eXtended IsoGeometric Analysis (X-IGA) is derived for a mechanical description of a strong discontinuity state's continuous boundaries through the inherited special properties of X-FEM. In X-IGA, control points and patches play the same role with nodes and sub-domains in the finite element method. While being similar to X-FEM, enrichment functions are added to finite element approximation without any mesh generation. The geometry of structures based on basic functions of Non-Uniform Rational B-Splines (NURBS) provides accurate and reliable results. Moreover, the basis function to define the geometry becomes a systematic p-refinement to control the field approximation order without altering the geometry or its parameterization. The accuracy of analytical solutions of X-IGA for the crack problem, which is superior to a conventional X-FEM, guarantees the reliability of the optimal multi-material retrofitting against external cracks through using topology optimization. Topology optimization is applied to the minimal compliance design of two-dimensional plane linear cracked structures retrofitted by multiple distinct materials to prevent the propagation of the present crack pattern. The alternating active-phase algorithm with optimality criteria-based algorithms is employed to update design variables of element densities. Numerical results under different lengths, positions, and angles of given cracks verify the proposed method's efficiency and feasibility in using X-IGA compared to a conventional X-FEM.

• 한국건축시공학회지
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• 제16권6호
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• pp.579-585
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• 2016

3차원 이미지 스캐닝 기술은 복잡한 비정형 건축물의 외피의 정확한 형상과 위치 데이터를 확보하는데 효과적이다. 3차원 이미지 스캐닝 기술의 세부 과정인 점 군집화, 메쉬표면 분리, 넙스 표면 생성, 파라메트릭 솔리드 모델을 통하여 비정형 건축물의 형상을 구축할 수 있다. 이에 본 연구는 비정형 건축물의 외장재 제작과 시공을 위한 3차원 이미지 스캐닝에 의한 역설계 프로세스와 사례 분석을 통하여 시사점을 도출한다. 본 연구의 결과는 역설계 기술을 사용한 3차원 형상 기술과 설계 요소화 방법을 다양한 건설 프로젝트에 활용할 수 있을 것으로 판단된다.