• 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.

• 한국정밀공학회지
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• 제16권6호
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• pp.148-159
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• 1999

A numerical method is presented for the dynamic analysis of spur gears rotating with very high angular speeds. For an efficient computation each gear is assumed to consist of a rotating rigid disk and an elastic tooth having mass, and finite element formulations are used for the equations of motion of the tooth. The geometric constraint is imposed between the rigid disk and the elastic tooth to fix them, and contact condition is imposed between the meshing teeth of the gears. At each iteration of each time step the Lagrange multiplier and contact force are revised by using the constraint error vector, and then the whole equations of motion are time integrated with the given Lagrange multiplier and contact force. For the accurate solution the velocity and acceleration constraints as well as the displacement constraint are satisfied by the monotone reductions of the constraint error vectors. Computing procedures associated with the iterative schemes are explained and numerical simulations are conducted with the spur gears.

• 한국전기전자재료학회:학술대회논문집
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• 한국전기전자재료학회 1998년도 춘계학술대회 논문집
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• pp.33-36
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• 1998

This paper is a study on a linear ultrasonic motor with a first longitudinal$(L_1)$ and fourth bending $(B_4)$ double-mode rectangular plate. The stator vibrator is composed of an elastic material plate and of a piezo-ceramic element having a motion by electrical excitation. Each strain vector differs by $90^{\circ}$ generate travelling wave with the elliptical displacement motion of a point on the surface. To magnify displacement of longitudinal direction in elliptical displacement motion, the motor has a mechanism of the.displacement enlargement. In this paper, the vibration shape of the stator is simulated using the finite element method. A detailed model considered of the piezoelectric effect and of the exact geometry of the stator is used to calculate the displacement. The position of displacement mechanism is decided by the maximum displacement.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2000년도 추계학술대회 논문집 학회본부 B
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• pp.262-264
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• 2000

A numerical method for the analysis of 3D eddy current in conductors due to applied time varying field is suggested using the finite element method. In the approximation of the field quantifies, the edge element is used, because it reduce the required computer memory and the computing time compared with the nodal elements. With edge elements, furthermore, the field governing equations become simple because the electric scalar potential ${\phi}$ can be set to zero. The modified magnetic vector potential($A^*$) is used as a state variable. The analysed results are compared with the experimentally measured ones for the TEAM workshop problem3.

• 대한전기학회논문지
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• 제41권7호
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• pp.723-734
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• 1992

In this paper, the characteristics of IPMSM(Interior-type Permanent Magnet Synchronous Motor) are simulated using 2-D. finite element method. This paper deals with the following characteristics : air gap flux density considering skew, back e.m.f., torque and inductance. Back e.m.f. is calculated using the flux obtained from the vector potential of FEM solution. Torque is calculated using improved Maxwell stress tensor method and current angle which is obtained from the controller. Direct axis inductance and quadrature axis inductance are also calculated using energy perturbation method. Computed results are found in satisfactory agreement with experimental ones. This method also can be applied for the computation and analysis of the characteristics of SPMSM, current-excited synchronous motor and reluctance motor.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2003년도 봄 학술발표회 논문집
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• pp.288-295
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• 2003

An adaptive procedure in finite element analysis is presented by p-refinement of meshes in conjunction with a posteriori error estimator that is based on the recovery technique. In case of the recovery technique, the SPR(superconvergent patch recovery) approach has been modified for p-adaptive mesh refinement. The strategy of finding a nearly optimal distribution of polynomial degrees on a fixed finite element mesh is discussed such that a particular element has to be refined automatically to obtain an acceptable level of accuracy by increasing p-levels non-uniformly. To verify the proposed algorithm, the limit value approach is proposed which utilizes the exact strain energy computed from the extrapolation equation. A new pre-processor is developed for the p-version finite element program in which the vector graphic editor is used for the automatic generation of node connection and coordinate by halfedge solid data structure according to uniform or nonuniform p-distribution. The general 2-D algorithm is also developed to generate face modes and internal modes in accordance with different mesh types. The quality of the error estimator is investigated with the help of two mumerical examples. The results show that the sequences of p-distributions obtained by the proposed error indicator closely follow the optimal trajectory.

• Structural Engineering and Mechanics
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• 제81권4호
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• pp.411-428
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• 2022

This paper presents the Campbell diagram analysis of the rotordynamic system using the full order model (FOM) and the reduced order model (ROM) techniques to determine the critical speeds, identify the stability and reduce the computational time. Due to the spin-speed-dependent matrices (e.g., centrifugal stiffening matrix), several model order reduction (MOR) techniques may be considered, such as the modal superposition (MS) method and the Krylov subspace-based MOR techniques (e.g., Ritz vector (RV), quasi-static Ritz vector (QSRV), multifrequency quasi-static Ritz vector (MQSRV), multifrequency/ multi-spin-speed quasi-static Ritz vector (MMQSRV) and the combined Ritz vector & modal superposition (RV+MS) methods). The proposed MMQSRV method in this study is extended from the MQSRV method by incorporating the rotational-speed-dependent stiffness matrices into the Krylov subspace during the MOR process. Thus, the objective of this note is to respond to the question of whether to use the MS method or the Krylov subspace-based MOR technique in establishing the Campbell diagram of the shaft-disc-blade assembly systems in three-dimensional (3D) finite element analysis (FEA). The Campbell diagrams produced by the FOM and various MOR methods are presented and discussed thoroughly by computing the norm of relative errors (ER). It is found that the RV and the MS methods are dominant at low and high rotating speeds, respectively. More precisely, as the spinning velocity becomes large, the calculated ER produced by the RV method is significantly increased; in contrast, the ER produced by the MS method is smaller and more consistent. From a computational point of view, the MORs have substantially reduced the time computing considerably compared to the FOM. Additionally, the verification of the 3D FE rotordynamic model is also provided and found to be in close agreement with the existing solutions.

• Earthquakes and Structures
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• 제17권1호
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• pp.63-73
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• 2019

This paper studies damage detection as an optimization problem. A new objective function based on changes in natural frequencies, and Natural Frequency Vector Assurance Criterion (NFVAC) was developed. Due to their easy and fast acquisition, natural frequencies were utilized to detect structural damages. Moreover, they are sensitive to stiffness reduction. The method presented here consists of two stages. Firstly, Finite Element Model (FEM) is updated. Secondly, damage severities and locations are determined. To minimize the proposed objective function, a new bio-inspired optimization algorithm called salp swarm was employed. Efficiency of the method presented here is validated by three experimental examples. The first example relates to three-story shear frame with two single damage cases in the first story. The second relates to a five-story shear frame with single and multiple damage cases in the first and third stories. The last one relates to a large-scale eight-story shear frame with minor damage case in the first and third stories. Moreover, the performance of Salp Swarm Algorithm (SSA) was compared with Particle Swarm Optimization (PSO). The results show that better accuracy is obtained using SSA than using PSO. The obtained results clearly indicate that the proposed method can be used to determine accurately and efficiently both damage location and severity in multi-story shear frames.

• 한국자기학회지
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• 제7권3호
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• pp.159-165
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• 1997

최근에 자계시스템을 해석함에 있어서 서로 다른 위상을 갖는 자속밀도와 자계의 세기간의 벡터적인 관계를 고려하는 것이중요시 되고 있으며 그 방법에 관한 연구도 많이 이루어지고 있다. 본 연구에서는 유한요소법과 이차원 투자율 텐서를 이용하여 자속밀도와 자계의 세기를 계산하였다. 특히 이 방법으로 회전이력현상을 정확하게 고려하여 회전자속밀도와 회전 자계의 세기를 계산할 수 있음을 보였으며 또한 기본파 성분만을 가진 자속 뿐만 아니라 고조파를 포함하고 있는 자속의 계산을 위한 방법을 제시하고 게산결과와 실험결과의 비교를 통해서 제안된 방법의 타당성을 제시한다.

• KIEE International Transaction on Electrical Machinery and Energy Conversion Systems
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• 제3B권1호
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• pp.23-31
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• 2003

A novel 3D shape optimization algorithm is presented for electromagnetic devices carry-ing eddy current. The algorithm integrates the 3D finite element performance analysis and the steepest descent method with design sensitivity and mesh relocation method. For the design sensitivity formula, the adjoint variable vector is defined in complex form based on the 3D finite element method for eddy current problems. A new 3D mesh relocation method is also proposed using the deformation theory of the elastic body under stress to renew the mesh as the shape changes. The design sensitivity f3r the sur-face nodal points is also systematically converted into that for the design variables for the parameterized optimization application. The proposed algorithm is applied to the optimum design of the tank shield model of the transformer and the effectiveness is proved.