• 대한기계학회논문집A
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• 제28권9호
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• pp.1255-1261
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• 2004

A variational approximation procedure is introduced to study the contact stresses between a representative asperity and a feature generally happening in superfinishing processes such as FAM. After a description of the model under consideration is presented, a system of governing equation for the model is derived fullowed by the assumptions made in order to make progress in model development. Final computation is made to evaluate contact stresses on an elastic asperity tip in small scale in size and a computer simulation is performed for detailed surface profile variations on a representative feature. Numerical results are presented along with a discussion of the conclusions that can be drawn from this analysis.

• 한국경영과학회지
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• 제19권3호
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• pp.203-217
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• 1994

In this paper we develop an exponentialization procedure for the modelling of open FMS networks with general processing time at each station and limited buffer size. By imposing a reasonable assumption on the solution set, the nonlinear equation system for the exponentialization procedure is formulated as a variational inequality problem and the solution existence is examined. The efficient algorithm for the nonlinear equation system is developed using linearized Jacobi approximation method.

• 한국기계가공학회지
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• 제20권2호
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• pp.72-79
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• 2021

The present paper aims to set forth a two-dimensional theory for the dynamics of plates that is valid over a large range of excitation. To construct a dynamic plate theory within the long-wavelength approximation, two dimensional-reduction procedures must be used for analyzing the low- and high-frequency behaviors under the dynamic variational-asymptotic method. Moreover, a separate and logically independent step for the short-wavelength regime is introduced into the present approach to avoid violation of the positive definiteness of the derived energy functional and to facilitate qualitative description of the three-dimensional dispersion curve in the short-wavelength regime. Two examples are presented to demonstrate the capabilities and accuracy of all of the formulas derived herein by using various dispersion curves through comparison with the three-dimensional finite element method.

• Journal of Computational Design and Engineering
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• 제3권2호
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• pp.102-111
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• 2016

In this paper, we study the problem of computing smooth feature curves from CAD type point clouds models. The proposed method reconstructs feature curves from the intersections of developable strip pairs which approximate the regions along both sides of the features. The generation of developable surfaces is based on a linear approximation of the given point cloud through a variational shape approximation approach. A line segment sequencing algorithm is proposed for collecting feature line segments into different feature sequences as well as sequential groups of data points. A developable surface approximation procedure is employed to refine incident approximation planes of data points into developable strips. Some experimental results are included to demonstrate the performance of the proposed method.

• 대한기계학회논문집A
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• 제25권4호
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• pp.574-581
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• 2001

Transient linear elastodynamic problems are numerically analyzed in a time-domain by the Finite Element Method, for which the variational formulation based upon the equations of motion in convolution integral is newly derived. This formulation is implicit and does not include the time derivative terms so that the computation procedure is simple and less assumptions are required comparing to the conventional time-domain dynamic numerical algorithms, being able to get the improved numerical accuracy and stability. That formulation is expanded using the semi-discrete approximation to obtain the finite element equations. In the temporal approximation, the time axis is divided equally and constant and linear time variations are assumed in those intervals. It is found that unconditionally stable numerical results are obtained in case of the constant time variation. Some numerical examples are given to show the versatility of the presented formulation.

• 대한기계학회논문집
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• 제16권8호
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• pp.1429-1437
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• 1992

본 연구에서는 이완형 물성방정식을 바탕으로 하며 프와송 비가 일정하다는 가정을 하지 않는다. 또한 점탄성 지배방정식에 변분원리를 적용하고 유도되어진 식 에 유한요소해법을 사용하여 시스템 기본해석을 위한 연립방정식을 유도한다. 이와 함께 점탄성 물성함수의 유도 및 응력계산을 위한 공식화 과정도 설명한다. 제시된 방법론의 타당성 및 정확성을 보이기 위해서 평면응력 및 평면변형 문제의 변위 및 응력을 수치해석하여 이론해와 비교 검토하며, 아울러 시간증분의 변화와 Gauss poi- nts수가 수치정확도에 끼치는 영향을 조사한다.

• ETRI Journal
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• 제21권1호
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• pp.1-27
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• 1999

We present a new description of envelope-function equation of the superlattice (SL). The SL wave function and corresponding effective-mass equation are formulated in terms of a linear combination of Bloch states of the constituent material with smaller band gap. In this envelope-function formalism, we review the fundamental concept on the motion of a wave packet in the SL structure subjected to steady and uniform electric fields F. The review confirms that the average of SL crystal momentums K = ($k_x,k_y,q$), where ($K_x,k_y$) are bulk inplane wave vectors and q SL wave vector, included in a wave packet satisfies the equation of motion = $_0+Ft/h$; and that the velocity and acceleration theorems provide the same type of group velocity and definition of the effective mass tensor, respectively, as in the Bulk. Finally, Schlosser and Marcus's method for the band theory of metals has been by Altarelli to include the interface-matching condition in the variational calculation for the SL structure in the multi-band envelope-function approximation. We re-examine this procedure more thoroughly and present variational equations in both general and reduced forms for SLs, which agrees in form with the proposed envelope-function formalism. As an illustration of the application of the present work and also for a brief investigation of effects of band-parameter difference on the subband energy structure, we calculate by the proposed variational method energies of non-strained $GaAs/Al_{0.32}Ga_{0.68}As$ and strained $In_{0.63}Ga_{0.37}As/In_{0.73}Ga_{0.27}As_{0.58}P_{0.42}SLs$ with well/barrier widths of $60{\AA}/500{\AA}$ and 30${\AA}/30{\AA}$, respectively.

• Structural Engineering and Mechanics
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• 제28권1호
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• pp.53-67
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• 2008

Anisotropic materials are increasingly required in modern technological applications. Certainly, civil, mechanical and naval engineers frequently deal with the situation of analyzing the dynamical behaviour of structural elements being composed of such materials. For example, panels of anisotropic materials must sometimes support electromechanical engines, and besides, holes are performed in them for operational reasons e.g., conduits, ducts or electrical connections. This study is concerned with the natural frequencies and normal modes of vibration of rectangular anisotropic plates supported by different combinations of the classical boundary conditions: clamped, simply - supported and free, and with additional complexities such holes of free boundaries and attached concentrated masses. A variational approach (the well known Ritz method) is used, where the displacement amplitude is approximated by a set of beam functions in each coordinate direction corresponding to the sides of the rectangular plate. Consequently each coordinate function satisfies the essential boundary conditions at the outer edge of the plate. The influence of the position and magnitude of both hole and mass, on the natural frequencies and modal shapes of vibration are studied for a generic anisotropic material. The classical Ritz method with beam functions as spatial approximation proved to be a suitable procedure to solve a problem of such analytical complexity.

• Structural Engineering and Mechanics
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• 제69권6호
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• pp.615-626
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• 2019

The 3-noded metric Timoshenko beam element with an offset of the internal node from the element centre is used here to demonstrate the best-fit paradigm using function space formulation under locking and mesh distortion. The best-fit paradigm follows from the projection theorem describing finite element analysis which shows that the stresses computed by the displacement finite element procedure are the best approximation of the true stresses at an element level as well as global level. In this paper, closed form best-fit solutions are arrived for the 3-noded Timoshenko beam element through function space formulation by combining field consistency requirements and distortion effects for the element modelled in metric Cartesian coordinates. It is demonstrated through projection theorems how lock-free best-fit solutions are arrived even under mesh distortion by using a consistent definition for the shear strain field. It is shown how the field consistency enforced finite element solution differ from the best-fit solution by an extraneous response resulting from an additional spurious force vector. However, it can be observed that when the extraneous forces vanish fortuitously, the field consistent solution coincides with the best-fit strain solution.