• 대한수학회지
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• 제46권6호
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• pp.1151-1164
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• 2009

Let E be a reflexive Banach space with a weakly sequentially continuous duality mapping, C be a nonempty closed convex subset of E, f : C $\rightarrow$C a contractive mapping (or a weakly contractive mapping), and T : C $\rightarrow$ C a nonexpansive mapping with the fixed point set F(T) ${\neq}{\emptyset}$. Let {$x_n$} be generated by a new composite iterative scheme: $y_n={\lambda}_nf(x_n)+(1-{\lambda}_n)Tx_n$, $x_{n+1}=(1-{\beta}_n)y_n+{\beta}_nTy_n$, ($n{\geq}0$). It is proved that {$x_n$} converges strongly to a point in F(T), which is a solution of certain variational inequality provided the sequence {$\lambda_n$} $\subset$ (0, 1) satisfies $lim_{n{\rightarrow}{\infty}}{\lambda}_n$ = 0 and $\sum_{n=0}^{\infty}{\lambda}_n={\infty}$, {$\beta_n$} $\subset$ [0, a) for some 0 < a < 1 and the sequence {$x_n$} is asymptotically regular.

• 대한기계학회논문집A
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• 제24권3호
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• pp.803-809
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• 2000

For the effective analysis of an engineering problem, meshless methods which require only positioning finite points without the element meshing recently have been proposed and being studied extensively. Meshless methods have difficulty in imposing essential boundary conditions directly, because non-interpolate shape functions originated from an approximation process are used. So some techniques, which are Lagrange multiplier method, modified variational principles and coupling with finite elements and so on, were introduced in order to impose essential boundary conditions. In spite of these methods, imposition of essential boundary conditions have still many problems like as non-positive definiteness, inaccuracy and negation of meshless characteristics. In this paper, we propose a new method which modifies shape function. Through numerical tests, convergence, accuracy and validity of this method are compared with the standard EFGM which uses Lagrange multiplier method or modified variational principles. According to this study, the proposed method shows the comparable accuracy and efficiency.

• 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.

• 대한기계학회논문집
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• 제12권5호
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• pp.944-951
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• 1988

본 연구에서는 두꺼운 복합적층판에 대한 응력해석을 할 수 있는 통합-세부 변분 모델(globallocal Variational Model)을 이용하여, 이 방법으로 섬유각도와 적 층순서가 다른 여러 유한폭을 가진 복합적층판의 층간응력해석을 수행하여 층간수직 응력의 거동을 살펴 보았다. 그리고 0, 90, 45, -45도 층들로 이루어진 준등방성 (quasiisotropic) 복합적층판에 대한 응력해석 결과로 층간수직응력의 근사해에 의한 결과와 상호 비교하며 근사해의 한계성을 검토 설명하였다. 또한, 층간분리에 큰 영향을 주는 층간수직응력을 고려한 두꺼운 복합적층판에 대한 최적의 적층방법으로 포와송 비에 대하여 대칭인 부적층판을 반복하는 적층방법을 제시하였으며, 통합-세부 변분 모델을 이용한 해로 이 적층방법에 의한 적층판의 층간수직 응력의 거동을 살펴 보았다. 그리고 이 적층방법에 의한 적층판과 다른 적층순서를 가진 적층판의 층간 수직응력을 서로 비교하여, 이 적층방법에 의한 적층판의 층간수직응력의 감소를 조사 하여 그 유용성을 보였다.

• Journal of Magnetics
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• 제21권1호
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• pp.6-11
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• 2016

The magnetic anisotropy energy (MAE) and the saturation magnetization $B_s$ of (110) $Fe_nCo_n$ heterostructures with n = 1, 2, and 3 are investigated in first-principles within the density functional theory by using the precise full-potential linearized augmented plane wave (FLAPW) method. We compare the results employing two different exchange correlation potentials, that is, the local density approximation (LDA) and the generalized gradient approximation (GGA), and include the spin-orbit coupling interaction of the valence states in the second variational way. The MAE is found to be enhanced significantly compared to those of bulk Fe and Co and the magnetic easy axis is in-plane in agreement with experiment. Also the MAE exhibits the in-plane angle dependence with a two-fold anisotropy showing that the $[1{\overline{I}}0]$ direction is the most favored spin direction. We found that as the periodicity increases, (i) the saturation magnetization $B_s$ decreases due to the reduced magnetic moment of Fe far from the interface, (ii) the strength of in-plane preference of spin direction increases yielding enhancement of MAE, and (iii) the volume anisotropy coefficient decreases because the volume increase outdo the MAE enhancement.

• Interaction and multiscale mechanics
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• 제6권2호
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• pp.237-255
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• 2013

In this paper, a meshfree-enriched finite element method (ME-FEM) is introduced for the large deformation analysis of nonlinear path-dependent problems involving contact. In linear ME-FEM, the element formulation is established by introducing a meshfree convex approximation into the linear triangular element in 2D and linear tetrahedron element in 3D along with an enriched meshfree node. In nonlinear formulation, the area-weighted smoothing scheme for deformation gradient is then developed in conjunction with the meshfree-enriched element interpolation functions to yield a discrete divergence-free property at the integration points, which is essential to enhance the stress calculation in the stage of plastic deformation. A modified variational formulation using the smoothed deformation gradient is developed for path-dependent material analysis. In the industrial metal forming problems, the mortar contact algorithm is implemented in the explicit formulation. Since the meshfree-enriched element shape functions are constructed using the meshfree convex approximation, they pose the desired Kronecker-delta property at the element edge thus requires no special treatments in the enforcement of essential boundary condition as well as the contact conditions. As a result, this approach can be easily incorporated into a conventional displacement-based finite element code. Two elasto-plastic problems are studied and the numerical results indicated that ME-FEM is capable of delivering a volumetric locking-free and pressure oscillation-free solutions for the large deformation problems in metal forming analysis.

• 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.

• 대한수학회논문집
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• 제24권3호
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• pp.381-393
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• 2009

Strong convergence theorems on viscosity approximation methods for finding a common zero of a finite family accretive operators are established in a reflexive and strictly Banach space having a uniformly G$\hat{a}$teaux differentiable norm. The main theorems supplement the recent corresponding results of Wong et al. [29] and Zegeye and Shahzad [32] to the viscosity method together with different control conditions. Our results also improve the corresponding results of [9, 16, 18, 19, 25] for finite nonexpansive mappings to the case of finite pseudocontractive mappings.

• 전산구조공학
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• 제4권2호
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• pp.77-85
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• 1991

선형탄성파괴역학에서 특히 균열 쉘의 응력집중계수 산정을 위해 p-version 유한요소법에 기초한 선진유한요소기법이 제안되었다. 세가지 균열된 쉘 예제를 통해 응력집중계수 산정은 종래의 h-version 유한요소모델에 비하여 p-version 유한요소 모델이 수렴성과 정확도 면에서 훨씬 더 적합함을 보여주고 있다. 이 기법의 주요 이점은 근사해의 정확도가 요소분할이나 균열선단요소 또는 혼합형 변분원리등의 특별고려가 없이 확보될 수 있다는데 있다.

• 대한수학회논문집
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• 제20권3호
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• pp.563-578
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• 2005

In [Z. Cai and B. C. Shin, SIAM J. Numer. Anal. 40 (2002), 307-318], we developed the discrete first-order system least squares method for the second-order elliptic boundary value problem by directly approximating $H(div){\cap}H(curl)-type$ space based on the Helmholtz decomposition. Under general assumptions, error estimates were established in the $L^2\;and\;H^1$ norms for the vector and scalar variables, respectively. Such error estimates are optimal with respect to the required regularity of the solution. In this paper, we study solution methods for solving the system of linear equations arising from the discretization of variational formulation which possesses discrete biharmonic term and focus on numerical results including the performances of multigrid preconditioners and the finite element accuracy.