• Steel and Composite Structures
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• 제24권5호
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• pp.523-536
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• 2017

A layerwise (LW) formulation based on the Galerkin method is presented to investigate the three-dimensional stress state in long sandwich plate which is subjected to tension force and pure bending moment. Based on the Galerkin method and the LW discretization approach, the equilibrium equations of elasticity for the long plate are written in the weak form and discretized through the thickness of the plate. The discretized equations are written in terms of displacement components of the numerical layers. The governing equations of the plate are solved analytically for the free edge boundary conditions. The distribution of stress state especially the 3D stress state in the vicinity of the edges of the sandwich plate which is subjected to tension and pure bending is studied. In order to increase the accuracy, the out of plane stresses are obtained by integrating the equilibrium equations of elasticity. The convergence and accuracy of the predictions are studied and various numerical results are presented for distribution of the in-plane and out of plane stresses in symmetric and un-symmetric sandwich plates.

• 대한수학회지
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• 제46권5호
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• pp.1041-1069
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• 2009

We study the periodic homogenization of the non-stationary Stokes equations. The fundamental homogenization theorem and corrector theorem are proved under a very general assumption on the viscosity coefficients and data. The proofs are based on a weak formulation suitable for an application of classical Tartar's method of oscillating test functions. Such a weak formulation is derived by adapting an argument in Teman's book [Navier-Stokes Equations: Theory and Numerical Analysis, North-Holland, Amsterdam, 1984].

• Structural Engineering and Mechanics
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• 제14권1호
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• pp.71-84
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• 2002

A finite element formulation for the time-domain analysis of linear transient elastodynamic problems is presented based on the weak form obtained by applying the Galerkin's method to the integro-differential equations which contain the initial conditions implicitly and does not include the inertia terms. The weak form is extended temporally under the assumptions of the constant and linear time variations of field variables, since the time-stepping algorithms such as the Newmark method and the Wilson ${\theta}$-method are not necessary, obtaining two kinds of implicit finite element equations which are tested for numerical accuracy and convergency. Three classical examples having finite and infinite domains are solved and numerical results are compared with the other analytical and numerical solutions to show the versatility and accuracy of the presented formulation.

• Structural Engineering and Mechanics
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• 제11권2호
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• pp.221-236
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• 2001

A local point interpolation method (LPIM) is presented for the stress analysis of two-dimensional solids. A local weak form is developed using the weighted residual method locally in two-dimensional solids. The polynomial interpolation, which is based only on a group of arbitrarily distributed nodes, is used to obtain shape functions. The LPIM equations are derived, based on the local weak form and point interpolation. Since the shape functions possess the Kronecker delta function property, the essential boundary condition can be implemented with ease as in the conventional finite element method (FEM). The presented LPIM method is a truly meshless method, as it does not need any element or mesh for both field interpolation and background integration. The implementation procedure is as simple as strong form formulation methods. The LPIM has been coded in FORTRAN. The validity and efficiency of the present LPIM formulation are demonstrated through example problems. It is found that the present LPIM is very easy to implement, and very robust for obtaining displacements and stresses of desired accuracy in solids.

• 지구물리와물리탐사
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• 제15권2호
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• pp.57-65
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• 2012

탄성파 수치 모형 계산에 있어서 다양한 방법들이 개발되어 적용되었다. 최근에는 특히 탄성파 수치 모형 계산에 있어 혁신적인 방법인 SEM (Spectral Element Method)가 개발되어 사용되어 왔다. 이 방법은 지형을 자유롭게 표현하는데 있어 유연한 유한요소법의 장점에 정확성을 높인 방법이다. 일반적으로 Weak Formulation 형태의 파동방정식에 육면체 요소와 Gauss-Lobatto-Legendre 적분법을 적용한 방법이 널리 사용된다. 일반적인 SEM에서는 PML (Perfectly Matched Layer)경계조건을 적용하기 어려워 속도-응력 변분식으로 파동방정식을 변경하였다. CFS-PML (Complex frequency Shifted PML)경계조건을 ADE (Auxiliary Differential Equation)방정식으로 변경하여 속도-응력 파동방정식에 적용함으로써 분리할 필요가 없는 PML을 적용한 SEM 수치 모형 계산 알고리듬을 구현하였다. 1차원 수치모형과 3차원 수치모형 실험을 통하여 SEM에 적용한 비분리 CFS-PML이 유한경계에서 인공적으로 반사되는 반사파를 효과적으로 제거하는 것을 확인하였다.

• 대한수학회지
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• 제44권2호
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• pp.443-453
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• 2007

We study the equation of a membrane with strong viscosity. Based on the variational formulation corresponding to the suitable function space setting, we have proved the fundamental results on existence, uniqueness and continuous dependence on data of weak solutions.

• 한국자원식물학회지
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• 제12권4호
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• pp.289-296
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• 1999

생강 근경썩음병 길항균 Bacillus polymyxa 'HB26-5' 균주를 이용한 생물적 방제 가능성을 알아보기 위한 배양적 특성 및 제형화, 근권정착률을 조사한 결과 배양적온은 $25^{\circ}C$였고, 배지의 산도는 7.0에서 생육이 좋았으나 시간이 지남에 따라 초기에는 pH6.I~6.5의 약산성으로 되었다가 7일 후에는 pH7.8~8.2의 약알칼리성으로 변하였다. 길항균의 토양정착을 돕기 위해 첨가된 유기물중 쌀겨와 피트 또는 쌀겨와 카올린을 혼합한 제제가 토양처리 후 7주까지 길항균의 밀도 변화가 가장 작았다. 그러나 실제 노지포장에 처리하였을 경우 3주 후부터 밀도가 떨어지기 시작하였다. 제형의 경도,크기 등 물리적 특성과 길항균의 밀도유지 등을 고려할 때 알긴산 나트륨 2%, kaolin 15%, 쌀겨 3%를 혼합한 제형이 가장 우수하였다.

• Structural Engineering and Mechanics
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• 제65권1호
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• pp.91-98
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• 2018

Three structure-dependent integration methods with no numerical dissipation have been successfully developed for time integration. Although these three integration methods generally have the same numerical properties, such as unconditional stability, second-order accuracy, explicit formulation, no overshoot and no numerical damping, there still exist some different numerical properties. It is found that TLM can only have unconditional stability for linear elastic and stiffness softening systems for zero viscous damping while for nonzero viscous damping it only has unconditional stability for linear elastic systems. Whereas, both CEM and CRM can have unconditional stability for linear elastic and stiffness softening systems for both zero and nonzero viscous damping. However, the most significantly different property among the three integration methods is a weak instability. In fact, both CRM and TLM have a weak instability, which will lead to an adverse overshoot or even a numerical instability in the high frequency responses to nonzero initial conditions. Whereas, CEM possesses no such an adverse weak instability. As a result, the performance of CEM is much better than for CRM and TLM. Notice that a weak instability property of CRM and TLM might severely limit its practical applications.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2013년도 춘계학술대회 논문집
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• pp.180-185
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• 2013

A new formulation of the MNDIF method is introduced to extract highly accurate natural frequencies of concave plates with arbitrary shape. Originally, the MNDIF method cannot yield accurate natural frequencies for concave plates. To overcome this weak point, a new approach of dividing a concave plate into two convex domains is proposed and the validity and accuracy is shown in a verification example.

• 대한수학회지
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• 제38권2호
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• pp.321-336
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• 2001

A Feynman functional formulation is given for the Global Positioning System, GPS. Both the sequential and analytic Feynman functionals are presented for the classical, exterior, gravity problems which included rigid body rotations, special relativity and some general relativity corrections. A mathematically rigorous approach is introduced whose solutions exist, are unique and which depend continuously on the intial data. This formulation is convergent and has the finite approximation property. It is emphasized that all of the problems studied are classical (not quantum) evolution systems.