• Interaction and multiscale mechanics
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• 제7권1호
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• pp.543-561
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• 2014

We present a full energy and force formulation of the quasicontinuum method with non-local and local transition elements. Non-local transition elements are developed to transmit inhomogeneity from the atomistic to the continuum regions. Local transition elements are developed to resolve the mathematical mismatch between non-local atoms and the local continuum. The rationale behind these transition elements is provided by analyzing the energy and force transitions between atoms and continuum under the Cauchy-Born rule. We show that breakdown of the Cauchy-Born rule occurs for slaved atoms of local elements within the cutoff of non-local atoms. The inadequacy of the Cauchy-Born rule at the transition region naturally leads to the need of atomistic treatment of transition slaved and transition representative atoms. Such an atomistic treatment together with a full or cutoff sampling allows non-local transition elements containing these transition entities to transmit inhomogeneity. Different force formulations for transition representative atoms and pure local representative atoms allow the local transition elements to resolve non-local and local mismatches. The method presented herein is validated by force calculations in an unstressed perfect crystal as well as an unrelaxed grain boundary model. A nanoindentation simulation in 3D is conducted to demonstrate the accuracy and efficiency of the proposed method.

• 전산구조공학
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• 제8권2호
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• pp.85-93
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• 1995

본 연구는 병렬전단벽 구조물의 변환부분의 효율적인 유한요소해석을 위한 보-변환요소 및 변환부분의 요소를 제시하고자 한다. 먼저 보-변환요소는 보요소와 벽체요소사이의 변형 및 힘의 구속조건을 근거로하여 보의 기본적인 거동을 동일하게 유지하면서 평면응력요소의 개념으로 대치된 유사보요소로 간주될 수 있으며, 이는 변환부분에서의 보요소와 벽체요소사이의 서로 다른 자유도에 기인한 변형의 부적합성을 합리적으로 해결해준다. 또한 보-변환요소와 직접 연결되는 변환부분의 요소는 보-변환요소의 경우와 동일한 구속조건이 적용됨으로써 변환부분에 대한 효율적인 요소분할방안을 제시해 준다. 이와 같이 본 연구에서 제시된 요소들은 기본적으로 병렬전단벽 구조물 뿐만아니라 보요소와 벽체요소의 상호작용이 고려되는 모든 구조물에 효율적으로 활용될 수 있다.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1993년도 가을 학술발표회논문집
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• pp.8-15
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• 1993

The transition membrane elements with drilling freedom have been developed. The functionals for the linear problem, in which the drilling rotations are introduced as independent variables, have been presented by Hughes & Bressi. And 4-node membrane elements with drilling degrees of freedom were developed by Ibrahimbegovic. The transition elements can be efficiently used in modelling the in-plane structures, in particular, where the stress concentration exists. A modified Gaussian quadrature adopted to evaluate the stiffness matrices of these transition elements which have slope discontinuity of displacement within the elements. Detailed numerical studies show the excellent performance of the transition elements.

• Structural Engineering and Mechanics
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• 제3권1호
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• pp.75-89
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• 1995

A transition membrane element designated as CLM which has variable mid-side nodes with drilling freedoms has been presented in this paper. The functional for the linear problem, in which the drilling rotations are introduced as independent variables, has been formulated. The transition elements with variable side nodes can be efficiently used in the local mesh refinement for the in-plane structures, which have stress concentrations. A modified Gaussian quadrature is needed to be adopted to evaluate the stiffness matrices of these transition elements mainly due to the slope discontinuity of displacement within the elements. Detailed numerical studies show the excellent performance of the new transition elements developed in this study.

• Structural Engineering and Mechanics
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• 제39권3호
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• pp.339-360
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• 2011

In the h-type adaptive analysis, when an element is refined or subdivided, new nodes are added. Among them are the transition nodes which are the corner nodes of the new elements formed by subdivision and, simultaneously, the mid-side nodes of the adjacent non-subdivided elements. To secure displacement compatibility, the slave-node approach in which the DOFs of a transition node are constrained by those of the adjacent nodes had been used. Alternatively, transition elements which possess the transition nodes as active mid-side/-face nodes can be used. For C0 plate analyses, the conventional slave-node constraints and the previously derived ANS transition elements are implemented. In both implementations, the four-node element is the ANS element. With reference to the predictions of the transition elements, the slave-node approach not only delivers erroneous results but also fails the patch test. In this paper, the patch test failure is resolved by developing a set of new constraints with which the slave-node approach surpasses the transition-element approach. The accuracy of the slave-node approach is further improved by developing a hybrid four-node element in which the assumed moment and shear force modes are in strict equilibrium.

• 대한전기학회논문지:전력기술부문A
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• 제54권2호
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• pp.67-72
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• 2005

In conventional small signal stability analysis, system is assumed to be invariant and the state space equations are used to calculate the eigenvalues of state matrix. However, when a system contains switching elements such as FACTS devices, it becomes non-continuous system. In this case, a mathematically rigorous approach to system small signal stability analysis is by means of eigenvalue analysis of the system periodic transition matrix based on discrete system analysis method. In this paper, RCF(Resistive Companion Form) method is used to analyse small signal stability of a non-continuous system including switching elements. Applying the RCF method to the differential and integral equations of power system, generator, controllers and FACTS devices including switching elements should be modeled in the form of state transition equations. From this state transition matrix eigenvalues which are mapped to unit circle can be calculated.

• Journal of Mechanical Science and Technology
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• 제15권11호
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• pp.1499-1506
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• 2001

Various transition elements are used in general for the effective finite element analysis of complicated mechanical structures. In this paper, a solid-to-beam transition finite element, which can b e used for connecting a C1-continuity beam element to a continuum solid element, is proposed. The shape functions of the transition finite element are derived to meet the compatibility condition, and a transition element equation is formulated by the conventional finite element procedure. In order to show the effectiveness and convergence characteristics of the proposed transition element, numerical tests are performed for various examples. As a result of this study, following conclusions are obtained. (1) The proposed transition element, which meets the compatibility of the primary variables, exhibits excellent accuracy. (2) In case of using the proposed transition element, the number of nodes in the finite element model may be considerably reduced and the model construction becomes more convenient. (3) This formulation method can be applied to the usage of higher order elements.

• KIEE International Transactions on Power Engineering
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• 제5A권4호
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• pp.344-349
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• 2005

In conventional small signal stability analysis, the system is assumed to be invariant and the state space equations are used to calculate the eigenvalues of the state matrix. However, when a system contains switching elements such as FACTS equipments, it becomes a non-continuous system. In this case, a mathematically rigorous approach to system small signal stability analysis is performed by means of eigenvalue analysis of the system's periodic transition matrix based on the discrete system analysis method. In this paper, the RCF (Resistive Companion Form) method is used to analyze the small signal stability of a non-continuous system including switching elements. Applying the RCF method to the differential and integral equations of the power system, generator, controllers and FACTS equipments including switching devices should be modeled in the form of state transition equations. From this state transition matrix, eigenvalues that are mapped into unit circles can be computed precisely.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1990년도 가을 학술발표회 논문집
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• pp.9-15
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• 1990

In this study, an adaptive mesh h-refinement procedure was presented in plate bending problems. By introducing the transition elements for the procedure, same drawbacks due to the irregular nodes are eliminated which are generated in the consequence of local mesh refinement in common adaptive h-version performed by single type of quadrilateral elements. For the above objective, compatible 5-node through 7-node transition plate bending elements are developed by including variable number of midside nodes. Using the Zienkiewicn-Zhu error estimator, some numerical examples are presented to show the effectiveness of the adaptive h-refinement using the transition elements.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1993년도 봄 학술발표회논문집
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• pp.3-10
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• 1993

A new three-dimensional transition solid elements was presented for the automated three-dimensional adaptive h-refinement where the steep stress gradient exists. To be consistent with 8-node solid element with nonconforming modes in accuracy, these transition elements were improved through the addition of the associated nonconforming modes. Numerical examples show that the performance of the element and the applicability to 3D adaptations are satisfactory.