• Structural Engineering and Mechanics
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• 제11권4호
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• pp.443-460
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• 2001

This paper presents an effective application of a variable-node axisymmetric solid element designated as AQV (Axisymmetric Quadrilateral Variable-node element). The variable-node element with physical midside nodes helps to overcome some problems in connecting the different layer patterns on a quadrilateral mesh in the adaptive h-refinement. This element alleviates the necessity of imposing displacement constraints on irregular (hanging) nodes in order to enforce the inter-element compatibility. Therefore, the elements with variable mid-side nodes can be used effectively in the local mesh refinement for the axisymmetric structures which have stress concentrations. A modified Gaussian quadrature should be adopted to evaluate the stiffness matrices of the variable-node elements mainly because of the slope discontinuity of assumed displacement within the elements. Some numerical examples show the usefulness of variable-node axisymmetric elements in the practical application.

• Structural Engineering and Mechanics
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• 제43권3호
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• pp.349-370
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• 2012

Variable-node finite element families, termed (4 + k + l + m + n)-node elements with an arbitrary number of nodes (k, l, m, and n) on each of their edges, are developed based on the generic point interpolation with special bases having slope discontinuities in two-dimensional domains. They retain the linear interpolation between any two neighboring nodes, and passes the standard patch test when subdomain-wise $2{\times}2$ Gauss integration is employed. Their shape functions are automatically generated on the master domain of elements although a certain number of nodes are inserted on their edges. The elements can provide a flexibility to resolve nonmatching mesh problems like mesh connection and adaptive mesh refinement. In the case of adaptive mesh refinement problem, so-called "1-irregular node rule" working as a constraint in performing mesh adaptation is relaxed by adopting the variable-node elements. Through several examples, we show the performance of the variable-node finite elements in terms of accuracy and efficiency.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2008년도 추계학술대회A
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• pp.1633-1637
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• 2008

In this study, we developed 3D MLS-based variable-node elements for easy meshing. These elements should be derived from 2D MLS-based variable-node elements and would be utilized as key elements of easy meshing technique we proposed. Using developed 3D MLS-based variable-node elements, we demonstrated several examples having complex configuration compared with conventional meshing technique. Moreover, we compared with the stress results of our model and conventional one.

• 전기의세계
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• 제22권5호
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• pp.12-18
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• 1973

This paper deals with Linear Programming by Signal Flow Graph technique which is different from that of Mason and Coates. The objective function is regarded as variable, and slack variable node, artificial variable node and objective function variable (constant) node are newly defined, which shows the process for optimization of solution very intuitively. Also methods for solving L.P. and examples with subject to Ax.leq.b, Ax=b and Ax.geq.b are presented.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1994년도 가을 학술발표회 논문집
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• pp.1-8
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• 1994

A variable-node-flat shell element designated as CLS which has variable mid-side nodes with drilling freedom has been presented in this paper. The shell element to be applied in finite element analysis has been developed by combining a membrane element named as CLM with drilling rotation d.o.f. and plate bending element. The combined shell element possess six degrees of freedom per node. By introducing the variable-node elements which have physical midside nodes, some difficulties associated with imposing displacement constraints on irregular nodes to enforce interelement compatibility in common adaptive h-refinement on quadrilateral mesh are easily overcome. Detailed numerical studies show the excellent performance of the new shell elements developed in this study.

• Structural Engineering and Mechanics
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• 제16권4호
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• pp.479-492
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• 2003

Non-conforming membrane elements which have variable number of mid-side nodes with drilling degrees of freedom and which is designated as NMDx have been presented in this paper. The non-conforming elements with variable number of mid-side nodes can be efficiently used in the local mesh refinement for the in-plane structures. To guarantee the developed elements always pass the patch test, the direct modification method is incorporated into the element formulation. Detailed numerical tests in this study show the validity of the variable node NC elements developed in this study and a wide applicability of these elements to practical problems.

• Structural Engineering and Mechanics
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• 제17권3_4호
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• pp.379-391
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• 2004

This paper deals with the development of h-version adaptive mesh refinement and recovery strategy using variable-node elements and its application to various engineering field problems with 2D quadrilateral and 3D hexahedral models. The variable-node elements which have variable mid-side nodes on edges or faces are effectively used in overcoming some problems in connecting the different layer patterns of the transition zone between the refined and coarse mesh. A modified recovery technique of gradients adequate for variable-node elements and proper selection of error norms for each engineering field problems are proposed. In the region in which the error is greater than the permissible refinement error, the mesh is locally refined by subdivision. Reversely, in some parts of the domain having the error smaller than the permissible recovery error, the mesh is locally recovered (coarsened) by combination. Hierarchical structures (e.g. quadtrees and octrees) and element-based storage structures are composed to perform this adaptive process of refinement and recovery. Some numerical examples of a 3D heat conduction analysis of the concrete with hydration heat and a 2D flow analysis of vortex shedding show effectiveness and validity of the proposed scheme.

• 한국전산구조공학회논문집
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• 제22권4호
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• pp.335-341
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• 2009

본 논문에서는 MLS기반 유한요소에 대한 현재 개발상황에 대한 개관과 향후 예상할 수 있는 응용분야에 대한 제안을 하였다. 이동최소제곱근사를 이용하여 형상함수를 생성하는 MLS기반 유한요소는, 요소의 경계에서 기존 유한요소의 성질-크로네커 델타 조건-을 가지면서도 기존 요소가 갖지 못했던 임의의 절점 추가가 자유롭다는 장점이 있어 다양한 변절점 요소로의 개발이 이루어져 왔다. 선형 또는 이차형상함수를 갖는 2차원 변절점요소 뿐 아니라, 균열선단과 균열면을 포함하고 있는 2차원 균열요소와 3차원에서의 제한적인 변절점요소 등이 개발되어 다양한 불연속성 문제에 적용 가능함이 입증되었다. 이러한 MLS기반 유한요소는 향후 2차원 변절점 3각요소, 2차원 삼각균열요소, 변절점 쉘요소, 균열 쉘요소, 마칭큐브알고리즘에 적합한 3차원 다면체요소로의 개발이 가능할 것으로 예상되며, 본 논문에서는 그 일례로 3차원 다면체요소를 이용한 대퇴골의 요소망 생성을 보였다.

• Structural Engineering and Mechanics
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• 제1권1호
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• pp.61-74
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• 1993

A new three-dimensional transition solid element was presented for the automated three-dimensional adaptive h-refinement or the local mesh refinement where the steep stress gradient exists. The proposed transition element was established by adding variable nodes(element nodes) to basic 8-node for an effective connection between the refined region and the coarse region with minimum degrees of freedom possible. To be consistent in accuracy with 8-node solid element with nonconforming modes, this transition element was also improved through the addition of the modified nonconforming modes. Numerical examples show that the performance of the element and the applicability to 3D adaptations are satisfactory.

• Steel and Composite Structures
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• 제33권6호
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• pp.767-776
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• 2019

In this article, a simple and robust multi-objective assessment method to control design angles and node positions connected among steel outrigger truss members is proposed to approve both structural safety and economical cost. For given outrigger member layouts, the present method utilizes general-purpose prototypes of outrigger members, having resistance to withstand lateral load effects directly applied to tall buildings, which conform to variable connecting node and design space deposition. Outrigger layouts are set into several initial design conditions of height to width of an arbitrary given design space, i.e., variable design space. And then they are assessed in terms of a proposed multi-objective function optimizing both minimal total displacement and material quantity subjected to design impact factor indicating the importance of objectives. To evaluate the proposed multi-objective function, an analysis model uses a modified Maxwell-Mohr method, and an optimization model is defined by a ground structure assuming arbitrary discrete straight members. It provides a new robust assessment model from a local design point of view, as it may produce specific optimal prototypes of outrigger layouts corresponding to arbitrary height and width ratio of design space. Numerical examples verify the validity and robustness of the present assessment method for controlling prototypes of outrigger truss members considering a multi-objective optimization achieving structural safety and material cost.