• 동력기계공학회지
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• 제4권1호
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• pp.68-73
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• 2000

A mixed degree finite element solutions using hierarchical elements are investigated for convergences on a 2-D simple cases. Elements are generated block by block and each block is assigned an arbitrary solution degree. The numerical study showed that a well constructed blocks can increase the convergence and accuracy of finite element solutions. Also, it has been found that for higher order elements, the convergence trends can be deteriorated for smaller mesh sizes. A procedure for a variable fixed boundary condition has been included.

• Structural Engineering and Mechanics
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• 제4권5호
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• pp.569-586
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• 1996

A new three-dimensional 8-node solid element with rotational degrees of freedom is presented. The proposed element is established by adding rotational degrees of freedom to the basic 8-node solid element. Thus the element has three translations and three rotational degrees of freedom per node. The corner rotations are introduced by transforming the hierarchical mid-edge displacements which are parabolic shape along an edge. The derivation of the element is based on the mixed variational principles in which the rotations are introduced as independent variables. Several types of non-conforming modes are selectively added to the displacement fields to obtain a series of improved elements. The resulting elements do not have the spurious zero energy modes and Poisson's ratio locking and pass patch test. Numerical examples show that presented non-conforming solid elements with rotational degrees of freedom show good performance even in the highly distorted meshes.

• 대한토목학회논문집
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• 제12권4_1호
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• pp.67-76
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• 1992

축대칭(軸對稱) 선형강성(線形彈性) 응력해석을 위해 p-version 유한요소법에 기초한 계층적(階層的) 정식화 과정이 제안되었다. 이 방식은 적분형 르장드르 다항식을 사용하여 절점좌표값을 갖지 않는 절점을 추가하여 형상함수의 조합형태로 변위함수(變位)를 근사시키는 방법이다. 형상함수(形狀函數)가 계층적 성질을 갖기 때문에 강성도(剛性度)행렬과 하중벡터도 계층적이 된다. 본 연구에서 제안된 요소(要所)의 장점(長點)은 다음과 같다. 첫째, 개선된 수치연산의 효율성이며 둘째, 요소간에 서로 다른 차수(次數)의 형상함수를 사용할 수 있고 셋째, p-세분화를 할 때 저차(低次)일 때 계산된 값을 그대로 사용할 수 있다. 수치예제를 통해 제안된 요소의 정확도(正確度), 효율성(效率性), 모델링의 간편성(簡便性), 적용성(適用性) 및 변위와 응력 그리고 에너지 Norm등을 사용하여 그 우월성을 입증하고 있다. 몇 가지 예제의 해석결과는 이미 발표된 논문과 아울러 해석적 방법에 의한 결과와 비교되었다.

• 소성∙가공
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• 제16권2호
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• pp.138-143
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• 2007

Superplastic forming/diffusion bonding (SPF/DB) processes were analyzed using a 3-D rigid visco-plastic finite element method. A constant-triangular element based on membrane approximation and an incremental theory of plasticity are employed for the formulation. The coulomb friction law is used for interface friction between tool and material. Pressure-time relationship for a given optimal strain rate is calculated by stress and pressure values at the previous iteration step. In order to improve the contact searching, hierarchical search algorithm has been applied and implemented into the code. Various geometries including sandwich panel and 3 sheet shape for 3-D SPF/DB model are analyzed using the developed program. The validity fer the analysis is verified by comparison between analysis and results in the literature.

• Korean Journal of Mathematics
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• 제22권4호
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• pp.599-609
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• 2014

We refer to the saturation assumptions on the finite element approximation for a one dimensional convection-diffusion model. By examining piecewise linear finite elements with refined mesh by half and hierarchical bases, we verify the saturation results, respectively.

• 한국실내디자인학회:학술대회논문집
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• 한국실내디자인학회 2001년도 춘계학술발표대회 논문집
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• pp.121-127
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• 2001

An unified measure of user interface efficiency and aesthetics for cyber museum is proposed. First, general structure of cyber museum is discussed and hierarchical analyses are done for sample sites. Usability tests based on the hierarchical analyses yield statistics of user access frequency and persistency for each page, on which access probability is deduced. Second, visual occupancy, a measure of efficiency of user interface element based on access probability is defined. The hierarchical statistics of visual occupancy can be an index for characterization and classification of cyber museums. Examples are provided.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2007년도 정기 학술대회 논문집
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• pp.487-492
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• 2007

The enhancement of the service life of damaged or cracked structures is a major issue for researchers and engineers. The hierarchical void element with the integrals of Legend polynomials is used to characterize the fracture behavior of unpatched crack as well as repaired crack with bonded composite patches by computing the stress intensity factors and stress contours at the crack tip. The numerical approach is based on the v-version degenerate shell element including the theory of anisotropic laminated composites. Since the equivalent single layer approach is adopted in this study, the proposed element is necessary to represent a discontinuous crack part as a continuum body with zero stiffness of materials. Thus the aspect ratio of this element to represent the crack should be extremely slender. The sensitivity of numerical solution with respect to energy release rate, displacement and stress has been tested to show the robustness of hierarchical void element as the aspect ratio is increased up to 2000. The stiffness derivative method and displacement extrapolation method have been applied to calculate the stress intensity factors of Mode I problem.

• Structural Engineering and Mechanics
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• 제14권5호
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• pp.595-610
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• 2002

This paper presents an efficiency of various non-conforming (NC) modes in development of a series of new finite elements with the special emphasis on 4-node quadrilateral elements. The NC modes have been used as a key scheme to improve the behaviors of various types of new finite elements, i.e., Mindlin plate bending elements, membrane elements with drilling degrees of freedom, flat shell elements. The NC modes are classified into three groups according to the 'correction constants' of 'Direct Modification Method'. The first group is 'basic NC modes', which have been widely used by a number of researchers in the finite element communities. The basic NC modes are effective to improve the behaviors of regular shaped elements. The second group is 'hierarchical NC modes' which improve the behaviors of distorted elements effectively. The last group is 'higher order NC modes' which improve the behaviors of plate-bending elements. When the basic NC modes are combined with hierarchical or higher order NC modes, the elements become insensitive to mesh distortions. When the membrane component of a flat shell has 'hierarchical NC modes', the membrane locking can be suppressed. A number of numerical tests are carried out to show the positive effect of aforementioned various NC modes incorporated into various types of finite elements.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제17권3호
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• pp.139-170
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• 2013

We extend a p-hierarchical decomposition of the second degree finite element space of N$\acute{e}$d$\acute{e}$lec for tetrahedral meshes in three dimensions given in [1] to meshes with hexahedral elements, and derive p-hierarchical decompositions of the second degree finite element space of Raviart-Thomas in two dimensions for triangular and quadrilateral meshes. After having proved stability of these subspace decompositions and requiring certain saturation assumptions to hold, we construct a local a posteriori error estimator for fem and bem coupling of a time-harmonic electromagnetic eddy current problem in $\mathbb{R}^3$. We perform some numerical tests to underline reliability and efficiency of the estimator and test its usefulness in an adaptive refinement scheme.

• 한국군사과학기술학회지
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• 제11권1호
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• pp.57-65
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• 2008

Superplastic forming/diffusion bonding(SPF/DB) processes with inner contact were analyzed using a 3-D rigid visco-plastic finite element method. A constant-triangular element based on membrane approximation and an incremental theory of plasticity are employed for the formulation. The hierarchical search algorithm for the contact searching has been applied. The algorithms for contact force processing were designed to handle equally well contact between deformable bodies, as well as rigid bodies. The plate of three and four sheets for 3-D SPF/DB model are analyzed using the developed program. The validity for the analysis is verified by comparison between analysis, experiment and results in the literature.