• Title, Summary, Keyword: 무한요소

### 무한요소(Infinite Elements)를 이용한 기초공학해석

• 양신추
• Computational Structural Engineering
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• v.4 no.2
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• pp.9-12
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• 1991
• 공학문제에 있어서, 해석적으로 접근할 수 없었던 많은 경우의 문제들이 유한요소법(Finite Element Methods)의 정형화된 모형화 및 해석과정을 통하여 쉽게 접근되어질 수 있었다. 최근 보다 효율적인 요소개발과 컴퓨터 기술의 발달로 유한요소법은 더욱 효과적인 해석 수단이 되어가고 있다. 그러나 지반공학 문제와 같은 무한영역 문제를 유한요소법으로 해석할 경우, 매우 큰 영역을 모형화하기 위하여 많은 수의 요소가 요구되며 이에 따른 자유도(Degree of Freedom) 수의 증가로 많은 계산시간을 요구하게 된다. 본 고는 무한영역 문제를 효과적으로 모형화하기 위하여 연구, 개발되어진 무한요소(Infinite Element)에 대하여 소개하려 한다. 무한요소의 기본개념과 강성행렬의 형성방법을 보인 후, 기초공학 문제를 예로 하여 이의 적용방법을 간략하게 설명하였다.

### Infinite Element for the Scaled Boundary Analysis of Initial Valued on-Homogeneous Elastic Half Space (초기값을 갖는 비동질무한영역의 해석을 위한 비례경계무한요소법)

• Lee, Gye-Hee;Deeks, Andrew J.
• Journal of the Computational Structural Engineering Institute of Korea
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• v.21 no.2
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• pp.199-208
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• 2008
• In this paper, to analyze the initial valued non-homogeneous elastic half space by the scaled boundary analysis, the infinite element approach was introduced. The free surface of the initial valued non-homogeneous elastic half space was modeled as a circumferential direction of boundary scaled boundary coordinate. The infinite element was used to represent the infinite length of the free surface. The initial value of material property(elastic modulus) was considered by the combination of the position of the scaling center and the power function of the radial direction. By use of the mapping type infinite element, the consistent elements formulation could be available. The performance and the feasibility of proposed approach are examined by two numerical examples.

### Coupled Distinct Element and Boundary Element Analysis of Problems Having Infinite or Semi-infinite Boundaries (개별요소와 경계요소 조합에 의한 무한 및 반무한 영역문제의 해석)

• Huh, Taik Nyung;Kim, Moon Kyum;Hwang, Hak Joo
• Journal of The Korean Society of Civil Engineers
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• v.12 no.4
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• pp.81-93
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• 1992
• Numerical modeling of problems having infinite and semi-infinite boundaries is studied using a coupled method of distinct elements and boundary elements. The regions which are restricted on stress concentration area of loading points, excavation surface, and geometric discontinuity in the underground structures, are modeled using distinct elements, while the infinite and semi-infinite regions are modeled using linear boundary elements. Linear boundary elements for infinite and semi-infinite region are respectively composed using the Kelvin's and the Melan's solution, respectively. For the completeness, the boundary element method, the distinct element, and the coupled method of distinct elements and boundary elements are studied independently. The coupled method is verified and is applied to underground structures of infinite and semi-infinite regions. Through the comparison of the results, it is concluded that the coupled analysis may be used for discontinuous underground structures in the effective manner.

### Infinite Elements for the Evaluation of Wave Forces (파랑하중 산정을 위한 무한요소)

• 박우선;윤정방;편종근
• Journal of Korean Society of Coastal and Ocean Engineers
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• v.1 no.1
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• pp.71-80
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• 1989
• In this paper, the concept of the infinite element is applied to the linear wave diffraction and radiation problems. The hydrodynamic pressure forces are assumed to be inertially dominated, and viscous effects are neglected. The near field region surrounding the solid body is modelled using the conventional finite elements, and the far field region is represented using the infinite elements .In order to represent the scattered wave potentials in the far field region more accurately, the infinite elements are developed using special shape functions derived from the asymptotic expressions for the analytical eigenseries solution of the scattered waves. The system matrices of the infinite elements are constructed by performing the integration in the infinite direction analytically to achieve computational efficiency. Numerical analyses are carried out for vertical axisymmetric bodies to validate the infinite elements developed here. Comparisons with the results by other available numerical solution methods show that the present method using the infinite elements gives fairly good results. Numerical experiments are per-formed to determine the suitable location of the infinite elements and the appropriate size of the finite elements which directly affect accuracy and efficiency of the solution.

### Implementation of semi-infinite boundary condition for dynamic finite element analysis (동적 유한요소해석에서의 반무한 경계조건의 실행)

• Choi, Chang-Ho;Chung, Ha-Ik
• Proceedings of the Korean Geotechical Society Conference
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• pp.600-606
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• 2006
• 실제 지반은 경계가 없는 무한상태로 존재하기 때문에 지반구조물의 동적거동을 유한요소법을 이용하여 해석할 시 모델의 영역을 성립하는 것은 특별한 고려가 필요하다. 유한요소법에서의 동적해석은 파동의 전달을 포함하기 때문에 모델의 경계에서 인공적인 경계조건이 필요하다. 인공적인 경계 조건은 유한요소내의 지반상태를 무한상태로 변형시킬 수 있어야 하며, 경계에 도달하는 응력 파동을 모델내로 반사시키지 않고 흡수 할 수 있어야 한다. 본 논문에서는 간단한 점 탄성 반무한 불연속 요소를 이용하여 지반구조물의 동적해석을 수행하는 방법을 보여준다. 반무한 요소의 실행은 OpenSees라는 유한요소 해석프로그램을 이용하여 수행되었으며, 예를 통하여 불연속 요소가 경계에 도달하는 응력 파동을 충분히 흡수하여 유한요소 모델을 반무한 상태로 전환 시킬 수 있다는 것을 보여준다.

### Cuboidal Infinite Elements for Soil-Structure-Interaction Analysis in Multi-Layered Half-Space (3차원 지반-구조물 상호작용해석을 위한 입방형 무한요소)

• Seo, Choon-Gyo;Yun, Chung-Bang;Kim, Jae-Min
• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.1
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• pp.39-50
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• 2007
• This paper presents 3D infinite elements for the elastodynamic problem with multi-layered half-space. Five different types of infinite elements are formulated by using approximate expressions of multiple wave components for the wave function in multi-layered soil media. They are horizontal, horizontal-corner, vortical, vertical-corner and vertical-horizontal-comer infinite elements. The elements can effectively be used for simulating wane radiation problems with multiple wave components. Numerical example analyses are presented for rigid disk, square footings and embedded footing on homogeneous and layered half-space. The numerical results show the effectiveness of the proposed infinite elements.

### Infinite Elements for Analysis of Diffraction and Radiation Problems in the Vertical Plane (연직 2차원 회절 및 방사문제 해석을 위한 무한요소)

• 박우선;이달수;오영민;정원무
• Journal of Korean Society of Coastal and Ocean Engineers
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• v.3 no.4
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• pp.235-243
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• 1991
• This paper is concerned with developing infinite elements which are applicable to wave diffraction and radiation problems in the vertical plane. The near need region surrounding the solid body is modeled using conventional finite elements. but the far fold region is represented using the infinite elements developed in this study. The shape functions for the infinite elements are derived from the analytical eigenseries solution of the scattered waves in the far field region. The system matrices of the elements are constructed by performing the integration in the infinite direction analytically to achieve computational efficiency. Numerical analysis is carried out for two floating bodies with different cross-sectional shapes to prove the efficiency and validity of the elements. Numerical experiments are also performed to determine the suitable location of the infinite elements which directly affect accuracy and efficiency of the solution.

### Infinite Element for the Analysis of Harbor Resonances (항만 부진동 해석을 위한 무한요소)

• Park, Woo-Sun;Chun, In-Sik;Jeong, Weon-Mu
• Journal of Korean Society of Coastal and Ocean Engineers
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• v.6 no.2
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• pp.139-149
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• 1994
• In this paper, a finite element technique is applied to the prediction of the wave resonance phenomena in harbors. The mild-slope equation is used with a partial reflection boundary condition introduced to model the energy dissipating effects on the solid boundary. For an efficient modeling of the radiation condition at infinity, a new infinite element is developed. The shape function of the infinite element is derived from the asymptotic behavior of the first kind of the Hankel's function in the analytical boundary series solutions. For the computational efficiency, the system matrices of the element are constructed by performing the relevant integrations in the infinite direction analytically. Comparisons with the results from experiments and other solution methods show that the present model gives fairly good results. Numerical experiments are also carried out to determine the proper distance to the infinite elements from the mouth of the halter, which directly affect the accuracy and efficiency of the solution.

### p-Version Static Infinite Element for Representing Various Displacement Decay Characteristics (다양한 변위감쇠특성을 고려할 수 있는 p-버전 정적 무한요소)

• 고광훈;이승래
• Geotechnical Engineering
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• v.13 no.1
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• pp.101-110
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• 1997
• This paper presents a two dimensional p-version static infinite element for analyzing $1/r^n$ displacement decay type problems in unbounded media. The proposed element is developed by using shape functions based on approximate expressions of an analytical solution. Numerical results are presented for an opening in a homogeneous elastic infinite medium and a rigid footing rested on a homogeneous elastic half-space. The numerical results show the effectiveness of the proposed infinite element.

### Two-Dimensional Infinite Element for Dynamic Analysis of Saturated Two-Phase Soil (포화된 2상 지반의 동적해석을 위한 2차원 무한요소)

• Kim, Jae-Min
• Journal of the Earthquake Engineering Society of Korea
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• v.9 no.4
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• pp.67-74
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• 2005
• This paper presents a new infinite element for modeling far-field region in dynamic analysis of a fluid-saturated two-phase medium. The infinite element method combined to the infinite element method has been effectively applied to several engineering problems where the full space or half-space medium should be modeled. However, the currently available infinite element for dynamic analysis of two-phase porous medium has a limitation that Pl and P2 waves can only be Included in shape function expressing behavior ol the body. In this paper, the infinite element method is extended to simulate arbitrary number of multi-component waves. For this purpose, the far-field of the porous medium is assumed to be a layered half-space, while the near-field Includes structures as well as irregular soil medium. The accuracy and effectiveness of the proposed element have demonstrated using 1-D and 2-D wave propagation problems.