• Title, Summary, Keyword: infinite elements

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Elastodynamic infinite elements based on modified Bessel shape functions, applicable in the finite element method

  • Kazakov, K.S.
    • Structural Engineering and Mechanics
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    • v.42 no.3
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    • pp.353-362
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    • 2012
  • In this paper decay and mapped elastodynamic infinite elements, based on modified Bessel shape functions and appropriate for Soil-Structure Interaction problems are described and discussed. These elements can be treated as a new form of the recently proposed Elastodynamic Infinite Elements with United Shape Functions (EIEUSF) infinite elements. The formulation of 2D horizontal type infinite elements (HIE) is demonstrated, but by similar techniques 2D vertical (VIE) and 2D corner (CIE) infinite elements can also be formulated. It is demonstrated that the application of the elastodynamical infinite elements is the easier and appropriate way to achieve an adequate simulation including basic aspects of Soil-Structure Interaction. Continuity along the artificial boundary (the line between finite and infinite elements) is discussed as well and the application of the proposed elastodynamical infinite elements in the Finite Element Method is explained in brief. Finally, a numerical example shows the computational efficiency of the proposed infinite elements.

Development of 3-D Dynamic Infinite Elements for 3D Soil-Structure Interaction Analysis in Multi-layered Halfspaces (적층 반무한지반에서 3차원 지반-구조물 상호작용해석을 위한 동적 무한요소의 개발)

  • 윤정방;서춘교;장수혁
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • pp.79-86
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    • 2003
  • In this paper, three dimensional dynamic infinite elements are developed for the soil-structure interaction analysis in multi-layered halfspace. For the efficient discretization of 3-D for field regions, five types of dynamic infinite elements are developed, they are the horizontal, vertical, upper horizontal conner, lower vertical conner and conner of conner infinite elements. The shape functions of the infinite elements are based on the approximate expressions of the analytical solutions of the propagation wave in the infinite region. Numerical example analyses are presented for demonstrating the effectiveness of the proposed infinite elements.

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Development of 3-D Dynamic Infinite Elements for 3D Soil-Structure Interaction Analysis in Multi-layered Halfspaces (적층 반무한지반에서 3차원 지반-구조물 상호작용해석을 위한 동적 무한요소의 개발)

  • 서춘교;윤정방
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • pp.304-311
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    • 2004
  • In this paper, three dimensional dynamic infinite elements are developed for the soil-structure interaction analysis in multi-layered halfspace. For the efficient discretization of 3-D for field regions, five types of dynamic infinite elements are developed. They are the horizontal, vertical, upper horizontal conner, lower vertical conner and conner of conner infinite elements. The shape functions of the infinite elements are based on the approximate expressions of the analytical solutions of the propagating waves in the infinite region. Numerical example analyses are presented for demonstrating the effectiveness of the proposed infinite elements.

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Dynamic Infinite Elements for 3D Soil-Structure Interaction Analysis (3차원 지반-구조물 상호작용해석을 위한 동적 무한요소)

  • Seo Choon-Kyo;Yun Chung-Bang
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • pp.521-528
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    • 2005
  • In this paper, three dimensional dynamic infinite elements are developed for the soil-structure interaction analysis in multi-layered halfspace. For the efficient discretization of 3-D for field regions, five types of dynamic infinite elements are developed. They are the horizontal, vertical, horizontal comer, vertical comer and horizontal/vertical corner infinite elements. The shape functions of the infinite elements are based on approximate expressions of analytical solutions of propagating waves in the infinite region. Numerical example analyses are presented for compliances of rigid circular and square plates to demonstrate the effectiveness of the proposed infinite elements.

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Vibration of elastic and viscoelastic multilayered spaces

  • Karasudhi, P.;Liu, Y.C.
    • Structural Engineering and Mechanics
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    • v.1 no.1
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    • pp.103-118
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    • 1993
  • The near field is discretized into finite elements, and the far field into infinite elements. Closed form far-field solutions to three fundamental problems are used as the shape functions of the infinite elements. Such infinite elements are capable of transmitting all surface and body waves. An efficient scheme to integrate numerically the stiffness and mass matrices of these elements in presented. Results agree closely with those obtained by others.

Development of 3-Dimensional Static Infinite Elements with Various Decay Characteristics for Tunnel Analysis (터널해석을 위한 다양한 감쇠특성의 3차원 정적무한요소 개발)

  • Koo, Hee-Dae;Koh, Hyun-Moo
    • Journal of The Korean Society of Civil Engineers
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    • v.26 no.3A
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    • pp.439-445
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    • 2006
  • Analysis problems of tunnels whose geometrical dimensions are very small compared with surrounding media can be treated as infinite region problems. In such cases, even if finite element models can be applied, excessive number of elements is required to obtain satisfactory accuracy. However, inaccurate results may be produced due to assumed artificial boundary conditions. To solve these problems, a hybrid model, which models the region of interest with finite elements and the surrounding infinite media with infinite elements, is introduced for the analysis of infinite region. Three-dimensional isoparametric infinite elements with various decay characteristics are formulated in this paper and the corresponding parameters are presented by means of parametric studies. Three-dimensional tunnel analysis performed on a representative example verifies the applicability of hybrid model using infinite elements.

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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.

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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.

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Study on the Formulation of Two Dimensional Infinite Elements (이차원 무한요소 형성에 관한 연구)

  • 신용태;임장근
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.17 no.5
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    • pp.1066-1073
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    • 1993
  • Using regular finite elements and infinite elements simultaneously, elastic boundary value problems with infinite domain can be analyzed more effectively and accurately. In this paper, two dimensional infinite elements have been formulated by means of applying the derived mapping function to the coordinates and multiplying the regular displacement shape functions by a decay function. Orders(m, n) of the mapping and decay functions are found for the purpose of obtaining the convergent solutions without respect to the various decay lengthes. As a result of numerical tests for an infinite plate with a hole under internal pressure, two sets of function orders are obtained as follows. (a) n=0, m=1.5 (b) n=m=0.65

Dynamic Infinite Elements for Soil-Structure Interaction Analysis (지반-구조물의 상호작용해석을 위한 동적무한요소)

  • Yang, Sin Chu;Yun, Chung Bang
    • Journal of The Korean Society of Civil Engineers
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    • v.11 no.3
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    • pp.47-58
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    • 1991
  • This paper presents dynamic infinite elements for soil-structure interaction analysis. In order to discretize the far field of the unbounded soil media, axisymmetric infinite elements which are capable of propagating multi-waves are proposed. An efficient numerical integration scheme for constructing the element characteristic matrices of the infinite elements in developed based on Gauss-Laguerre quadrature. The efficiency of the infinite elements is demonstrated by comparing the computed impedances of rigid circular footings on an elastic half space and on a layered half spaces with those obtained analytically.

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