• Title, Summary, Keyword: infinite elements

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Dynamic response of a lined tunnel with transmitting boundaries

  • Fattah, Mohammed Y.;Hamoo, Mohammed J.;Dawood, Shatha H.
    • Earthquakes and Structures
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    • v.8 no.1
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    • pp.275-304
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    • 2015
  • The objective of this paper is to investigate the validity of transmitting boundaries in dynamic analysis of soil-structure interaction problems. As a case study, the proposed Baghdad metro line is considered. The information about the dimensions and the material properties of the concrete tunnel and surrounding soil were obtained from a previous study. A parametric study is carried out to investigate the effect of several parameters including the peak value of the horizontal component of earthquake displacement records and the frequency of the dynamic load. The computer program (Mod-MIXDYN) is used for the analysis. The numerical results are analyzed for three conditions; finite boundaries (traditional boundaries), infinite boundaries modelled by infinite elements (5-node mapped infinite element) presented by Selvadurai and Karpurapu, 1988), and infinite boundaries modelled by dashpot elements (viscous boundaries). It was found that the transmitting boundary absorbs most of the incident energy. The distinct reflections observed for the "fixed boundaries" disappear by using "transmitted boundaries". This is true for both cases of using viscous boundaries or mapped infinite elements. The type and location of the dynamic load represent two controlling factors in deciding the importance of using infinite boundaries. It was found that the results present significant differences when earthquake is applied as a base motion or a pressure load is applied at the surface ground. The peak value of the vertical displacement at nodes A, B, E and F (located at the tunnel's crown and side walls, and at the surface above the tunnel and at the surface 6.5 m away from tunnel's centre respectively) increases with the frequency of the surface pressure load for both cases 1 and 2 (traditional boundaries and mapped infinite elements respectively) while it decreases for case 3 (viscous boundaries). The modular ratio Ec/Es (modulus of elasticity of the concrete lining to that of the surrounding soil) has a considerable effect on the peak value of the horizontal displacement at node B (on the side wall of the tunnel lining) increase about (17.5) times, for the three cases (1, 2, and 3).

Analysis of Multi-Layered Structural Systems Using Nonlinear Finite Elements-Boundary Elements (반무한 다중 구조계의 비선형 유한요소 - 경계요소 해석)

  • 김문겸;장정범;이상도;황학주
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • pp.58-64
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    • 1992
  • It is usual that underground structures are constructed within multi-layered medium. In this paper, an efficient numerical model ling of multi-layered structural systems is studied using coupled analysis of finite elements and boundary elements. The finite elements are applied to the area in which the material nonlinearity is dominated, and the boundary elements are applied to the far field area where the nonlinearity is relatively weak. In the boundary element model 1 ins of the multi-layered medium, fundamental solutions are restricted. Thus, methods which can utilize existing Kelvin and Melan solution are sought for the interior multi-layered domain problem and semi infinite domain problem. Interior domain problem which has piecewise homogeneous layers is analyzed using boundary elements with Kelvin solution; by discretizing each homogeneous subregion and applying compatibility and equilibrium conditions between interfaces. Semi-infinite domain problem is analyzed using boundary elements with Melan solution, by superposing unit stiffness matrices which are obtained for each layer by enemy method. Each methodology is verified by comparing its results which the results from the finite element analysis and it is concluded that coupled analysis using boundary elements and finite elements can be reasonable and efficient if the superposition technique is applied for the multi-layered semi-infinite domain problems.

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A Comparative Study on Coupling of Element-free Galerkin Method and Infinite Element by IE's Shape Function (무한요소 형상함수에 따른 무요소법과의 조합 방법 비교 연구)

  • 이상호;김명원;윤영철
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • pp.279-287
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    • 2003
  • This paper deals with a comparative study on coupling of Element-free Galerkin(EFG) method and Infinite Element(IE) by IE's shape function. In this study, mapped infinite elements(mapped IE) and decay function infinite elements(decay IE) are coupled with the EFG method. A coupling procedure of EFG-Mapped IE is much easier to be integrated than a coupled EFG-Decay IE. A coupled EFG-IE method used well-defined functions to preserve the continuity and linear consistency on the interface of the EFG region and IE region. Several benchmark problems are solved to verify the effectiveness and accuracy of the coupling algorithms by IE's shape function. The numerical results show that the developed algorithms work well for the elastic problems with infinite boundaries.

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Development and Applications of Infinite Elements for Dynamic Soil-Structure Interaction Analysis (동적 지반-구조물 상호작용해석을 위한 무한요소법의 개발 및 응용사례)

  • Yun, C.B.;Yang, S.C.;Kim, J.M.;Choi, J.S.;Kim, D.K.;Seo, C.G.;Chang, S.H.;Park, K.L.
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • pp.14-19
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    • 2008
  • This paper presents dynamic infinite element formulations which have been developed for soil-structure interaction analysis both in frequency and in time domains by the present authors during the past twenty years. Axisymmetric, 2D and 3D layered half-space soil media were considered in the developments. The displacement shape functions of the infinite elements were established using approximate expressions of analytical solutions in frequency domain to represent the characteristics of multiple waves propagating into the unbounded outer domain of the media. The proposed infinite elements were verified using benchmark examples, which showed that the present formulations are very effective for the soil-structure interaction analysis either in frequency or in time domain. Example applications to actual interaction problems are also given to demonstrate the capability and versatility of the present methodology.

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Wave Propagation Analysis of a Strip Foundation in Layered Soils using Infinite Elements (무한요소를 사용한 층상지반에 놓인 스트립기초의 진동전파해석)

  • 윤정방;김두기;김유진;박종찬
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • pp.202-209
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    • 1996
  • In this paper, two dimensional vertical and comer infinite elements which can include multiple wave components to model underlying half space are developed. These elements are natural and economical to model underlying stiff half space or rock. To verify the behavior of these infinite elements, vertical, horizontal, and rocking compliances of a rigid strip foundation on a viscoelastic soil profile are analyzed and compared with those of Tzong and Penzien who used the boundary solution method. Good agreements are noticed between the two methods. The influence of material properties like Poisson's ratio, material damping, and stiffness ratio of layers as well as the influence of geometrical properties such as layer thicknesses and depth of foundation embedment are studied. Example analysis is carried out for the shaking table which is located in KIMM(Korea Institute of Machinery and Materials), and the vertical and horizontal displacements of the analysis are compared with the measured, and show good results and demonstrate the efficiency of the proposed method.

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Use of infinite elements in simulating liquefaction phenomenon using coupled approach

  • Kumari, Sunita;Sawant, V.A.
    • Coupled systems mechanics
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    • v.2 no.4
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    • pp.375-387
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    • 2013
  • Soils consist of an assemblage of particles with different sizes and shapes which form a skeleton whose voids are filled with water and air. Hence, soil behaviour must be analyzed by incorporating the effects of the transient flow of the pore-fluid through the voids, and therefore requires a two-phase continuum formulation for saturated porous media. The present paper presents briefly the Biot's basic theory of dynamics of saturated porous media with u-P formulation to determine the responses of pore fluid and soil skeleton during cyclic loading. Kelvin elements are attached to transmitting boundary. The Pastor-Zienkiewicz-Chan model has been used to describe the inelastic behavior of soils under isotropic cyclic loadings. Newmark-Beta method is employed to discretize the time domain. The response of fluid-saturated porous media which are subjected to time dependent loads has been simulated numerically to predict the liquefaction potential of a semi-infinite saturated sandy layer using finite-infinite elements. A settlement of 17.1 cm is observed at top surface. It is also noticed that liquefaction occurs at shallow depth. The mathematical advantage of the coupled finite element analysis is that the excess pore pressure and displacement can be evaluated simultaneously without using any empirical relationship.

Soil-Structure Interaction Analysis in the Time Domain Using Explicit Frequency-Dependent Two Dimensional Infinite Elements (명시적 주파수종속 2차원 무한요소를 사용한 지반-구조물 상호작용의 시간영역해석)

  • 윤정방;김두기
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • pp.42-49
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    • 1997
  • In this paper, the method for soil-structure interaction analyses in the time domain is proposed. The far field soil region which is the outside of the artificial boundary is modeled by using explicit frequency-dependent two dimensional infinite elements which can include multiple wave components propagating into the unbounded medium. Since the dynamic stiffness matrix of the far field soil region using the proposed infinite elements is obtained explicitly in terms of exciting frequencies and constants in the frequency domain, the matrix can be easily transformed into the displacement unit-impulse response matrix, which corresponds to a convolution integral of it in the time domain. To verify the proposed method for soil-structure interaction analyses in the time domain, the displacement responses due to an impulse load on the surface of a soil layer with the rigid bed rock are compared with those obtained by the method in the frequency domain and those by models with extend finite element meshes. Good agreements have been found between them.

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Infinite Boundary Elements for Soil-Structure Interaction Analysis in Time Domain (지반-구조물 상호작용의 시간영역 해석을 위한 무한경계요소)

  • 윤정방;최준성
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • pp.137-144
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    • 1994
  • In this study, a new procedure for solving 2-D dynamic problems of semi-infinite medium in time domain by boundary element method (BEM) is presented. Efficient modelling of the far field region, infinite boundary elements are introduced. The shape function of the infinite boundary element is a combination of decay functions and Laguerre functions. Though the present shape functions have been developed for the time domain analysis, they may be also applicable to the frequency domain analysis. Through the response analysis in a 2-D half space under a uniformly distributed dynamic load, it has been found that an excellent accuracy can be achieved compared with the analytical solution

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Seismic Response Analysis for Three Dimensional Soil-structure Interaction System using Dynamic Infinite Elements (동적 무한요소를 이용한3차원 지반-구조물 상호작용계의 지진응답해석)

  • Seo, Choon-Gyo;Ryu, Jeong-Soo;Kim, Jae-Min
    • Journal of the Earthquake Engineering Society of Korea
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    • v.12 no.6
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    • pp.55-63
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    • 2008
  • This paper presents a seismic analysis technique for a 3D soil-structure interaction system in a frequency domain, based on the finite element formulation incorporating frequency-dependent infinite elements for the far field soil region. Earthquake input motions are regarded as traveling P, SV and SH waves which are incident vertically from the far-field soil region, and then equivalent earthquake forces are calculated using impedances of infinite soil by dynamic infinite elements and traction and displacement from free field response analysis. For verification and application, seismic response analyses are carried out for a multi-layered soil medium without structure and a typical nuclear power plant in consideration of soil-structure interaction. The results are compared with the free field response using a one-dimensional analytic solution, and a dynamic response of an example structure from another SSI package.