Infinite boundary elements

Beer, Gernot; Watson, J. O.

doi:10.1002/nme.1620280602

Cited by 60 publications

(18 citation statements)

References 4 publications

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“…For dynamic loading at the boundary with harmonic time-dependent excitation e iot the solution to (13) will be of the form u f 1 e bx w f 2 e bx 14 where b, f 1 and f 2 are constants to be determined. Substituting (14) in (13),…”

Section: Analytical Solutionmentioning

confidence: 99%

1D infinite element for dynamic problems in saturated porous media

Khalili¹,

Valliappan²,

Yazdi³

et al. 1997

Commun. Numer. Meth. Engng.

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SUMMARYA fully coupled 1D in®nite element for frequency domain analysis of wave propagation problems in unbounded saturated porous media is presented. The element wave propagation function is derived using an analytical solution for Biot's formulation (1962). The eectiveness and the accuracy of the in®nite element proposed are demonstrated through a simple wave propagation problem in a semi-in®nite soil column subjected to a harmonic surface loading. It is shown that an accurate representation of the problem can be obtained by coupling the conventional ®nite elements with the proposed in®nite element. The accuracy of the solution signi®cantly deteriorates when free or ®xed boundary conditions are imposed at the truncated boundary instead of the in®nite element. #

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Section: Analytical Solutionmentioning

confidence: 99%

1D infinite element for dynamic problems in saturated porous media

Khalili¹,

Valliappan²,

Yazdi³

et al. 1997

Commun. Numer. Meth. Engng.

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“…On the other hand, for IBEs: (8) is analogous to eqn (7), and the calculation of Jacobian | ∞ J| is discussed in Section 3. Integrals of eqns (7) and (8) are calculated by standard BEM techniques.…”

Section: Boundary Element Formulationmentioning

confidence: 99%

“…The first reference to an IBE was Kagawa et al [6], in which the shape functions of an origin BE are multiplied by special decay functions. Another type of IBE may be obtained by using mapped functions to relate the local system of coordinates to the global one, as originally shown by Beer and Watson [7]. In those studies that make use of two-dimensional IBEs, such as performed by Moser et al [8], it may be noted that they are generally based on quadrilateral BEs.…”

Section: Introductionmentioning

confidence: 99%

Analyzing layered soil problems with an alternative multi-region BEM technique and a new infinite boundary element formulation

Ribeiro

Paiva

2010

Boundary Elements and Other Mesh Reduction Methods XXXII

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The main objective of this work is to obtain an efficient three-dimensional boundary element (BE) formulation for layered soil simulation. This formulation is obtained by combining an alternative multi-region technique with an infinite boundary element (IBE) formulation. Kelvin fundamental solutions are employed, considering the static analysis of isotropic and linear-elastic domains.Establishing relations between the displacement fundamental solutions of the different domains, the alternative technique used in this paper allows analyzing all domains as a single solid, not requiring equilibrium or compatibility equations. This approach also leads to a smaller system of equations when compared to the usual subregion technique, and the results obtained are more accurate.The two-dimensionally mapped infinite boundary element (IBE) formulation here used is based on a triangular BE with linear shape functions. One advantage of this formulation over quadratic or higher order elements is that no additional degrees of freedom are added to the original BE mesh by the presence of the IBEs. Thus, the IBEs allow the mesh to be reduced without compromising the accuracy of the result.The use of IBEs improves the advantages of the alternative multi-region technique, contributing for the low computational cost and allowing a considerable mesh reduction. Furthermore, the results show good agreement with the ones given in other work, confirming the accuracy of the presented formulation.

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“…Desde então, surgiram na literatura muitos outros trabalhos tratando do MECI. Entre eles podem ser citados Kumar (1984), Kagawa et al (1985), Beer e Watson (1989), Zhang et al (1989), Zhang et al (1991), Zhang et al (1992), Liu e Farris (1993), Chuhan et al (1995), Davies e Bu (1996), Bu (1996) e Bu (1997. Merecem maior destaque alguns trabalhos mais recentes, apresentados a seguir.…”

Section: Comentários Sobre a Revisão Bibliográficaunclassified

Estudo e aplicação de um elemento de contorno infinito na análise da interação solo-estrutura via combinação MEC/MEF

Ribeiro¹

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Infinite boundary elements

Cited by 60 publications

References 4 publications

1D infinite element for dynamic problems in saturated porous media

1D infinite element for dynamic problems in saturated porous media

Analyzing layered soil problems with an alternative multi-region BEM technique and a new infinite boundary element formulation

Estudo e aplicação de um elemento de contorno infinito na análise da interação solo-estrutura via combinação MEC/MEF

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