Symmetric coupling of Galerkin boundary elements with finite elements

Ganguly, S.; Layton, Jeffrey

doi:10.2514/6.1997-1301

Cited by 6 publications

(5 citation statements)

References 19 publications

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“…This is a limiting case and was used to develop the basic formulation of SFEBE. As previously mentioned, the case of non-matching nodes was developed in Reference [34]. The resulting equations are symmetric and just as e$cient as the present SFEBE method.…”

Section: Fracture Problem Using Sfebementioning

confidence: 92%

“…As an example, a generic two zone problem can be reexamined. The governing Boundary integral formulation for this type of problem is the SomiGliana's identity [33,34] which is reproduced below:…”

Section: Transforming Boundary Element Subdomains To Equivalent Finitmentioning

confidence: 99%

“…The case of non-matching nodes has also been addressed in Reference [34], but is not discussed here for the sake of brevity.…”

Section: Design Studiesmentioning

confidence: 99%

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Symmetric coupling of multi-zone curved Galerkin boundary elements with finite elements in elasticity

Ganguly

Layton

Balakrishna

2000

Int. J. Numer. Meth. Engng.

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SUMMARYThe coupling of Finite Element Method (FEM) with a Boundary Element Method (BEM) is a desirable result that exploits the advantages of each. This paper examines the e$cient symmetric coupling of a Symmetric Galerkin Multi-zone Curved Boundary Element Analysis method with a Finite Element Method for 2-D elastic problems. Existing collocation based multi-zone boundary element methods are not symmetric. Thus, when they are coupled with FEM, it is very di$cult to achieve symmetry, increasing the computational work to solve the problem. This paper uses a fully Symmetric curved Multi-zone Galerkin Boundary Element Approach that is coupled to an FEM in a completely symmetric fashion. The symmetry is achieved by symmetrically converting the boundary zones into equivalent ¯o "nite elements', that are symmetric, so that symmetry in the coupling is retained. This computationally e$cient and fast approach can be used to solve a wide range of problems, although only 2-D elastic problems are shown. Three elasticity problems, including one from the FEM-BEM literature that explore the e$cacy of the approach are presented.

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Section: Fracture Problem Using Sfebementioning

confidence: 92%

Section: Transforming Boundary Element Subdomains To Equivalent Finitmentioning

confidence: 99%

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Symmetric coupling of multi-zone curved Galerkin boundary elements with finite elements in elasticity

Ganguly

Layton

Balakrishna

2000

Int. J. Numer. Meth. Engng.

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“…The following sections of the paper discuss an approach to FEM-BEM coupling that uses a recently developed symmetric multi-zone (multiple subdomain) BEM method for elastic problems [42,43]. The symmetric Galerkin multi-zone boundary element analysis (SGMZBEA) method can be coupled with a FEM in 2D elastic problems via two approaches.…”

Section: Literature Review On Fem-bem Coupling and Corner Nodesmentioning

confidence: 99%

“…However, that type of modelling is not used in the present paper. Here, the problem is solved by changing FEM subdomain to equivalent BEM subdomain [42,44]. This approach is not fully symmetric, but it has block symmetry.…”

Section: Non-matching Node Formulationmentioning

confidence: 99%

A coupling of multi‐zone curved Galerkin BEM with finite elements for independently modelled sub‐domains with non‐matching nodes in elasticity

Ganguly¹,

Layton²,

Balakrishna³

2004

Numerical Meth Engineering

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SUMMARYWhen the different parts of a structure are modelled independently by BEM or FEM methods, it is sometimes necessary to put the parts together without remeshing of the nodes along the part interfaces. Frequently the nodes do not match along the interface. In this work, the symmetric Galerkin multi-zone curved boundary element is a fully symmetric formulation and is the method used for the boundary element part. For BEM-FEM coupling it is then necessary to interpolate the tractions in-between the non-matching nodes for the FEM part. Finally, the coupling is achieved by transforming the finite element domains to equivalent boundary element domains in a block symmetric formulation. This system is then coupled with a boundary element domain with non-matching nodes in-between.

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An efficient time-domain FEM/BEM coupling approach based on FEM implicit Green’s functions and truncation of BEM time convolution process

Soares

Mansur

Estorff

2007

Computer Methods in Applied Mechanics and Engineering

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Symmetric coupling of Galerkin boundary elements with finite elements

Cited by 6 publications

References 19 publications

Symmetric coupling of multi-zone curved Galerkin boundary elements with finite elements in elasticity

Symmetric coupling of multi-zone curved Galerkin boundary elements with finite elements in elasticity

A coupling of multi‐zone curved Galerkin BEM with finite elements for independently modelled sub‐domains with non‐matching nodes in elasticity

An efficient time-domain FEM/BEM coupling approach based on FEM implicit Green’s functions and truncation of BEM time convolution process

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