An iterative finite element-boundary element algorithm

Lin, Chia Ching; Lawton, Evert C.; Caliendo, Joseph A.; Anderson, Loren R.

doi:10.1016/0045-7949(95)00285-5

Cited by 67 publications

(46 citation statements)

References 12 publications

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“…The coefficient matrices N and N σ in Eqs. (29) and (31) are related to the volume integral of the initial stress term, such as [1]…”

Section: Numerical Implementationmentioning

confidence: 99%

“…In such approach, subregions are assembled into a large single equation system and solved either by direct or iterative method. In order to avoid solving the large global equation system and difficult programming issues, the iterative coupling approaches have been introduced mostly in the context of FEM-BEM coupling techniques [28][29][30][31][32]. Soares et al [33] presented iterative coupling between two BEM formulations, namely the so-called D-BEM (D stands for domain) and the TD-BEM (TD stands for time-domain) for 2D nonlinear elastodynamic analysis.…”

Section: Introductionmentioning

confidence: 99%

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A BEM formulation for inelastic transient dynamic analysis using domain decomposition and particular integrals

2010

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This study deals with the domain decomposition method and particular integrals for multi-region inelastic transient dynamic analysis. The particular integral formulation for single-region inelastic transient dynamic analysis is obtained by eliminating the acceleration volume integral and treating the initial stress term by volume cell. The Houbolt time integration scheme is used for the timemarching process. The Newton-Raphson algorithm for plastic multiplier is used to solve the system equation. In order to extend to multi-region problems, the domain decomposition method is examined. The domain of the original problem is subdivided into subregions. The interface boundary conditions are updated by using the iterative coupling employing Schwarz algorithm. Numerical results of two example problems are given to demonstrate the validity and accuracy of the present formulation.

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“…The coefficient matrices N and N σ in Eqs. (29) and (31) are related to the volume integral of the initial stress term, such as [1]…”

Section: Numerical Implementationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A BEM formulation for inelastic transient dynamic analysis using domain decomposition and particular integrals

2010

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“…Again, however, the problem is exacberated by the unsymmetric BEM subdomain when using typical collocation approaches. An alternative approach, termed as iterative domain decomposition coupling, uses an iterative approach [32]. In the case of elastic problems, it solves the problem by continuously adjusting the unbalanced forces or displacements from the subdomains to an artificial interface until continuity and equilibrium are satisfied.…”

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

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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“…Again, however, the problem is exacerated by the unsymmetric BEM subdomain when using typical collocation approaches. An alternative method, termed as iterative domain decomposition coupling, uses an iterative approach [30,31]. In the case of elastic problems, it solves the problem by continuously adjusting the unbalanced forces or displacements from the subdomains to an arti"cial interface until continuity and equilibrium are satis"ed.…”

Section: Past Work In Fem-bem Couplingmentioning

confidence: 99%

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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An iterative finite element-boundary element algorithm

Cited by 67 publications

References 12 publications

A BEM formulation for inelastic transient dynamic analysis using domain decomposition and particular integrals

A BEM formulation for inelastic transient dynamic analysis using domain decomposition and particular integrals

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

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

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