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

Ganguly, S.; Layton, Jeffrey; Balakrishna, C.

doi:10.1002/nme.893

Cited by 7 publications

(4 citation statements)

References 34 publications

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“…However, as an alternative a coupling of an FE shell model with the so-called symmetric Galerkin boundary-element method (SGBEM) may be applied [33]. An extensive review of the developments regarding the SGBEM can be found in the work by Ganguly et al [34,35].…”

Section: Coupling Of Fe and Be Regionsmentioning

confidence: 99%

Impedance of flexible suction caissons

Liingaard

Andersen

Ibsen

2007

Earthq Engng Struct Dyn

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SUMMARYThe dynamic response of offshore wind turbines is affected by the properties of the foundation and the subsoil. The aim of this paper is to evaluate the dynamic soil-structure interaction of suction caissons for offshore wind turbines. The investigations include evaluation of the vertical and coupled sliding-rocking vibrations, influence of the foundation geometry and examination on the properties of the surrounding soil. The soil is simplified as a homogenous linear viscoelastic material and the dynamic stiffness of the suction caisson is expressed in terms of dimensionless frequency-dependent coefficients corresponding to different degrees of freedom. The dynamic stiffness coefficients for the skirted foundation are evaluated using a three-dimensional coupled boundary element/finite element model. Comparisons with known analytical and numerical solutions indicate that the static and dynamic behaviours of the foundation are predicted accurately using the applied model. The analysis has been carried out for different combinations of the skirt length, Poisson's ratio of the subsoil and the ratio of the soil stiffness to the skirt stiffness.

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Section: Coupling Of Fe and Be Regionsmentioning

confidence: 99%

Impedance of flexible suction caissons

Liingaard

Andersen

Ibsen

2007

Earthq Engng Struct Dyn

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“…A symmetric coupling of the BEM and FEM was proposed later by Costabel and Stephan [409] followed by the variationally based coupling procedure between the FEM and an indirect ver sion of the Galerkin BEM developed by Polizzotto and Zito [410]. In many papers, the BEM subdomains, see for instance the work by Haas and Kuhn [411] and by Ganguly, Layton and Balakrishna [412], or the FEM subdomains, e.g., the work by Ganguly, Layton and Balakrishna [413], are handled as equivalent finite or bound ary macro elements, respectively. In recent years, however, the idea of adapting one of the two techniques to the other in a sort of master slave technique with macroelements has been gradually abandoned for a more balanced approach.…”

Section: Fast Methodologiesmentioning

confidence: 99%

“…A non matching node coupling of SGBEM and FEM is devel oped by Ganguly, Layton and Balakrishna [413] in the context of a BE based approach. In fracture mechanics, a coupling approach which preserves the independence of the FE and BE meshes is the so called hybrid surface integral finite element technique, see the works by Keat, Annigeri and Cleary [414], Han and Atluri [415] and Forth and Staroselsky [280].…”

Section: Fast Methodologiesmentioning

confidence: 99%

Recent Advances and Emerging Applications of the Boundary Element Method

Liu

Mukherjee

Nishimura

et al. 2011

Applied Mechanics Reviews

145

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Sponsored by the U.S. National Science Foundation, a workshop on the boundary element method (BEM) was held on the campus of the University of Akron during September 1–3, 2010 (NSF, 2010, “Workshop on the Emerging Applications and Future Directions of the Boundary Element Method,” University of Akron, Ohio, September 1–3). This paper was prepared after this workshop by the organizers and participants based on the presentations and discussions at the workshop. The paper aims to review the major research achievements in the last decade, the current status, and the future directions of the BEM in the next decade. The review starts with a brief introduction to the BEM. Then, new developments in Green's functions, symmetric Galerkin formulations, boundary meshfree methods, and variationally based BEM formulations are reviewed. Next, fast solution methods for efficiently solving the BEM systems of equations, namely, the fast multipole method, the pre-corrected fast Fourier transformation method, and the adaptive cross approximation method are presented. Emerging applications of the BEM in solving microelectromechanical systems, composites, functionally graded materials, fracture mechanics, acoustic, elastic and electromagnetic waves, time-domain problems, and coupled methods are reviewed. Finally, future directions of the BEM as envisioned by the authors for the next five to ten years are discussed. This paper is intended for students, researchers, and engineers who are new in BEM research and wish to have an overview of the field. Technical details of the BEM and related approaches discussed in the review can be found in the Reference section with more than 400 papers cited in this review.

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“…Symmetric Galerkin BEM (SGBEM) schemes applied to DD problems [10,[24][25][26][27][28] and contact problems [29][30][31][32][33] represent a valuable alternative numerical technique as they combine the boundary character of BEM with the symmetrical and energy-based formulation typical for FEM. SGBEM also enables an easy and straightforward coupling with finite element subdomains [34][35][36].…”

Section: Introductionmentioning

confidence: 99%

SGBEM with Lagrange multipliers applied to elastic domain decomposition problems with curved interfaces using non‐matching meshes

Vodička

Mantič

Parı́s

2010

Numerical Meth Engineering

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SUMMARYAn original approach to the solution of linear elastic domain decomposition problems by the symmetric Galerkin boundary element method is developed. The approach is based on searching for the saddle-point of a new potential energy functional with Lagrange multipliers. The interfaces can be either straight or curved, open or closed. The two coupling conditions, equilibrium and compatibility, along an interface are fulfilled in a weak sense by means of Lagrange multipliers (interface displacements and tractions), which enables non-matching meshes to be used at both sides of interfaces between subdomains. The accuracy and robustness of the method is tested by several numerical examples, where the numerical results are compared with the analytical solution of the solved problems, and the convergence rates of two error norms are evaluated for h-refinements of matching and non-matching boundary element meshes.

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

Cited by 7 publications

References 34 publications

Impedance of flexible suction caissons

Impedance of flexible suction caissons

Recent Advances and Emerging Applications of the Boundary Element Method

SGBEM with Lagrange multipliers applied to elastic domain decomposition problems with curved interfaces using non‐matching meshes

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