The nsBETI method: an extension of the FETI method to non‐symmetrical BEM‐FEM coupled problems

González, José Luís Galán; Rodríguez-Tembleque, Luis; Park, K. C.; Abascal, Ramón

doi:10.1002/nme.4418

Cited by 7 publications

(5 citation statements)

References 67 publications

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“…To the best of the authors' knowledge, in spite of the BETI algorithm has been successfully extended to contact problems using SGBEM formulation [50,51], its application using a non-symmetrical boundary element formulation has not been completed. The extension of BETI technique to non-symmetrical boundary element formulations has only been only considered in domain decomposition elastic problems by González et al [52], but its extension to frictional contact problems is not straightforward. So the implementation of BETI schemes for non-symmetrical boundary element PE contact problems could be considered in future works.…”

Section: ψ (Z) ≤ ε Being ψ (Z) = H T (Z)h(z)/2)mentioning

confidence: 99%

3D BEM for orthotropic frictional contact of piezoelectric bodies

2015

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A numerical methodology to model the threedimensional frictional contact interaction of piezoelectric materials in presence of electric fields is presented in this work. The boundary element method (BEM) is used in order to compute the electro-elastic influence coefficients. The proposed BEM formulation employs an explicit approach for the evaluation of the corresponding fundamental solutions, which are valid for general anisotropic behaviour meanwhile mathematical degeneracies in the context of the Stroh formalism are allowed. The contact methodology is based on an augmented Lagrangian formulation and uses an iterative Uzawa scheme of resolution. An orthotropic frictional law is implemented in this work so anisotropy is present both in the bulk and in the surface. The methodology is validated by comparison with benchmark analytical solutions. Some additional examples are presented and discussed in detail, revealing the importance of considering orthotropic frictional contact conditions in the electro-elastic analysis of this kind of problems.

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Section: ψ (Z) ≤ ε Being ψ (Z) = H T (Z)h(z)/2)mentioning

confidence: 99%

3D BEM for orthotropic frictional contact of piezoelectric bodies

2015

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“…After discretization, Equation transforms into

δ W_{c} MathClass-rel= δ ({}, λ T ([], {bold-italicB}^{T} ((), {bold-italicR}_{t} {bold-italicA}^{T} {bold-italicX}_{0} MathClass-bin+ bold-italicr MathClass-bin+ {scriptP}^{T} bold-italicd) MathClass-bin- {bold-italicA}^{T} {bold-italicL}_{f} {bold-italicX}_{f}))

where B is a Boolean matrix used to extract the boundary‐node DOFs from the displacement vector and matrix L f is another Boolean matrix mapping from frame DOFs to substructure DOFs .…”

Section: Variational Formulationmentioning

confidence: 99%

“…If that is the case, after discretization, functional (40) can be approximated by the discrete equation:…”

Section: Virtual Work Of External Forcesmentioning

confidence: 99%

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Partitioned analysis of flexible multibody systems using filtered linear finite element deformational modes

González¹,

Abascal²,

Park

2014

Numerical Meth Engineering

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SUMMARYThis work presents a partitioned finite element formulation for flexible multibody systems, based on the floating frame (FF) approach, under the assumption of small deformations but arbitrarily large rotations of the bodies. In classical FF of reference methods, deformational modes are normally computed by modal analysis. In this approach, free‐floating modes are eliminated from the linear model using projection techniques and substituted by a complete set of non‐linear finite rotations. In this way, all deformational modes are retained, and no modal selection is needed. The main difference between this work and a classical FF of reference formulation is an algebraic separation of pure deformational modes from rigid‐body motions. The proposed methodology presents the following advantages. First, the position and orientation of the FF has no restriction and can be freely located in the body with identical results. Second, the formulation uses only the linear finite element matrices of a classical vibration problem; hence, they can be easily obtained from linear FEM packages. Third, no selection of modes is needed, all deformational modes are retained through the filtering process. And finally, thanks to the use of localized Lagrangian multipliers (LLM), a partitioned system is obtained that can be solved iteratively and in a distributed manner by available scalable solvers. Copyright © 2014 John Wiley & Sons, Ltd.

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“…where vectors t and u contain the solid boundary tractions and displacements respectively, H and G are the BEM system matrices obtained when assembling elemental contributions and vector b is a known function of the boundary conditions, see [35] for more details.…”

Section: Wear and Contact Mechanicsmentioning

confidence: 99%

A Partitioned Formulation for FEM/BEM Coupling in Contact Problems Using Localized Lagrange Multipliers

González

Park

Abascal

2014

KEM

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This paper presents a state-of-the-art in the use of localized Lagrange multipliers (LLMs)for 3D frictional contact problems coupling the Finite Element Method (FEM) and the BoundaryElement Method (BEM). Resolution methods for the contact problem between non-matching mesheshave traditionally been based on a direct coupling of the contacting solids using classical Lagrangemultipliers. These methods tend to generate strongly coupled systems that require a deep knowledgeof the discretization characteristics on each side of the contact zone complicating the process ofmixing different numerical techniques. In this work a displacement contact frame is inserted betweenthe FE and BE interface meshes, discretized and ﬁnally connected to the contacting substructuresusing LLMs collocated at the mesh-interface nodes. This methodology will provide a partitionedformulation which preserves software modularity and facilitates the connection of non-matching FEand BE meshes.

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The nsBETI method: an extension of the FETI method to non‐symmetrical BEM‐FEM coupled problems

Cited by 7 publications

References 67 publications

3D BEM for orthotropic frictional contact of piezoelectric bodies

3D BEM for orthotropic frictional contact of piezoelectric bodies

Partitioned analysis of flexible multibody systems using filtered linear finite element deformational modes

A Partitioned Formulation for FEM/BEM Coupling in Contact Problems Using Localized Lagrange Multipliers

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