A simple explicit–implicit finite element tearing and interconnecting transient analysis algorithm

2014

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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.

([], \begin{matrix} falsenone nonefalsearray \\ arraycenter {\overset{MathClass-opF}{true}}_{bb} & arraycenter - R_{b} & arraycenter {\overset{L}{true}}_{f} \\ arraycenter - R_{b}^{T} & arraycenter 0 & arraycenter 0 \\ arraycenter {\overset{L}{true}}_{f}^{T} & arraycenter 0 & arraycenter 0 \end{matrix}) ({}, \begin{matrix} falsenonefalsearray \\ arraycenter Δ λ \\ arraycenter Δ α \\ arraycenter Δ X_{f} \end{matrix}) MathClass-rel= ({}, \begin{matrix} falsenonefalsearray \\ arraycenter - r_{λ} \\ arraycenter - r_{α} \\ arraycenter - r_{X_{f}} \end{matrix})

where the definitions

{bold \overset{MathClass-op̂}{L}}_{f} MathClass-rel= {bold-italicA}^{T} {bold-italicL}_{f}

and R b = B T R have been introduced. Very effective and well documented parallel iterative methods exist to solve this arrow‐head profile system .…”

Section: Partitioned Solution Algorithm: Afeti Methodsmentioning

confidence: 99%

scriptP MathClass-rel= bold-italicI MathClass-bin- bold-italicM bold-italicR {bold-italicM}_{α}^{MathClass-bin- 1} {bold-italicR}^{T}

Section: Filtered Deformational Modesmentioning

confidence: 99%

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

González¹,

Abascal²,

2014

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“…AFETI method provides an iterative algorithm for the solution of the flexibility equations . The algorithm proposes a decomposition of the localized multipliers in the following form: using two symmetric projectors: where represents the self‐equilibrated part of the localized multipliers and λ α contains the net component of the multipliers, that is, .…”

Section: Solution Algorithm: Classical Afeti Methodsmentioning

confidence: 99%

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

González

Rodríguez-Tembleque

et al. 2012

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SUMMARYThe finite element tearing and interconnecting (FETI) method is recognized as an effective domain decomposition tool to achieve scalability in the solution of partitioned second-order elasticity problems. In the boundary element tearing and interconnecting (BETI) method, a direct extension of the FETI algorithm to the BEM, the symmetric Galerkin BEM formulation, is used to obtain symmetric system matrices, making possible to apply the same FETI conjugate gradient solver. In this work, we propose a new BETI variant labeled nsBETI that allows to couple substructures modeled with the FEM and/or non-symmetrical BEM formulations. The method connects non-matching BEM and FEM subdomains using localized Lagrange multipliers and solves the associated non-symmetrical flexibility equations with a Bi-CGstab iterative algorithm. Scalability issues of nsBETI in BEM-BEM and combined BEM-FEM coupled problems are also investigated.

“…First, the interface forces λ n are computed solving Equation . This step can be performed iteratively or in a direct form as described in Algorithm 1, solving first for the frame accelerations

{\ddot{u}}_{f}^{n}

and then for the multipliers λ n . Once we know the interface forces, the accelerations

{\ddot{u}}^{n}

are obtained from Equation .…”

Section: Partitioned Analysismentioning

confidence: 99%

Large‐step explicit time integration via mass matrix tailoring

González

2019

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Summary A method for tailoring mass matrices that allows large time‐step explicit transient analysis is presented. It is shown that the accuracy of the present tailored mass matrix preserves the low‐frequency contents while effectively replacing the unwanted higher mesh frequencies by a user‐desired cutoff frequency. The proposed mass tailoring methods are applicable to elemental, substructural as well as global systems, requiring no modifications of finite element generation routines. It becomes most computationally attractive when used in conjunction with partitioned formulation as the number of higher (or lower) modes to be filtered out (or retained) are significantly reduced. Numerical experiments with the proposed method demonstrate that they are effective in filtering out higher modes in bars, beams, plain stress, and plate bending problems while preserving the dominant low‐frequency contents.