Cracks in three dimensions: A dynamic dual boundary element analysis

Wen, P.H.; Aliabadi, M.H.; Rooke, D.P.

doi:10.1016/s0045-7825(98)00116-9

Cited by 60 publications

(38 citation statements)

References 21 publications

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“…With the assumption that displacements and strains are continuous over the boundary, the solutions of equation (2), using BEM formulation, are written as [22] …”

Section: Dual Boundary Element Methodsmentioning

confidence: 99%

A boundary element model for structural health monitoring using piezoelectric transducers

Zou

Benedetti

Aliabadi

2013

Smart Mater. Struct.

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In this paper, for the first time, the boundary element method (BEM) is used for modelling smart structures instrumented with piezoelectric actuators and sensors. The host structure and its cracks are formulated with the 3D dual boundary element method (DBEM), and the modelling of the piezoelectric transducers implements a 3D semi-analytical finite element approach. The elastodynamic analysis of the structure is performed in the Laplace domain and the time history is obtained by inverse Laplace transform. The sensor signals obtained from BEM simulations show excellent agreement with those from FEM simulations and experiments. This work provides an alternative methodology for modelling smart structures in structural health monitoring (SHM) applications.

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“…With the assumption that displacements and strains are continuous over the boundary, the solutions of equation (2), using BEM formulation, are written as [22] …”

Section: Dual Boundary Element Methodsmentioning

confidence: 99%

A boundary element model for structural health monitoring using piezoelectric transducers

Zou

Benedetti

Aliabadi

2013

Smart Mater. Struct.

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“…After enforcing the boundary conditions, system (14) can be written as To analyze a general elastodynamic problem using the Laplace transform technique, one has to compute the solution of system (14) for many values of the Laplace parameter. A set of values s k with k = 1, .…”

Section: The Dbem In Laplace Transform Variablesmentioning

confidence: 99%

“…The use of hierarchical matrices for the fast solution of static DBEM systems has been successfully developed for isotropic and anisotropic crack problems by Benedetti et al [26,27]. The form of the system (14) suggests the extension of the technique developed in [26] to the solution of the elastodynamic DBEM problems in the Laplace transform domain.…”

Section: Fast Solutionmentioning

confidence: 99%

“…However, to give a more visual representation of the solution accuracy for engineering purposes, the DSIF for two specific crack problems is computed in this section. The transformed DSIFs are computed directly from the transformed displacements on the crack surface and the time-dependent values are then obtained by the Durbin's Laplace transform inversion, following the procedure used in [14], to which the reader is referred for further details.…”

Section: Dsifs Evaluationmentioning

confidence: 99%

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A fast hierarchical dual boundary element method for three‐dimensional elastodynamic crack problems

Benedetti

Aliabadi

2010

Numerical Meth Engineering

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In this work a fast solver for large-scale three-dimensional elastodynamic crack problems is presented, implemented, and tested. The dual boundary element method in the Laplace transform domain is used for the accurate dynamic analysis of cracked bodies. The fast solution procedure is based on the use of hierarchical matrices for the representation of the collocation matrix for each computed value of the Laplace parameter. An ACA (adaptive cross approximation) algorithm is used for the population of the low rank blocks and its performance at varying Laplace parameters is investigated. A preconditioned GMRES is used for the solution of the resulting algebraic system of equations. The preconditioners are built exploiting the hierarchical arithmetic and taking full advantage of the hierarchical format. An original strategy, based on the computation of some local preconditioners only, is presented and tested to further speed up the overall analysis. The reported numerical results demonstrate the effectiveness of the technique for both uncracked and cracked solids and show significant reductions in terms of both memory storage and computational time

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“…Fedelinski et al (1995) have developed a general formulation for modelling elastodynamic crack problems in a single domain by the DBEM. The DBEM is further extended by Wen et al (1998) to address 3-D problems subjected to dynamic loading.…”

Section: Elastodynamic Analysismentioning

confidence: 99%

A review of SIF evaluation and modelling of singularities in BEM

Mukhopadhyay

Maiti

Kakodkar

2000

Computational Mechanics

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Various boundary element method (BEM) based approaches to solve crack problems are discussed. The displacement method, J-integral method and the modi®ed crack closure integral (MCCI) method for the evaluation of the stress intensity factors (SIFs) are reviewed. Effects of partial and total modelling of singularities on the accuracy of the results have been presented. Elements capable of partial and total modelling of the wellknown square root singularities, variable order singularities, neighbouring variable order singularities, etc., are also reviewed. Case studies are included to illustrate the effectiveness of the various methods of calculation of the SIFs and the performance of the special elements.

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Cracks in three dimensions: A dynamic dual boundary element analysis

Cited by 60 publications

References 21 publications

A boundary element model for structural health monitoring using piezoelectric transducers

A boundary element model for structural health monitoring using piezoelectric transducers

A fast hierarchical dual boundary element method for three‐dimensional elastodynamic crack problems

A review of SIF evaluation and modelling of singularities in BEM

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