Boundary Integral Equation Methods for Elastic and Plastic Problems

Bonnet, Marc

doi:10.1002/0470091355.ecm047

Cited by 187 publications

(345 citation statements)

References 144 publications

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“…The integral operator L ij is non-local and hypersingular (see Mogilevskaya (2014);Bonnet (1999); Hills et al (1996) for more details on elastic fracture problems and their integral representations). Its numerical discretization results in a fully populated matrix.…”

Section: Linear Elasticitymentioning

confidence: 99%

Numerical methods for hydraulic fracture propagation: A review of recent trends

Lecampion

Bunger

Zhang

2018

Journal of Natural Gas Science and Engineering

350

172

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Section: Linear Elasticitymentioning

confidence: 99%

Numerical methods for hydraulic fracture propagation: A review of recent trends

Lecampion

Bunger

Zhang

2018

Journal of Natural Gas Science and Engineering

350

172

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“…One technique for the construction of Z ΓE (ω) consists of using the boundary integral formulations (Refs. [18,[108][109][110][111][112][113][114][115]). In the time domain, it uses the so-called Kirchhoff retarded potential formula (see for instance Refs.…”

Section: Symmetric Boundary Element Methods Without Spurious Frequencimentioning

confidence: 99%

Advanced Computational Dissipative Structural Acoustics and Fluid-Structure Interaction in Low-and Medium-Frequency Domains. Reduced-Order Models and Uncertainty Quantification

Ohayon¹,

Soize²

2012

International Journal of Aeronautical and Space Sciences

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This paper presents an advanced computational method for the prediction of the responses in the frequency domain of general linear dissipative structural-acoustic and fluid-structure systems, in the low-and medium-frequency do mains and this includes uncertainty quantification. The system under consideration is constituted of a deformable dissipative structure that is coupled with an internal dissipative acoustic fluid. This includes wall acoustic impedances and it is surrounded by an infinite acoustic fluid. The system is submitted to given internal and external acoustic sources and to the prescribed mechanical forces. An efficient reduced-order computational model is constructed by using a finite element discretization for the structure and an internal acoustic fluid. The external acoustic fluid is treated by using an appropriate boundary element method in the frequency domain. All the required modeling aspects for the analysis of the medium-frequency domain have been introduced namely, a viscoelastic behavior for the structure, an appropriate dissipative model for the internal acoustic fluid that includes wall acoustic impedance and a model of uncertainty in particular for the modeling errors. This advanced computational formulation, corresponding to new extensions and complements with respect to the state-of-the-art are well adapted for the development of a new generation of software, in particular for parallel computers. Key words:Computational mechanics, Structural acoustics, Vibroacoustic, Fluid-structure interaction, Uncertainty quantification, Reduced-order model, Medium frequency, Low frequency, Dissipative system, Viscoelasticity, Wall acoustic impedance, Finite element discretization, Boundary element method Nomenclature a ijkh = elastic coefficients of the structure b ijkh = damping coefficients of the structure c 0 = speed of sound in the internal acoustic fluid c E = speed of sound in the external acoustic fluid f = vector of the generalized forces for the internal acoustic fluid f S = vector of the generalized forces for the structure g = mechanical body force field in the structure i = imaginary complex number i k = wave number in the external acoustic fluid n = number of internal acoustic DOF n s = number of structure DOF n j = component of vector n n = outward unit normal to Abstract This paper presents an advanced computational method for the prediction of the responses in the frequency domain of general linear dissipative structural-acoustic and uid-structure systems, in the low-and medium-frequency domains and this includes uncertainty quantication. The system under consideration is constituted of a deformable dissipative structure that is coupled with an internal dissipative acoustic uid. This includes wall acoustic impedances and it is surrounded by an innite acoustic uid. The system is submitted to given internal and external acoustic sources and to the prescribed mechanical forces. An efcient reduced-order computational model is constructed by using a nite element discret...

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“…For further details regarding this key treatment of the integral in (3.10), the reader is directed to standard textbooks (see Brebbia, Telles & Wrobel 1984;Bonnet 1995) and also to Sellier (2010). The discretized counterpart of (3.10) then becomes a linear system A · X = B, with the 3N-dimensional unknown discretized density vector X and a 3N × 3N square, dense, non-symmetric so-called influence matrix A.…”

Section: Determination Of the Green's Tensormentioning

confidence: 99%

Motion of a solid particle in a shear flow along a porous slab

et al. 2012

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The flow field around a solid particle moving in a shear flow along a porous slab is obtained by solving the coupled Stokes-Darcy problem with the Beavers and Joseph slip boundary condition on the slab interfaces. The solution involves the Green's function of this coupled problem, which is given here. It is shown that the classical boundary integral method using this Green's function is inappropriate because of supplementary contributions due to the slip on the slab interfaces. An 'indirect boundary integral method' is therefore proposed, in which the unknown density on the particle surface is not the actual stress, but yet allows calculation of the force and torque on the particle. Various results are provided for the normalized force and torque, namely friction factors, on the particle. The cases of a sphere and an ellipsoid are considered. It is shown that the relationships between friction coefficients (torque due to rotation and force due to translation) that are classical for a no-slip plane do not apply here. This difference is exhibited. Finally, results for the velocity of a freely moving particle in a linear and a quadratic shear flow are presented, for both a sphere and an ellipsoid.

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Boundary Integral Equation Methods for Elastic and Plastic Problems

Cited by 187 publications

References 144 publications

Numerical methods for hydraulic fracture propagation: A review of recent trends

Numerical methods for hydraulic fracture propagation: A review of recent trends

Advanced Computational Dissipative Structural Acoustics and Fluid-Structure Interaction in Low-and Medium-Frequency Domains. Reduced-Order Models and Uncertainty Quantification

Motion of a solid particle in a shear flow along a porous slab

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