A regularized boundary integral equation method for elastodynamic crack problems

Nishimura, Naoshi; Kobayashi, Shun–ichi

doi:10.1007/bf00301390

Cited by 84 publications

(61 citation statements)

References 13 publications

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“…The new kernels B ikqs (x, x) and A ik (x, x), given by Eqs. (88), (89), are associated with the decomposition (87) of the kernel D ik (x, x) (given in [38] and generalized to anisotropic elasticity in [3]), by virtue of which the Stokes formula (13) could be applied. An identity similar to (51), with S, u, v replaced with Γ, φ, ψ, has been used to obtain (41).…”

Section: Symmetric Galerkin Bie Formulationmentioning

confidence: 99%

“…The derivative BIEs in symmetric Galerkin form can be established in a straightforward fashion by calculating the material derivative of the set of symmetric Galerkin equations (38). Before giving detailed expressions, it is useful to point out that the material derivative of generic bilinear and linear operators B(a, b) and F(â, b) (where a,â, b denote unknown, prescribed and trial functions, respectively) must have the following form:…”

Section: Symmetric Galerkin Derivative Biesmentioning

confidence: 99%

“…having omitted the terms involving the derivatives b of the test functions (they merely repeat the initial set of equations (38), so that b= 0 can be assumed without loss of generality); the new operators B and F depend linearly on θ. In particular, the governing bilinear operators for (p, u, φ)…”

Section: Symmetric Galerkin Derivative Biesmentioning

confidence: 99%

“…in (52) is obtained by taking the material derivative of the third equation of the initial SGBIE system (38). In particular, to establish Eq.…”

Section: Symmetric Galerkin Derivative Biesmentioning

confidence: 99%

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Boundary element based formulations for crack shape sensitivity analysis

Bonnet

2001

Engineering Analysis with Boundary Elements

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The present paper addresses several BIE-based or BIE-oriented formulations for sensitivity analysis of integral functionals with respect to the geometrical shape of a crack. Functionals defined in terms of integrals over the external boundary of a cracked body and involving the solution of a frequency-domain boundary-value elastodynamic problem are considered, but the ideas presented in this paper are applicable, with the appropriate modifications, to other kinds of linear field equations as well. Both direct differentiation and adjoint problem techniques are addressed, with recourse to either collocation or symmetric Galerkin BIE formulations. After a review of some basic concepts about shape sensitivity and material differentiation, the derivative integral equations for the elastodynamic crack problem are discussed in connection with both collocation and symmetric Galerkin BIE formulations. Building upon these results, the direct differentiation and the adjoint solution approaches are then developed. In particular, the adjoint solution approach is presented in three different forms compatible with boundary element method (BEM) analysis of crack problems, based on the discretized collocation BEM equations, the symmetric Galerkin BEM equations and the direct and adjoint stress intensity factors, respectively. The paper closes with a few comments

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Section: Symmetric Galerkin Bie Formulationmentioning

confidence: 99%

Section: Symmetric Galerkin Derivative Biesmentioning

confidence: 99%

Section: Symmetric Galerkin Derivative Biesmentioning

confidence: 99%

“…in (52) is obtained by taking the material derivative of the third equation of the initial SGBIE system (38). In particular, to establish Eq.…”

Section: Symmetric Galerkin Derivative Biesmentioning

confidence: 99%

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Boundary element based formulations for crack shape sensitivity analysis

Bonnet

2001

Engineering Analysis with Boundary Elements

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“…Following an argument given by Nishimura and Kobayashi [16] and using the symmetry property (9), one notes that, for x = y:…”

Section: Evaluation Of δE Tmentioning

confidence: 99%

Regularized direct and indirect symmetric variational BIE formulations for three-dimensional elasticity

Bonnet

1995

Engineering Analysis with Boundary Elements

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Evaluations of hypersingular integrals using Gaussian quadrature

Hui

Shia

1999

Int. J. Numer. Meth. Engng.

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A Gaussian quadrature formula for hypersingular integrals with second‐order singularities is developed based on previous Gaussian quadrature formulae for Cauchy principal value integrals. The formula uses classical orthonormal polynomials, and the formula is then specialized to the case of Legendre and Chebyshev polynomials. Numerical experiments are carried out using the current formula and a previous formula developed by Kutt. It is found that the two methods generally give similar results, and in some cases the current method works better. It has also been shown that the current method allows the choice of an appropriate weight which can increase the convergence rate and the accuracy of the results. Copyright © 1999 John Wiley & Sons, Ltd.

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A regularized boundary integral equation method for elastodynamic crack problems

Cited by 84 publications

References 13 publications

Boundary element based formulations for crack shape sensitivity analysis

Boundary element based formulations for crack shape sensitivity analysis

Regularized direct and indirect symmetric variational BIE formulations for three-dimensional elasticity

Evaluations of hypersingular integrals using Gaussian quadrature

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