Sur l'approximation des solutions du probleme de Dirichlet dans un ouvert avec coins

Moussaoui, Mohand

doi:10.1007/bfb0076272

Cited by 19 publications

(19 citation statements)

References 4 publications

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“…Thus, the unknown coefficients a¡± are the solutions of a homogeneous linear system of eighth order given by equations (12) and (13) and written in condensed form as…”

Section: Singularity-order Determinationmentioning

confidence: 99%

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Some theoretical aspects in computational analysis of adhesive lap joints

Destuynder

Michavila²,

Santos³

et al. 1992

Numerical Meth Engineering

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SUMMARYThis paper is devoted to the numerical analysis of bidimensional bonded lap joints. For this purpose, the stress singularities occurring at the intersections of the adherend-adhesive interfaces with the free edges are first investigated and a method for computing both the order and the intensity factor ofthese singularities is described briefly. After that, a simplified model, in which the adhesive domain is reduced to a line, is derived by using an asymptotic expansion method. Then, assuming that the assembly debonding is produced by a macro-crack propagation in the adhesive, the associated energy release rate is computed. Finally, a homogenization technique is used in order to take into account a preliminary adhesive damage consisting of periodic micro-cracks. Sorne numerical results are presented.

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“…Thus, the unknown coefficients a¡± are the solutions of a homogeneous linear system of eighth order given by equations (12) and (13) and written in condensed form as…”

Section: Singularity-order Determinationmentioning

confidence: 99%

“…When A is real, one has a3 = al and a4 = a2, where ais the complex conjugate of a. Then, equations (12) and (13) reduce to those given by Rao 5 ( Table 2c, column 1 and Table 2b, column B, respectively).…”

Section: Singularity-order Determinationmentioning

confidence: 99%

Some theoretical aspects in computational analysis of adhesive lap joints

Destuynder

Michavila²,

Santos³

et al. 1992

Numerical Meth Engineering

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“…For the approximation of the singular coefficients α i (δ h ), we use an extraction formula of Moussaoui [13] (see also [4]). We first introduce the dual singular functions Definition 4.1.…”

Section: Remark 43 the Constant Functions Belong Towmentioning

confidence: 99%

Numerical study of a new global minimizer for the Mumford-Shah functional in R³

Merlet

2007

ESAIM: COCV

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Abstract.In [Progress Math. 233 (2005)], David suggested the existence of a new type of global minimizers for the Mumford-Shah functional in R 3 . The singular set of such a new minimizer belongs to a three parameters family of sets (0 < δ1, δ2, δ3 < π). We first derive necessary conditions satisfied by global minimizers of this family. Then we are led to study the first eigenvectors of the Laplace-Beltrami operator with Neumann boundary conditions on subdomains of S 2 with three reentrant corners. The necessary conditions are constraints on the eigenvalue and on the ratios between the three singular coefficients of the associated eigenvector. We use numerical methods (Singular Functions Method and Moussaoui's extraction formula) to compute the eigenvalues and the singular coefficients. We conclude that there is no (δ1, δ2, δ3) for which the necessary conditions are satisfied and this shows that the hypothesis was wrong.Mathematics Subject Classification. 35J25, 49R50, 65N38.

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“…In the above citations, the given formulas are based on the explicit knowledge of the dual singular solution of the adjoint problem. Furthermore, there exist several algorithms for the numerical computation of the coefficients c k , see for example, Assous et al (1998Assous et al ( , 2000Assous et al ( , 2003a, Blum and Dobrowolski (1982), Bourlard et al (1992), , , Destuynder and Djaoua (1980), Fix et al (1973), Moussaoui (1985), Strang and Fix (1973).…”

Section: Introductionmentioning

confidence: 99%

Flux intensity functions for the Laplacian at polyhedral edges

Nkemzi

Jung

2012

Int J Fract

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We present explicit representation formulas for the coefficients of the singularities associated with mixed boundary value problems for the Poisson equation in two-dimensional domains with corners and three-dimensional domains with straight edges including cracks. We rely on partial Fourier analysis of the boundary value problem in the vicinity of the singularities to derive an asymptotic expansion of the solution. Hence, the edge flux intensity functions are expressed in terms of Fourier series and we give integral expressions from which the associated Fourier coefficients can be computed independently and in parallel. Our method does not require the knowledge of the dual singular solutions of the adjoint problems. Moreover, the constructive nature of the formulas provides in a straight forward way a strategy for the construction of efficient numerical methods for the accurate computation of the stress intensity factors and the edge flux intensity functions. Also, the formulas can be used to construct postprocessing algorithms for the standard finite element approximation of the solution of the boundary value problem to improve the accuracy.Examples that illustrate the efficiency and robustness of the formulas are also given.

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Sur l'approximation des solutions du probleme de Dirichlet dans un ouvert avec coins

Cited by 19 publications

References 4 publications

Some theoretical aspects in computational analysis of adhesive lap joints

Some theoretical aspects in computational analysis of adhesive lap joints

Numerical study of a new global minimizer for the Mumford-Shah functional in R³

Flux intensity functions for the Laplacian at polyhedral edges

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Sur l'approximation des solutions du probleme de Dirichlet dans un ouvert avec coins

Cited by 19 publications

References 4 publications

Some theoretical aspects in computational analysis of adhesive lap joints

Some theoretical aspects in computational analysis of adhesive lap joints

Numerical study of a new global minimizer for the Mumford-Shah functional in R3

Flux intensity functions for the Laplacian at polyhedral edges

Contact Info

Product

Resources

About

Numerical study of a new global minimizer for the Mumford-Shah functional in R³