Boundary element based formulations for crack shape sensitivity analysis

Bonnet, Marc

doi:10.1016/s0955-7997(01)00025-x

Cited by 14 publications

(6 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In particular (Section 6), the direct and adjoint SIFs can be computed from the BEM solution using, for example, any of the techniques mentioned in Section 6.2. BE-based formulations for crack shape sensitivity analysis are surveyed in Bonnet (2001).…”

Section: Sensitivity To Crack Shape In Terms Of Boundary Integralsmentioning

confidence: 99%

Boundary Integral Equation Methods for Elastic and Plastic Problems

Bonnet

2004

Encyclopedia of Computational Mechanics

Self Cite

187

318

View full text Add to dashboard Cite

This chapter deals with formulations based on boundary integral equations (BIEs) for elastic and plastic problems. After a brief review of the basic integral identities of solid mechanics and issues associated with the singular character of the fundamental solutions, the collocation and symmetric Galerkin BIE formulations and the associated boundary element methods (BEMs) are presented, in their conventional form where the complete matrix equation is set up using numerical integration and stored. This approach being inadequate for large problem sizes, fast solution techniques are then reviewed, with emphasis on the fast multipole method. Next, BEMs in both collocation and symmetric Galerkin form are described for fracture mechanics and small‐strain elastoplasticity. The treatment of the hypersingular integrals arising in the integral representation of tractions on the crack surface or of strains at potentially plastic interior points is discussed, along with other issues. Shape sensitivity analysis techniques are also presented, based on either the direct differentiation of the primary elastic BIE or an adjoint solution. Finally, the symmetric Galerkin BIE is used to define a symmetric formulation for BEM–FEM coupling.

show abstract

Section: Sensitivity To Crack Shape In Terms Of Boundary Integralsmentioning

confidence: 99%

Boundary Integral Equation Methods for Elastic and Plastic Problems

Bonnet

2004

Encyclopedia of Computational Mechanics

Self Cite

187

318

View full text Add to dashboard Cite

show abstract

“…If (1) velocity field V(x) is defined such that traction-loading boundary is fixed, i.e., V(x) = 0 on the traction-loading boundary ; and (2)z is replaced with z in Eq. (15), noting that a (ż, z) = a (z,ż) = −a V (z, z), then…”

Section: Homogeneous Materialsmentioning

confidence: 99%

“…For homogeneous materials, several shape sensitivity methods involving discrete [9][10][11] and continuum [12][13][14][15] formulations have appeared in calculating SIFs. Both FEM and BEM have been employed for the shape sensitivity analysis of cracks.…”

Section: Introductionmentioning

confidence: 99%

A continuum shape sensitivity method for fracture analysis of isotropic functionally graded materials

Rao

Rahman

2005

Comput Mech

View full text Add to dashboard Cite

This paper presents a new continuum shape sensitivity method for calculating mixed-mode stress-intensity factors for a stationary crack in two-dimensional, linearelastic, isotropic FGMs with arbitrary geometry. The method involves the material derivative concept taken from continuum mechanics, the mutual potential energy release rate, and direct differentiation. Since the governing variational equation is differentiated prior to discretization, resulting sensitivity equations are independent of approximate numerical techniques, such as the finite element method, boundary element method, mesh-free method, or others. The discrete form of the mutual potential energy release rate is simple and easy to calculate, as it only requires multiplication of displacement vectors and stiffness sensitivity matrices. By judiciously selecting the velocity field, the method only requires displacement response in a subdomain close to the crack tip, thus making the method computationally efficient. Seven finite-element based numerical examples, which comprise mode-I and mixed-mode deformations and/or single or multiple interacting cracks, are presented to evaluate the accuracy of the fracture parameters calculated by the proposed method. Comparisons have been made between stress-intensity factors predicted by the proposed method and available reference solutions in the literature, generated either analytically or numerically using various other fracture integrals or analyses. Excellent agreement is obtained between the results of the proposed method and previously obtained solutions. Therefore, shape sensitivity analysis provides an attractive alternative to fracture analysis of cracks in homogeneous and non-homogeneous materials.

show abstract

“…For homogeneous materials, several shape sensitivity methods involving discrete (Fuenmayor et al, 1997;Hwang et al, 1998;Giner et al, 2002) and continuum (Feijó o et al, 2000;Taroco, 2000;Lee and Grosse, 1993;Bonnet, 2001) formulations have appeared in calculating SIFs. Both FEM and BEM have been employed for the shape sensitivity analysis of cracks.…”

Section: Introductionmentioning

confidence: 99%