Topological sensitivity analysis

Novotny, Antônio André; Feijóo, Raúl A.; Taroco, E.; Padra, Claudio

doi:10.1016/s0045-7825(02)00599-6

Cited by 273 publications

(241 citation statements)

References 12 publications

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“…In Section 3 the shape and orientation sensitivity analysis is presented. It is demonstrated that the topological derivative with respect to the hole area can be obtained from the shape sensitivity analysis assuming vanishing size parameter, as it was proposed by Novotny et al (2003). The transition to the case of plane crack is obtained by setting the minor ellipse semiaxis length to tend to zero.…”

Section: Introductionmentioning

confidence: 89%

“…The topological sensitivity analysis related to crack nucleation and growth was applied in several papers by Van Goethem and Novotny (2010), Feijóo et al (2000), Khludnev et al (2009), Novotny et al (2003), Silva et al (2010Silva et al ( , 2011. Taroco (2000) derived first and second order shape sensitivity derivatives of the potential energy expressed in terms of path independent integrals and next related to crack growth.…”

Section: Introductionmentioning

confidence: 99%

“…To express sensitivity derivative with respect to the hole area A = πξ 2 ab, the following formula is obtained using the relation (21) and the incremental form d A = 2πξab dξ , thus (cf. Novotny et al 2003)…”

mentioning

confidence: 99%

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Topological sensitivity derivative with respect to area, shape and orientation of an elliptic hole in a plate

Bojczuk

Mróz

2011

Struct Multidisc Optim

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The topological sensitivity derivative of a functional expressed in terms of displacement, strain or stress fields and boundary tractions is derived for the case of an elliptical hole introduced in the plate. The derivative is specified with respect to the hole area, the length of ellipse axes and their orientation in terms of primary and adjoint state fields. The shape sensitivity derivative for a finite hole can be applied and the topological derivative with respect to the hole area is obtained in the limiting case. The transition to a plane crack occurs for vanishing length of minor axis and the topological derivative with respect to crack length is then derived from the general formulae. The results can be useful in optimal design procedures by selecting positions, shape and orientation of elliptical cutouts.

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Section: Introductionmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

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Topological sensitivity derivative with respect to area, shape and orientation of an elliptic hole in a plate

Bojczuk

Mróz

2011

Struct Multidisc Optim

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“…This definition is suitable for Neumann-type boundary conditions on ∂ B ρ . In many cases this characterization is constructive [5,2,3,8,12,14,15], i.e. TD can be evaluated for shape functionals depending on solutions of partial differential equations defined in the domain Ω .…”

Section: Topological Derivatives Of Shape Functionals In Isotropic Elmentioning

confidence: 99%

Topological Derivatives in Plane Elasticity

Sokołowski

Żochowski

2009

IFIP Advances in Information and Communication Technology

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Abstract. We present a method for construction of the topological derivatives in plane elasticity. It is assumed that a hole is created in the subdomain of the elastic body which is filled out with isotropic material. The asymptotic analysis of elliptic boundary value problems in singularly perturbed geometrical domains is used in order to derive the asymptotics of the shape functionals depending on the solutions to the boundary value problems. Our method allows for the asymptotic expansions of arbitrary order, since the explicit solutions to the boundary value problems are obtained by the method of elastic potentials. Some numerical results are presented to show the applicability of the proposed method in numerical analysis of elliptic problems.

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“…Our aim in this paper is to quantitatively evaluate the outcomes of a recently introduced image segmentation method based on a discrete version of the well established concept of configurational derivative (see [1,2,8,12,13] and references therein). More specifically, we compute the configurational derivative for an appropriate functional associated to the image indicating the cost endowed to an specific image segmentation.…”

Section: Introductionmentioning

confidence: 99%