First- and second-order topological sensitivity analysis for inclusions

Faria, Jairo Rocha de; Novotny, Antônio André; Feijóo, Raúl A.; Taroco, E.

doi:10.1080/17415970802394186

Cited by 11 publications

(10 citation statements)

References 27 publications

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“…For example, a Tikhonov-Philips term for the level set function can be added to (81), which will yield the minimization problem…”

Section: Regularization By Explicitly Penalizing Rough Level Set Funcmentioning

confidence: 99%

Level Set Methods for Structural Inversion and Image Reconstruction

Dorn

Lesselier

2015

Handbook of Mathematical Methods in Imaging

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“…For example, a Tikhonov-Philips term for the level set function can be added to (81), which will yield the minimization problem…”

Section: Regularization By Explicitly Penalizing Rough Level Set Funcmentioning

confidence: 99%

Level Set Methods for Structural Inversion and Image Reconstruction

Dorn

Lesselier

2015

Handbook of Mathematical Methods in Imaging

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“…Using (40), (41) and arclength element scaling (25), and invoking definition (37) ofL, one thus finds…”

Section: With Summation Implied Over All Repeated Indices (Einstein Cmentioning

confidence: 99%

“…As G(x, ξ) is a smooth function of ξ ∈ D a for any x ∈ D a , the leading contribution of v a (x) as a → 0 is found by setting φ a (ξ) = aV 1 (ξ) + o(a) and invoking scaling (25) in (58), to obtain…”

Section: Topological Expansion Of Misfit Functionalmentioning

confidence: 99%

“…where coefficients T 2 , T 3 , T 4 depend on the assumed characteristics of the small nucleating object, is established in [9] (for arbitrary cost functionals expressed as boundary integrals and inclusions of arbitrary shape) and [25] (for potential energy and circular inclusions), while similar expansions for the scattering by sound-hard obstacles are established in [8] for problems governed by the 3-D Helmholtz equation. The concept of topological sensitivity, and higher-order topological expansions such as (1), are particular instances of the broader class of asymptotic methods, where approximate solutions to problems featuring a small geometrical parameter a are sought in the form of expansions with respect to a, see e.g.…”

Section: Introductionmentioning

confidence: 99%

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Fast identification of cracks using higher-order topological sensitivity for 2-D potential problems

Bonnet¹

2011

Engineering Analysis with Boundary Elements

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To cite this version:Marc Bonnet. Fast identification of cracks using higher-order topological sensitivity for 2-D potential problems. Engineering Analysis with Boundary Elements, Elsevier, 2011, 35, pp.223-235 Abstract This article concerns an extension of the topological sensitivity (TS) concept for 2D potential problems involving insulated cracks, whereby a misfit functional J is expanded in powers of the characteristic size a of a crack. Going beyond the standard TS, which evaluates (in the present context) the leading O(a 2 ) approximation of J, the higher-order TS established here for a small crack of arbitrarily given location and shape embedded in a 2-D region of arbitrary shape and conductivity yields the O(a 4 ) approximation of J. Simpler and more explicit versions of this formulation are obtained for a centrally-symmetric crack and a straight crack. A simple approximate global procedure for crack identification, based on minimizing the O(a 4 ) expansion of J over a dense search grid, is proposed and demonstrated on a synthetic numerical example. BIE formulations are prominently used in both the mathematical treatment leading to the O(a 4 ) approximation of J and the subsequent numerical experiments.

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“…The topology optimization of non-linear problems may also require the inclusion of material which is presented in [13].…”

Section: Methodsmentioning

confidence: 99%

Topological sensitivity analysis for a two-parameter Mooney-Rivlin hyperelastic constitutive model

Pereira

Bittencourt

2010

Lat. Am. j. solids struct.

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The Topological Sensitivity Analysis (TSA) is represented by a scalar function, called Topological Derivative (TD), that gives for each point of the domain the sensitivity of a given cost function when an infinitesimal hole is created. Applications to the Laplace, Poisson, Helmoltz, Navier, Stokes and Navier-Stokes equations can be found in the literature. In the present work, an approximated TD expression applied to nonlinear hyperelasticity using the two parameter Mooney-Rivlin constitutive model is obtained by a numerical asymptotic analysis. The cost function is the total potential energy functional. The weak form of state equation is the constraint and the total Lagrangian formulation used. Numerical results of the presented approach are considered for hyperelastic plane problems.

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First- and second-order topological sensitivity analysis for inclusions

Cited by 11 publications

References 27 publications

Level Set Methods for Structural Inversion and Image Reconstruction

Level Set Methods for Structural Inversion and Image Reconstruction

Fast identification of cracks using higher-order topological sensitivity for 2-D potential problems

Topological sensitivity analysis for a two-parameter Mooney-Rivlin hyperelastic constitutive model

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