Energy change due to the appearance of cavities in elastic solids

Lewiński, Tomasz; Sokołowski, Jan

doi:10.1016/s0020-7683(02)00641-8

Cited by 59 publications

(35 citation statements)

References 16 publications

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“…See also applications of the topological derivative in the context of multiscale constitutive modeling ; Giusti et al (2010aGiusti et al ( , 2009a; Novotny et al (2010)), fracture mechanics sensitivity analysis (Ammari et al (2014); Van Goethem and Novotny (2010)) and damage evolution modeling (Allaire et al (2011)). Regarding the theoretical development of the topological asymptotic analysis, see for instance (Amstutz (2006(Amstutz ( , 2010 ;Feijóo et al (2003); Garreau et al (2001); Hlaváček et al (2009); Khludnev et al (2009); Lewinski and Sokołowski (2003); Nazarov and Sokołowski (2003a,b, 2005, 2006, 2011; Żochowski (2003, 2005)), as well as the book by Novotny and Sokołowski (2013).…”

Section: Introductionmentioning

confidence: 99%

Topological derivative-based topology optimization of structures subject to multiple load-cases

Lopes

Santos

Novotny

2015

Lat. Am. j. solids struct.

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The topological derivative measures the sensitivity of a shape functional with respect to an infinitesimal singular domain perturbation, such as the insertion of holes, inclusions or source-terms. The topological derivative has been successfully applied in obtaining the optimal topology for a large class of physics and engineering problems. In this paper the topological derivative is applied in the context of topology optimization of structures subject to multiple load-cases. In particular, the structural compliance under plane stress or plane strain assumptions is minimized under volume constraint. For the sake of completeness, the topological asymptotic analysis of the total potential energy with respect to the nucleation of a small circular inclusion is developed in all details. Since we are dealing with multiple load-cases, a multi-objective optimization problem is proposed and the topological sensitivity is obtained as a sum of the topological derivatives associated with each load-case. The volume constraint is imposed through the Augmented Lagrangian Method. The obtained result is used to devise a topology optimization algorithm based on the topological derivative together with a level-set domain representation method. Finally, several finite element-based examples of structural optimization are presented. Keywords

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Section: Introductionmentioning

confidence: 99%

Topological derivative-based topology optimization of structures subject to multiple load-cases

Lopes

Santos

Novotny

2015

Lat. Am. j. solids struct.

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“…On the basis of metallographic observations of plastically damaged areas, models of spherical voids are assumed for description of plastic damage processes both in neck of tension specimens and specimen of colliding plates, [12,13,14]. …”

Section: Dynamic Properties Of Alzn5mg2crzr Alloy In Function Of Stramentioning

confidence: 99%

Dynamic properties of 7000 - series aluminum alloys at large strain rates

Jurczak¹,

Kyzioł²

2012

Polish Maritime Research

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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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Energy change due to the appearance of cavities in elastic solids

Cited by 59 publications

References 16 publications

Topological derivative-based topology optimization of structures subject to multiple load-cases

Topological derivative-based topology optimization of structures subject to multiple load-cases

Dynamic properties of 7000 - series aluminum alloys at large strain rates

Topological Derivatives in Plane Elasticity

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