Bubble method for topology and shape optimization of structures

Eschenauer, H.; Kobelev, Vladimir; Schumacher, Axel

doi:10.1007/bf01742933

Cited by 541 publications

(306 citation statements)

References 20 publications

(9 reference statements)

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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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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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“…Here the concept of the bubble method ( [15]) should no doubt receive further attention, especially in the light of recent work on the concept of a general topologieal derivative, see [38]. Work in this direction could also be helpful in an effort to rej uvenate the field of optimal boundary shape design, an important area, unfortunately currently lingering an idle life.…”

Section: Difficulties -Future Workmentioning

confidence: 99%

Topology Design of Structures, Materials and Mechanisms — Status and Perspectives

Bendsøe

2000

System Modelling and Optimization

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INTRODUCTIONThe field of variable-topology shape design in structural optimization has its origins in theoretical studies of existence of solutions in variational problems, in particular shape optimization problems, and in studies in theoretical material science of variational bounds on material properties. Progress in computational methods and the ever increasing computer power has oriented the area towards applications, with significant developments being achieved over the last decade, leading to a fairly widespread use of the methodology in industry.In this short paper we outline some of the basic ideas and methods of existing methods, but it is not our purpose to cover all work and approaches in this field. Instead we refer to existing literat ure containing rather comprehensive surveys, see e.g., [7,8,31]. Moreover, note that reference is mostly made to recent papers that include bibliographies useful for on overview of the area. Thus the presentation does not try to present a complete historie al perspective.The area of computational variable-topology shape design of continuum structures is presently dominated by methods which employ a material distribution approach for a fixed reference domain, in the spirit of the so-called 'homogenization method' for topology design ([3, 9]). That is, the geometrie representation of a structure is similar to a grey-scale rendering of an image, in discrete form corresponding to araster representation of the geometry on a fixed reference domain. The physics of the problem is also represented by boundary conditions and forcing The original version of this chapter was revised: The copyright line was incorrect. This has been corrected. The Erratum to this chapter is available at DOI: 10.1007/978-0-387-35514-6_15 2 Martin P. BendsrJe terms defined on this fixed reference domain, much in analogy to fictitious domain methods for FEM analysis.One can normally distinguish between three versions of raster based geometry models for continuum topology optimization. The basic problem is an unrestricted '0-1' integer design problem (generalized shape optimization), that is, a design specifies unambiguously whether there is solid material or void at every point in a candidate design region. Otherwise, there are no restrictions on the shape. Unfortunately, in general, this dass of problems is ill-posed in the continuum setting (cf., [11,20]). Well-posed problems can be obtained by either extending the space of admissible solutions to obtain their relaxed versions, usually by incorporating microstructure (see, e.g., [3]), or by restricting the space of admissible solutions. The latter can be accomplished by enforcing an upper bound on the perimeter of the structure (see [28], and references therein), by imposing constraints on the slopes of the parameters defining geometry (see [29], and references therein), by the introduction of a filtering function limiting the minimum scale (see [10,36] for an overview), or one can introduce a ground structure with a fixed number of design degrees of...

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“…Chang and Youn, 2006), spline-based topology optimization (e.g. Eschenauer et al, 1993) and level set method (e.g. Wang et al, 2003).…”

Section: Introductory Remarksmentioning

confidence: 99%

GOTICA - generation of optimal topologies by irregular cellular automata

Bochenek

Tajs-Zielińska

2016

Struct Multidisc Optim

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In recent years the Cellular Automata (CA) concept has been successfully applied to structural topology optimization problems. In the engineering implementation of CA, the design domain is decomposed into a lattice of cells, and a particular cell together with the cells to which it is connected forms a neighborhood. It is assumed that the interaction between cells takes place only within the neighborhood and the states of cells are updated synchronously in subsequent time steps according to some local rules.The majority of results that have been obtained so far were based on regular lattices of cells. However, a practical engineering analysis and design in many cases require using highly irregular meshes for complicated geometries and/or stress concentration regions. The aim of the present paper is to extend the concept of CA towards the implementation of unstructured grid of cells related to non-regular mesh of finite elements. Introducing an irregular lattice of cells allows to reduce the number of design variables without loosing the accuracy of results and without an excessive increase of the number of elements caused by using a fine mesh for a whole structure. The implementation of non-uniform cells of Cellular Automaton requires a reformulation of standard local rules, for which the influence of

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Bubble method for topology and shape optimization of structures

Cited by 541 publications

References 20 publications

Topological Derivatives in Plane Elasticity

Topological Derivatives in Plane Elasticity

Topology Design of Structures, Materials and Mechanisms — Status and Perspectives

GOTICA - generation of optimal topologies by irregular cellular automata

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