SKO (soft kill option): the biological way to find an optimum structure topology

Baumgartner, Andreas; Harzheim, Lothar; Mattheck, C.

doi:10.1016/0142-1123(92)90226-3

Cited by 105 publications

(46 citation statements)

References 6 publications

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“…The use of the Voigt upper-bound interpolation for general topology optimization is nevertheless fairly popular, especially in the so-called evolutionary design methods, [47,48]. Also note that striving for black-and-white designs requires some form of penalization of`grey', and such measures necessitates the reintroduction of geometric constraints in order to obtain a well-posed problem.…”

Section: Variable Thickness Sheets ± the Voigt Boundmentioning

confidence: 98%

Material interpolation schemes in topology optimization

Bendsøe

Sigmund

1999

Archive of Applied Mechanics (Ingenieur Archiv)

1,908

933

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In topology optimization of structures, materials and mechanisms, parametrization of geometry is often performed by a grey-scale density-like interpolation function. In this paper we analyze and compare the various approaches to this concept in the light of variational bounds on effective properties of composite materials. This allows us to derive simple necessary conditions for the possible realization of grey-scale via composites, leading to a physical interpretation of all feasible designs as well as the optimal design. Thus it is shown that the socalled arti®cial interpolation model in many circumstances actually falls within the framework of microstructurally based models. Single material and multi-material structural design in elasticity as well as in multi-physics problems is discussed. IntroductionThe area of computational variable-topology shape design of continuum structures is presently dominated by methods which employ a material distribution approach for a ®xed reference domain in the spirit of the so-called`homogenization method' for topology design, [1]. That is, the geometric representation of a structure is similar to a grey-scale rendering of an image, in discrete form corresponding to a raster representation of the geometry. This concept has proven very powerful, but it does involve a number of dif®culties. One is the issue of existence of solutions, another the issue of solution method. Here, the notion of physical models for grey' material is of great importance, and it is these interpolation schemes and their relation to characterizations of composite materials which are the themes in the following.In many applications, the optimal topology of a structure should consist solely of a macroscopic variation of one material and void, meaning that the density of the structure is given by a``0±1'' integer parametrization (often called a black-and-white design). Unfortunately, this class of optimal design problems is ill-posed in that, for example, nonconvergent, minimizing sequences of admissible designs with ®ner and ®ner geometrical details can be found, see [2,3]. Existence of black-and-white solutions can be achieved by con®ning the solution space to limit the complexity of the admissible designs, making the designs dependent on the choice of parameters in the geometrical constraint. Such a restriction of the design space can be accomplished in a number of ways, e.g. by enforcing an upper bound on the perimeter of the

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Section: Variable Thickness Sheets ± the Voigt Boundmentioning

confidence: 98%

Material interpolation schemes in topology optimization

Bendsøe

Sigmund

1999

Archive of Applied Mechanics (Ingenieur Archiv)

1,908

933

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“…However, they emphasized more on the theoretical framework of the respective optimization methodologies, than on materials and manufacturing, in which, are of equal importance in any structural optimization study. Despite the developments and advancements of various generalized layout methods (Bendsøe and Kikuchi, 1988;Baumgartner et al, 1992;Anagnostou et al, 1992;Xie and Steven, 1993;Chapman et al, 1994;Liu et al, 2000), investigations on the performance viability and application of optimized granular-solid beams for 'end-use' purposes were scarce. The benefits of optimized structures are seldom realized, often due to geometric complexities, which restrict the necessary tooling access required by convectional subtractive-based manufacturing.…”

Section: Introductionmentioning

confidence: 99%

Design optimization of consolidated granular-solid polymer prismatic beam using metamorphic development

Ngim

Liu

Soar

2009

International Journal of Solids and Structures

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a b s t r a c tTopologically optimized granular-solid structures from additive manufacturing processes have impending applications as lightweight load bearing structures. To facilitate application, a procedure for characterizing optimal structural performance is devised for the design optimization of 'end-use' functional structures. An approach capable of realizing this objective is presented and demonstrated for horizontal prismatic beams produced from Nylon-12 granular-solid polymer, by Selective Laser Sintering (SLS). It combines topology (or layout) optimization, calibration of material parameters, and finite element (FE) modelling. The metamorphic development (MD) method forms the basis of an adaptive growth and degeneration optimization by material distribution approach. Experimental measurements are used to calibrate a bimodulus constitutive Drucker-Prager (D-P) model. Simply-supported three-point bending (3PB) tests are used to assess the fidelity of optimized beams on the basis of numerically predicted performance.

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“…For that reason, this optimisation class is regarded as one of the most challenging optimisation problems. Much research has been devoted to topology optimisation over the last 10 years; this has included methods based on microstruc- tures such as the homogenisation method [7] and the solid isotropic microstructure with penalty (SIMP) method [8], and methods that deal with elements on a macro basis approach such as the soft-kill option (SKO) [9], the evolutionary structural optimisation (ESO) method [10] and the bubble method [11]. Hassani and Hinton [12] present a useful review of topology optimisation methods.…”

Section: Introductionmentioning

confidence: 99%