On optimum design of structures and materials

Olhoff, Niels

doi:10.1007/bf00426257

Cited by 20 publications

(11 citation statements)

References 41 publications

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“…The derivative at zero density of the lower bound in (25) is positive. Thus, condition (25) implies that a SIMP model in the form (23) will never satisfy the Hashin-Shtrikman bounds for all densities. However, it is possible to keep the SIMP model fairly close to the behaviour governed by these bounds, see Fig.…”

Section: Two Materials With Non-vanishing Stiffnessmentioning

confidence: 96%

Material interpolation schemes in topology optimization

Bendsøe

Sigmund

1999

Archive of Applied Mechanics (Ingenieur Archiv)

1,876

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: Two Materials With Non-vanishing Stiffnessmentioning

confidence: 96%

Material interpolation schemes in topology optimization

Bendsøe

Sigmund

1999

Archive of Applied Mechanics (Ingenieur Archiv)

1,876

933

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“…For a full description, one may refer to the works of Rozvany et al [4] or Olho! [5]. The method of topology optimization can be applied to the tunnel support [3].…”

Section: Introductionmentioning

confidence: 99%

Topology optimization for tunnel support in layered geological structures

Yin

Yang

2000

Int. J. Numer. Meth. Engng.

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Tunnel construction commonly proceeds in an environment of layered geological formation. Design for tunnel support relies on the tunnel location and the mismatch of di!erent layers. The present paper proposes a topology optimization method for the design of tunnel support. The design domain is discretized by "nite elements. An element is composed of the original rock (hard or soft) and the reinforcing material (rock reinforced by grouting or bolting). The design issue involves the distribution of reinforcements. We model the reinforced host ground by a power-weighted mixture law. The ratios of two phases in various elements are optimized to minimize the deformation of the tunnel. The method enables a computer-aided design for the supports of underground tunnels embedded within layered geological structures. The reinforced areas for the tunnel are displayed under the passive geological stress and the active external loading. Four kinds of rock formations are examined. They are homogeneous rock, hard}soft}hard (HSH) sandwich structure, two-layer structure with the soft rock at the top and the hard rock at the bottom (SH), and the one with the hard rock at the top and the soft rock at the bottom (HS). The simulation reveals the high e$ciency of tunnel support by optimizing its topologies.

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“…Moreover, it is possible to increase the safety range of a component under operating conditions simply by changing its natural frequencies. Optimization methods are usually classified as follows ( Figure 1): 2,3 parametric optimization (where the size of considered elements changes during the optimization routine), 4 shape optimization (where the shape of the structures is subjected to modifications during the optimization), 5,6 and topology optimization (TO). 7 Despite TO methods are commonly used for civil applications 8 and for optimizing automotive components, 9 they have not been fully explored in the turbomachinery field.…”

Section: Introductionmentioning

confidence: 99%

Toward the integration of lattice structure-based topology optimization and additive manufacturing for the design of turbomachinery components

Boccini

Furferi

Governi

et al. 2019

Advances in Mechanical Engineering

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Used in several industrial fields to create innovative designs, topology optimization is a method to design a structure characterized by maximum stiffness properties and reduced weights. By integrating topology optimization with additive layer manufacturing and, at the same time, by using innovative materials such as lattice structures, it is possible to realize complex three-dimensional geometries unthinkable using traditional subtractive techniques. Surprisingly, the extraordinary potential of topology optimization method (especially when coupled with additive manufacturing and lattice structures) has not yet been extensively developed to study rotating machines. Based on the above considerations, the applicability of topology optimization, additive manufacturing, and lattice structures to the fields of turbomachinery and rotordynamics is here explored. Such techniques are applied to a turbine disk to optimize its performance in terms of resonance and mass reduction. The obtained results are quite encouraging since this approach allows improving existing turbomachinery components’ performance when compared with traditional one.

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On optimum design of structures and materials

Cited by 20 publications

References 41 publications

Material interpolation schemes in topology optimization

Material interpolation schemes in topology optimization

Topology optimization for tunnel support in layered geological structures

Toward the integration of lattice structure-based topology optimization and additive manufacturing for the design of turbomachinery components

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