Topology and Generalized Layout Optimization of Elastic Structures

Bendsøe, Martin P.; Diaz, Alfredo Peña; Kikuchi, Noboru

doi:10.1007/978-94-011-1804-0_13

Cited by 114 publications

(48 citation statements)

References 20 publications

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“…This indicates that one will obtain a stiff structure with "good" contact stresses, and this was also experienced by Benedict. Moreover, this feature is in accordance with the statement in [5] saying that if a (nonzero) displacement is prescribed, then the external work is to be maximized. The initial gaps play the role of prescribed displacements and "contact stress values weighted by the initial gaps" is minus the external work by the contact stresses.…”

Section: Introductionsupporting

confidence: 88%

“…These conditions show that optimum structures are optimal not only in the meaning of the objective functional, but also in a broader sense. For instance, the stress field tends to be very "democratic" due to an inherent property of uniform distribution of strain energy density, twice of which is an upper bound of the Mises equivalent stress [5]. Furthermore, a corresponding formulation for truss structures shows that an optimal design always has the same stress value in all (of the remaining) bars.…”

Section: Introductionmentioning

confidence: 99%

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On stiffness maximization of variable thickness sheet with unilateral contact

Petersson¹

1996

Quart. Appl. Math.

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Abstract.The problem of maximizing the stiffness of a linearly elastic sheet, in unilateral contact with a rigid frictionless support, is considered.The design variable is the thickness distribution, which is subject to an isoperimetric volume constraint and upper and lower bounds.The bounds may vary over the domain of the sheet, and the lower one is allowed to be zero, hence giving the possibility of obtaining topology information about an optimal design.By using saddle point theory, the existence of solutions, i.e., thickness functions and corresponding displacement states, is proved. In general, one cannot expect uniqueness of solutions, unless the lower bound is strictly positive, and the uniqueness of optimal states is shown in this case. Introduction.Traditionally, one categorizes structural optimization into three major groups: sizing, shape, and topology optimization problems. The first deals with, e.g., choosing optimal thicknesses of a (two-dimensional) structure, the second involves picking a good shape of the boundary to the domain occupied by the structure, and the last one concerns holes in and connectivities of the domain. The problem considered in this paper, namely that of finding a thickness distribution in a linearly elastic sheet, such that a suitable objective functional is extremized, can clearly be put in the first category. However, by allowing the design variable to be equal to zero, one obtains in effect (also) a topology optimization.Moreover, if the design is a distributed parameter, as in the case of a thickness distribution in a sheet, a solution will also generate a three-dimensional shape.

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Section: Introductionsupporting

confidence: 88%

Section: Introductionmentioning

confidence: 99%

On stiffness maximization of variable thickness sheet with unilateral contact

Petersson¹

1996

Quart. Appl. Math.

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“…Embora tenham restrições das tensões, os critérios que maximizam a rigidez não garantem explicitamente a minimização das tensões, o que equivaleria a maximizar a resistência. Ainda assim, embora não exista uma correspondência direta e precisa entre os resultados da otimização topológica obtidos segundo os critérios de maximização da resistência e da rigidez, alguns estudos indicam que, para muitos casos, há uma proximidade da geometria final obtida (BENDSOE et al, 1993, ROSVANY apud DUYSINX, 1996, LI et al, 1999, LAM et al, 2000SIGMUND, 2003).…”

Section: -Otimização Topológicaunclassified

Análise da distribuição do reforço com fibras de carbono em vigas de concreto armado

Ferreira¹,

Cunha²

2017

Cieng

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RESUMONeste trabalho foi realizada uma análise da distribuição do reforço externo de vigas de concreto armado, utilizando Polímeros Reforçados por Fibras de Carbono (PRFC), por meio de modelos dimensionados, simulações numéricas e otimização topológica. Foram considerados os reforços pela ação do momento fletor e da força cortante. Devido à alta relação resistência/peso específico do PRFC, pode-se aumentar a resistência e rigidez de elementos estruturais sem aumento significativo do peso. Fazendo uso do método convencional de dimensionamento de reforços, foram realizadas diversas simulações, visando obter uma disposição que reduz a quantidade de material. As simulações numéricas foram realizadas por meio do Método dos Elementos Finitos, fazendo uso do software ANSYS ® , onde foi utilizada a otimização topológica como ferramenta para a determinação da região de distribuição ótima do reforço. A comparação com o método convencional mostrou que o uso da otimização topológica pode levar a economia de material de reforço, com o mesmo desempenho estrutural. Palavras-chave: simulação numérica, fibras de carbono, reforço estrutural, vigas de concreto, otimização topológica. ABSTRACTIn this paper, an analysis of the distribution of external concrete beams reinforcement has been performed, by using Carbon Fiber Reinforced Polymer (CFRP), through designed models, numerical simulations and topology optimization. Reinforcement design has been performed considering bending moment and shear actions. Due the CFPR's high strength/weight ratio, the strength and stiffness of structural elements can be raised without significant weight increase. Employing the conventional method for reinforcement design, several simulations were performed in order to obtain an arrangement which reduces the amount of material. Numerical simulations were performed by Finite Element Method, using ANSYS ® program, where the topology optimization was used as tool for determining the optimal region to place the reinforcement. Comparison with the conventional method shows that the use of topology optimization minimizes the quantity of material, reducing costs while maintaining the same structural performance.

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“…Bendsoe and Kikuchi [6] introduced a microstructure comprised of microscale rectangular holes, while Bendsoe et al [5] studied a`Rank-2' microstructure.…”

Section: Homogenization-basedmentioning

confidence: 99%

Continuum structural topology design with genetic algorithms

Jakiela

Chapman

Duda

et al. 2000

Computer Methods in Applied Mechanics and Engineering

172

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The genetic algorithm (GA), an optimization technique based on the theory of natural selection, is applied to structural topology design problems. After reviewing the GA and previous research in structural topology optimization, we describe a binary material/void design representation that is encoded in GA chromosome data structures. This representation is intended to approximate a material continuum as opposed to discrete truss structures. Four examples, showing the broad utility of the approach and representation, are then presented. A ®fth example suggests an alternate representation that allows continuously-variable material density. Concluding discussion suggests recommended uses of the technique and describes ongoing and possible future work. Ó 2000 Elsevier Science S.A. All rights reserved.

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Topology and Generalized Layout Optimization of Elastic Structures

Cited by 114 publications

References 20 publications

On stiffness maximization of variable thickness sheet with unilateral contact

On stiffness maximization of variable thickness sheet with unilateral contact

Análise da distribuição do reforço com fibras de carbono em vigas de concreto armado

Continuum structural topology design with genetic algorithms

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