Topology design for maximization of fundamental frequency of couple-stress continuum

Su, Wenzheng; Liu, Shutian

doi:10.1007/s00158-015-1316-y

Cited by 11 publications

(6 citation statements)

References 37 publications

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“…So, the iterative curves are relatively smooth, which indicates that the proposed optimization procedure is applicable. And the second eigenfrequency is gradually close to the first when l is smaller and smaller than r , that is as the influence of couple stress decreases, the second eigenfrequency approaches the fundamental eigenfrequency, which is similar to the results in the reference (Su and Liu, 2016).…”

Section: Numerical Examplessupporting

confidence: 86%

“…As far as the author knows, only Bruggi and Taliercio (2012) investigated the topology optimization problem subjected to dynamic loads with the aim of maximizing the lowest eigenfrequency of the body for micropolar solids. And Su and Liu (2016) researched the size effect in the topological design of continuum structures for maximizing fundamental frequency. However, these works are confined to macroscale.…”

Section: Introductionmentioning

confidence: 99%

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Size-dependent two-scale topological design for maximizing structural fundamental eigenfrequency

Liu

Xue

et al. 2020

Journal of Vibration and Control

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A two-scale concurrent topology optimization method based on the couple stress theory is proposed for maximizing structural fundamental eigenfrequency. Because of the fact that the classical mechanics theory cannot reveal the size effect because of neglecting the influence of microstructure, the theory of couple stress including the microscopic properties of materials can be used to describe the size effect in deformations. On the foundation of the couple stress theory, the two-scale optimization model for finding optimal configurations of macrostructures and their periodic composite material microstructures is built. And the fundamental eigenfrequency of the macrostructure is maximized. The effective macroscopic couple stress constitutive constants of macrostructures are calculated by the representative volume element method. And a modified solid isotropic material with a penalization model is used to effectively avoid the localized mode. The optimization algorithm based on the bidirectional evolutionary structural optimization method is proposed. The optimal results of numerical examples show that the optimal topologies and natural frequencies obtained by the couple stress theory may differ significantly from those obtained by the typical Cauchy theory. It is obvious that couple stress theory can effectively describe the size effect in topology optimization.

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Section: Numerical Examplessupporting

confidence: 86%

Section: Introductionmentioning

confidence: 99%

Size-dependent two-scale topological design for maximizing structural fundamental eigenfrequency

Liu

Xue

et al. 2020

Journal of Vibration and Control

View full text Add to dashboard Cite

show abstract

“…Rovati & Veber (2007), Liu & Su (2010) and Veber & Taliercio (2011) firstly embedded the Cosserat continuum model in this formulation showing that trusslike layouts can be replaced by bending-resistant layouts depending on the value of the characteristic length. This was later confirmed by Bruggi & Taliercio (2012) and Su & Liu (2015), dealing with a min-max problem involving the natural frequencies of micropolar bodies.…”

Section: Introductionmentioning

confidence: 73%

Synthesis of auxetic structures using optimization of compliant mechanisms and a micropolar material model

Bruggi

Zega

Corigliano

2016

Struct Multidisc Optim

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Aim of this work is the synthesis of auxetic structures using a topology optimization approach for micropolar (or Cosserat) materials. A distributed compliant mechanism design problem is formulated, adopting a SIMP–like model to approximate the constitutive parameters of 2D micropolar bodies. The robustness of the proposed approach is assessed through numerical examples concerning the optimal design of structures that can expand perpendicularly to an applied tensile stress. The influence of the material characteristic length on the optimal layouts is investigated. Depending on the inherent flexural stiffness of micropolar solids, truss–like solutions typical of Cauchy solids are replaced by curved beam–like material distributions. No homogenization technique is implemented, since the proposed design approach applies to elements made of microstructured material with prescribed properties and not to the material itself

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“…Attenuation of unwanted vibrations is important in engineering structures as they could have detrimental effects on structural performances. Precious topology optimization focuses mainly on maximizing single dynamic performance like natural frequency [11,12], modal damping [13], or frequency response [14]. Topology optimization minimizing dynamic responses in time domain is another case of more difficulties.…”

Section: Introductionmentioning

confidence: 99%

A Modified Bi-Directional Evolutionary Structural Optimization Procedure with Variable Evolutionary Volume Ratio Applied to Multi-Objective Topology Optimization Problem

Jiang¹,

Ma²,

Teng³

2023

Computer Modeling in Engineering &Amp; Sciences

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Natural frequency and dynamic stiffness under transient loading are two key performances for structural design related to automotive, aviation and construction industries. This article aims to tackle the multi-objective topological optimization problem considering dynamic stiffness and natural frequency using modified version of bi-directional evolutionary structural optimization (BESO). The conventional BESO is provided with constant evolutionary volume ratio (EVR), whereas low EVR greatly retards the optimization process and high EVR improperly removes the efficient elements. To address the issue, the modified BESO with variable EVR is introduced. To compromise the natural frequency and the dynamic stiffness, a weighting scheme of sensitivity numbers is employed to form the Pareto solution space. Several numerical examples demonstrate that the optimal solutions obtained from the modified BESO method have good agreement with those from the classic BESO method. Most importantly, the dynamic removal strategy with the variable EVR sharply springs up the optimization process. Therefore, it is concluded that the modified BESO method with variable EVR can solve structural design problems using multi-objective optimization.

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Topology design for maximization of fundamental frequency of couple-stress continuum

Cited by 11 publications

References 37 publications

Size-dependent two-scale topological design for maximizing structural fundamental eigenfrequency

Size-dependent two-scale topological design for maximizing structural fundamental eigenfrequency

Synthesis of auxetic structures using optimization of compliant mechanisms and a micropolar material model

A Modified Bi-Directional Evolutionary Structural Optimization Procedure with Variable Evolutionary Volume Ratio Applied to Multi-Objective Topology Optimization Problem

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