A multilevel method for structural synthesis

Schmit, L. A.; Chang, K. J.

doi:10.2514/6.1984-853

Cited by 13 publications

(4 citation statements)

References 15 publications

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“…Topology optimization [30][31][32] is one of a structural optimization method, along with sizing optimization 55 and shape optimization, 56 and among these three, topology optimization is known to be the most flexible design method. It replaces the structural optimization problem to a material distribution problem and allows topological changes such as creating holes as well as shape change.…”

Section: Level-set Based Topology Optimizationmentioning

confidence: 99%

Multiscale optimal design method of acoustic metamaterials using topology optimization

Kurioka

NAKAYAMA

Furuta

et al. 2023

Numerical Meth Engineering

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Acoustic anisotropic metamaterials are known for its potential of applications to various acoustic devices, such as hyperlens and waveguides. Anisotropic metamaterial typically has a periodic structure constituted of unit cells, and exhibits highly anisotropic wave propagation based on local resonance induced by its periodic medium. In previous works, design methods for anisotropic metamaterials which shows unusual wave propagation properties have been proposed, though since metamaterials comprised of only a single type of unit cell were in interest, the macroscopic wave propagation properties that could be obtained were limited. Therefore, in the present work, we propose a design method for acoustic structures which are composed of several unit cells, in order to realize waveguides that navigate acoustic waves and achieve complex wave propagation overall. First, we introduce the high-frequency homogenization method, which is capable of evaluating the macroscopic property of periodic structures based on local resonance. We construct a multiscale optimal design method by formulating the macro-scale optimization problem for obtaining the properties required for different unit cells in order to realize the waveguide, along with the micro-scale optimization problem for designing each unit cell based on topology optimization. Numerical examples are introduced to demonstrate the validity of our proposed method.

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Section: Level-set Based Topology Optimizationmentioning

confidence: 99%

Multiscale optimal design method of acoustic metamaterials using topology optimization

Kurioka

NAKAYAMA

Furuta

et al. 2023

Numerical Meth Engineering

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“…Early research used mathematical programming techniques to obtain the optimal solution (Arora, 1997;Belegundu et al, 2011;Doan et al, 2012;Perez et al, 2007;Schmit, 1960). They found that, mathematical programming techniques such as linear and nonlinear programming are not easy to apply to real structures and can only be used for steel structures with limited design variables.…”

Section: State Of Artmentioning

confidence: 99%

“…The problem of the overall design of steel structures can be posed as an optimization problem which consists in minimizing the overall cost of the structure while respecting the constraints of time, resources and dimensioning, thus forcing designers to limit the number of configurations to be considered in the early design phase. Most structural optimization methods use mathematical algorithms that require a large amount of data, where the choice of initial values is important for the convergence of the algorithm toward an optimal solution by Schmit (1960).…”

Section: Introductionmentioning

confidence: 99%

A comparative approach for the optimal design of steel structures using biogeography-based optimization (BBO) algorithm and genetic algorithm (GA)

Amamra,

Bensoula,

Bahar

2023

J. Eng. Exact Sci.

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Structural optimization is one of the key concerns of civil engineering designers, but from a mathematical point of view, this optimization problem is highly complex and complicated due to a large number of non-linear design constraints and the iterative procedure of structural analysis. Introducing optimization algorithms such as biogeography-Based Optimization (BBO) and genetic algorithms (GA) into applications can help the user to optimize the cost of the structure to be adopted more quickly and with fewer errors in the preliminary phase of the design study. The aim of this research is to carry out a comparative approach to structure weight minimization using biogeography-Based Optimization (BBO) algorithm and genetic algorithms (GA), examining the influence of the number of populations and the number of iterations in the final results. In this study, both algorithms gave reliable results, but a comparison of the results obtained by the two methods reveals that the biogeography-Based Optimization algorithm (BBO) can be successfully used for the optimization of steel structures while ensuring verification of the strength, serviceability and stability criteria defined by Eurocode 3 (Union, 2006), as it has certain advantages in detecting the global minimum over genetic algorithms (GA). It is capable of finding solutions that are lighter, stiffer and have lower deflection than the original designs.

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“…Optimization by LinearDecomposition (OLD),or "hierarchical decomposition" [5][6][7][8][9][10][11][12],reflects thestructuralperspective, as doesthe approach thathasrecentlyreceived attention under thename Collaborative Optimization (CO) [13][14][15][16]. Theunderlying ideaof Collaborative Optimization--the notionof decoupling thedisciplines by introducing interdisciplinary consistency constraints, whileminimizing a measure of interdisciplinary inconsistency indisciplinary subproblems-appeared previously in [17][18][19] and [10][11][12]20,21]. In OLD,thedisciplines aregiven theautonomous taskof minimizing disciplinary design infeasibility (thelowerleveldisciplinary problem) whilemaintaining systemlevel consistency.…”

Section: Two Perspectives On Problem Formulationmentioning

confidence: 99%

Analytical and computational properties of distributed approaches to MDO

Alexandrov

Lewis²

2000

8th Symposium on Multidisciplinary Analysis and Optimization

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Historical evolution of engineering disciplines and the complexity of the MDO problem suggest that disciplinary autonomy is a desirable goal in formulating and solving MDO problems. We examine the notion of disciplinary autonomy and discuss the analytical properties of three approaches to formulating and solving MDO problems that achieve varying degrees of autonomy by distributing the problem along disciplinary lines. Two of the approaches--Optimization by Linear Decomposition and Collaborative Optimization--are based on bilcvel optimization and reflect what we call a structural perspective.The third approach, Distributed Analysis Optimization, is a single-level approach that arises from what we call an algorithmic perspective.The main conclusion of the paper is that disciplinary autonomy may come at a price: in the bilevet approaches, the system-level constraints introduced to relax the interdisciplinary coupling and enable disciplinary autonomy can cause analytical and computational difficulties for optimization algorithms. The singlelevel alternative we discuss affords a more limited degree of autonomy than that of the bilevel approaches, but without the computational difficulties of the bilevel methods.

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A multilevel method for structural synthesis

Cited by 13 publications

References 15 publications

Multiscale optimal design method of acoustic metamaterials using topology optimization

Multiscale optimal design method of acoustic metamaterials using topology optimization

A comparative approach for the optimal design of steel structures using biogeography-based optimization (BBO) algorithm and genetic algorithm (GA)

Analytical and computational properties of distributed approaches to MDO

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