Alternating active-phase algorithm for multimaterial topology optimization problems: a 115-line MATLAB implementation

Tavakoli, Rouhollah; Mohseni, Saeid-Reza

doi:10.1007/s00158-013-0999-1

Cited by 194 publications

(87 citation statements)

References 35 publications

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“…In the first two examples, the results are compared with an alternative optimization method, i.e., the alternating active-phase multimaterial topology optimization algorithm [61], which is available in MATLAB. In the last two examples, a parametric study on the number of clusters is included.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…The minimum thermal compliance example is adopted from [61]. The design problem is illustrated in Fig.…”

Section: Thermal Compliancementioning

confidence: 99%

“…For comparison, this problem is also solved using the alternating active-phase multimaterial topology optimization (MTOP) algorithm [61]. The MTOP algorithm consists of outer and inner iterations.…”

Section: Thermal Compliancementioning

confidence: 99%

“…Both results have the same material parameters µ µ µ * k and mass fractions m * µk . As stated in [61], the filter is a key success of the optimization procedure and should be gradually reduced during the multimaterial topology optimization; hence, the filter is applied and gradually reduced in MTOP. A penalization power is also utilized.…”

Section: Thermal Compliancementioning

confidence: 99%

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Optimal Design of Nonlinear Multimaterial Structures for Crashworthiness Using Cluster Analysis

Liu

Detwiler

Tovar

2017

Journal of Mechanical Design

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This study presents an efficient multimaterial design optimization algorithm that is suitable for nonlinear structures. The proposed algorithm consists of three steps: conceptual design generation, clustering, and metamodel-based global optimization. The conceptual design is generated using a structural optimization algorithm for linear models or a heuristic design algorithm for nonlinear models. Then, the conceptual design is clustered into a predefined number of clusters (materials) using a machine learning algorithm. Finally, the global optimization problem aims to find the optimal material parameters of the clustered design using metamodels. The metamodels are built using sampling and cross-validation, and sequentially updated using an expected improvement function until convergence. The proposed methodology is demonstrated using examples from multiple physics and compared with traditional multimaterial topology optimization method. The proposed approach is applied to nonlinear, multi-objective design problems for crashworthiness.

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Section: Numerical Examplesmentioning

confidence: 99%

“…The minimum thermal compliance example is adopted from [61]. The design problem is illustrated in Fig.…”

Section: Thermal Compliancementioning

confidence: 99%

Section: Thermal Compliancementioning

confidence: 99%

Section: Thermal Compliancementioning

confidence: 99%

See 2 more Smart Citations

Optimal Design of Nonlinear Multimaterial Structures for Crashworthiness Using Cluster Analysis

Liu

Detwiler

Tovar

2017

Journal of Mechanical Design

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“…Apart from homogenization-based methods, different versions of level-set methods have also been introduced to solve multi-phase material distribution problems (see for example Zhou and Wang 2007;Wang and Wang 2004;Wang et al 2015). For other notable recent works in this area, the reader is referred to the works of Gao and Zhang (2011);Bruyneel (2011); Blasques and Stolpe (2012) ;Gao et al (2013); Tavakoli and Mohseni (2014); Tavakoli (2014); Park and Sutradhar (2015); Querin et al (2015).…”

Section: Introductionmentioning

confidence: 99%

An improved soft-kill BESO algorithm for optimal distribution of single or multiple material phases

Ghabraie

2015

Struct Multidisc Optim

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Finding the optimum distribution of material phases in a multi-material structure is a frequent and important problem in structural engineering which involves topology optimization. The Bi-directional Evolutionary Structural Optimization (BESO) method is now a well-known topology optimization method. In this paper an improved soft-kill BESO algorithm is introduced which can handle both single and multiple material distribution problems. A new filtering scheme and a gradual procedure inspired by the continuation approach are used in this algorithm. Capabilities of the proposed method are demonstrated using different examples. It is shown that the proposed method can result in considerable improvements compared to the normal BESO algorithm particularly when solving problems involving very soft material or void phase.

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An isogeometric approach to topology optimization of multi-material and functionally graded structures

Taheri

Suresh

2016

Int. J. Numer. Meth. Engng

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Summary A new isogeometric density‐based approach for the topology optimization of multi‐material structures is presented. In this method, the density fields of multiple material phases are represented using the isogeometric non‐uniform rational B‐spline‐based parameterization leading to exact modeling of the geometry, removing numerical artifacts and full analytical computation of sensitivities in a cost‐effective manner. An extension of the perimeter control technique is introduced where restrictions are imposed on the perimeters of density fields of all phases. Consequently, not only can one control the complexity of the optimal design but also the minimal lengths scales of all material phases. This leads to optimal designs with significantly enhanced manufacturability and comparable performance. Unlike the common element‐wise or nodal‐based density representations, owing to higher order continuity of density fields in this method, their gradients required for perimeter control restrictions are calculated exactly without additional computational cost. The problem is formulated with constraints on either (1) volume fractions of different material phases or (2) the total mass of the structure. The proposed method is applied for the minimal compliance design of two‐dimensional structures consisting of multiple distinct materials as well as functionally graded ones. Copyright © 2016 John Wiley & Sons, Ltd.

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Alternating active-phase algorithm for multimaterial topology optimization problems: a 115-line MATLAB implementation

Cited by 194 publications

References 35 publications

Optimal Design of Nonlinear Multimaterial Structures for Crashworthiness Using Cluster Analysis

Optimal Design of Nonlinear Multimaterial Structures for Crashworthiness Using Cluster Analysis

An improved soft-kill BESO algorithm for optimal distribution of single or multiple material phases

An isogeometric approach to topology optimization of multi-material and functionally graded structures

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