Material interpolation schemes for unified topology and multi-material optimization

Hvejsel, Christian Frier; Lund, Erik

doi:10.1007/s00158-011-0625-z

Cited by 200 publications

(87 citation statements)

References 27 publications

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“…Moreover, IPOPT and SNOPT have already used for certain topology optimization problems in e.g. (Burger and Stainko 2006;Hvejsel and Lund 2011). These solvers accept both equality and inequality constraints, hence it is possible to benchmark the SAND formulation.…”

Section: Chosen Optimization Methodsmentioning

confidence: 99%

Benchmarking optimization solvers for structural topology optimization

Labanda

Stolpe

2015

Struct Multidisc Optim

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The purpose of this article is to benchmark different optimization solvers when applied to various finite element based structural topology optimization problems. An extensive and representative library of minimum compliance, minimum volume, and mechanism design problem instances for different sizes is developed for this benchmarking. The problems are based on a material interpolation scheme combined with a density filter. Different optimization solvers including Optimality Criteria (OC), the Method of Moving Asymptotes (MMA) and its globally convergent version GCMMA, the interior point solvers in IPOPT and FMINCON, and the sequential quadratic programming method in SNOPT, are benchmarked on the library using performance profiles. Whenever possible the methods are applied to both the nested and the Simultaneous Analysis and Design (SAND) formulations of the problem. The performance profiles conclude that general solvers are as efficient and reliable as classical structural topology optimization solvers. Moreover, the use of the exact Hessians in SAND formulations, generally produce designs with better objective function values. However, with the benchmarked implementations solving SAND formulations consumes more computational time than solving the corresponding nested formulations.

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Section: Chosen Optimization Methodsmentioning

confidence: 99%

Benchmarking optimization solvers for structural topology optimization

Labanda

Stolpe

2015

Struct Multidisc Optim

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“…Conventionally, there are well-established theoretical basis supporting the geometry and material optimization, such as solid isotropic material penalization (SIMP), 46,47 discrete material optimization (DMO), 45,48 and evolutionary structural optimization (ESO). 49 However, in this article, the level set geometry Figure 2.…”

Section: Braidingmentioning

confidence: 99%

Computer-aided design–computer-aided engineering associative feature-based heterogeneous object modeling

Liu

Duke

2015

Advances in Mechanical Engineering

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Conventionally, heterogeneous object modeling methods paid limited attention to the concurrent modeling of geometry design and material composition distribution. Procedural method was normally employed to generate the geometry first and then determine the heterogeneous material distribution, which ignores the mutual influence. Additionally, limited capability has been established about irregular material composition distribution modeling with strong local discontinuities. This article overcomes these limitations by developing the computer-aided design-computer-aided engineering associative feature-based heterogeneous object modeling method. Level set functions are applied to model the geometry within computer-aided design module, which enables complex geometry modeling. Finite element mesh is applied to store the local material compositions within computer-aided engineering module, which allows any local discontinuities. Then, the associative feature concept builds the correspondence relationship between these modules. Additionally, the level set geometry and material optimization method are developed to concurrently generate the geometry and material information which fills the contents of the computer-aided design-computer-aided engineering associative feature model. Micro-geometry is investigated as well, instead of only the local material composition. A few cases are studied to prove the effectiveness of this new heterogeneous object modeling method. KeywordsComputer-aided design-computer-aided engineering associative feature, heterogeneous object modeling, level set, geometry and material optimization Date

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“…The penalized problem, however, may have a large number of local minima. A continuation approach is therefore employed to increase the possibility of obtaining a good design (see Sigmund and Petersson [30], Borrval and Petersson [31], and Hvejsel and Lund [18]). The practical use of the penalty parameter p within the continuation approach is further discussed in Section 5.2.…”

Section: Multi-materials Topology Optimizationmentioning

confidence: 99%

“…Hvejsel and Lund [18] and Hvejsel et al [19] studied the parametrization presented above in great detail and compared it with other equivalent techniques. This parameterization is a generalization of the SIMP approach and typical topology optimization techniques and formulations are therefore directly extendible to the multi-material case (e.g., the density filtering technique presented next).…”

Section: Multi-materials Topology Optimizationmentioning

confidence: 99%

“…A change in the material distribution in the cross section results in a consequent change of its stiffness and mass properties and in turn, of the structural response of the beam. This optimal design problem is solved using the multi-material topology optimization framework presented by Blasques and Stolpe [11], Hvejsel and Lund [18], and Hvejsel et al [19]. The framework is based on the principles of topology optimization (see, e.g., Bendsøe and Sigmund [20]) and relies on extensions to include multiple anisotropic materials of the Solid Isotropic Material with Penalization (SIMP) material interpolation technique (Bendsøe and Kikuchi [21] and Rozvany et al [22]), and the density filtering scheme by Bruns and Tortorelli [23].…”

Section: Introductionmentioning

confidence: 99%

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Multi-material topology optimization of laminated composite beams with eigenfrequency constraints

Blasques

2014

Composite Structures

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Link back to DTU Orbit Citation (APA):Blasques, J. P. A. A. (2014). Multi-material topology optimization of laminated composite beams with eigenfrequency constraints. Composite Structures, 111, 45-55. DOI: 10.1016/j.compstruct.2013 Multi-material topology optimization of laminated composite beams with eigenfrequency constraints AbstractThis paper describes a methodology for simultaneous topology and material optimization in optimal design of laminated composite beams with eigenfrequency constraints. The structural response is analyzed using beam finite elements. The beam sectional properties are evaluated using a finite element based cross section analysis tool which is able to account for effects stemming from material anisotropy and inhomogeneity in sections of arbitrary geometry. The optimization is performed within a multi-material topology optimization framework where the continuous design variables represent the volume fractions of different candidate materials at each point in the cross section. An approach based on the Kreisselmeier-Steinhauser function is proposed to deal with the non-differentiability issues typically encountered when dealing with eigenfrequency constraints. The framework is applied to the optimal design of a laminated composite cantilever beam with constant cross section. Solutions are presented for problems dealing with the maximization of the minimum eigenfrequency and maximization of the gap between consecutive eigenfrequencies with constraints on the weight and shear center position. The results suggest that the devised methodology is suitable for simultaneous optimization of the cross section topology and material properties in design of beams with eigenfrequency constraints.

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Material interpolation schemes for unified topology and multi-material optimization

Cited by 200 publications

References 27 publications

Benchmarking optimization solvers for structural topology optimization

Benchmarking optimization solvers for structural topology optimization

Computer-aided design–computer-aided engineering associative feature-based heterogeneous object modeling

Multi-material topology optimization of laminated composite beams with eigenfrequency constraints

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