Spectral decomposition for graded multi-scale topology optimization

Kumar, Tej; Sridhara, Saketh; Prabhune, Bhagyashree; Suresh, Krishnan

doi:10.1016/j.cma.2021.113670

Cited by 12 publications

(5 citation statements)

References 65 publications

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“…Extension to 3D, non-compliance problems (such as energy absorption [62], orthopedic implants [63], resonant frequencies [64]) using more generic multi-parameter microstructures need to be explored. Furthermore, while we relied on polynomials for directly interpolating the elasticity components, it is desirable to consider an Eigen-value decomposition ( [54]) for increased robustness. The framework can complement and might benefit from data driven approaches ( [44,45]).…”

Section: Discussionmentioning

confidence: 99%

“…To obtain [C m (v)], we adopt a simple constrained polynomial scheme ( [54]). Specifically, the homogenized constitutive matrix [55] for microstructure m is evaluated at a few instances of volume fractions.…”

Section: Materials Modelmentioning

confidence: 99%

“…8a. [54] reported compliance values between 76 and 88 when considering only one microstructure at a time. In comparison, we achieve a compliance of 68 when all microstructures are allowed; see fig.…”

Section: Validationmentioning

confidence: 99%

“…9. Using only a single X-type microstructure, [54] achieved a compliance of 1130, 283, 171 for volume fractions of 0.1, 0.3 and 0.5 respectively. By considering all microstructures (fig.…”

Section: Validationmentioning

confidence: 99%

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GM-TOuNN: Graded Multiscale Topology Optimization using Neural Networks

Chandrasekhar¹,

Sridhara²,

Suresh³

2022

Preprint

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Multiscale topology optimization (M-TO) entails generating an optimal global topology, and an optimal set of microstructures at a smaller scale, for a physics-constrained problem. With the advent of additive manufacturing, M-TO has gained significant prominence. However, generating optimal microstructures at various locations can be computationally very expensive. As an alternate, graded multiscale topology optimization (GM-TO) has been proposed where one or more pre-selected and graded (parameterized) microstructural topologies are used to fill the domain optimally. This leads to a significant reduction in computation while retaining many of the benefits of M-TO. A successful GM-TO framework must: (1) be capable of efficiently handling numerous pre-selected microstructures, (2) be able to continuously switch between these microstructures during optimization, (3) ensure that the partition of unity is satisfied, and (4) discourage microstructure mixing at termination. In this paper, we propose to meet these requirements by exploiting the unique classification capacity of neural networks. Specifically, we propose a graded multiscale topology optimization using neural-network (GM-TOuNN) framework with the following features: (1) the number of design variables is only weakly dependent on the number of pre-selected microstructures, (2) it guarantees partition of unity while discouraging microstructure mixing, and (3) it supports automatic differentiation, thereby eliminating manual sensitivity analysis. The proposed framework is illustrated through several examples.

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Section: Discussionmentioning

confidence: 99%

Section: Materials Modelmentioning

confidence: 99%

Section: Validationmentioning

confidence: 99%

“…9. Using only a single X-type microstructure, [54] achieved a compliance of 1130, 283, 171 for volume fractions of 0.1, 0.3 and 0.5 respectively. By considering all microstructures (fig.…”

Section: Validationmentioning

confidence: 99%

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GM-TOuNN: Graded Multiscale Topology Optimization using Neural Networks

Chandrasekhar¹,

Sridhara²,

Suresh³

2022

Preprint

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“…Matrices interpolated from a database can loose positive definiteness (Kumar et al 2021). For every case that is presented in this paper, we checked the positive definiteness of every surrogate elastic tensor throughout the optimization, using Sylvester's criterion.…”

Section: Surrogate Predictionmentioning

confidence: 99%

A well connected, locally-oriented and efficient multi-scale topology optimization (EMTO) strategy

Duriez

Morlier

Charlotte

et al. 2021

Struct Multidisc Optim

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Multi-scale topology optimization (a.k.a. micro-structural topology optimization, MTO) consists in optimizing macro-scale and micro-scale topology simultaneously. MTO could improve structural performance of products significantly. However, a few issues related to connectivity between micro-structures and high computational cost have to be addressed, without resulting in loss of performance. In this paper, a new efficient multi-scale topology optimization (EMTO) framework has been developed for this purpose. Connectivity is addressed through adaptive transmission zones which limit loss of performance. A pre-computed database of micro-structures is used to speed up the computing. Design variables have also been chosen carefully and include the orientation of the micro-structures to enhance performance. EMTO has been successfully tested on two-dimensional compliance optimization problems. The results show significant improvements compared to mono-scale methods (compliance value lower by up to 20% on a simplistic case or 4% on a more realistic case), and also demonstrate the versatility of EMTO.

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