Coupled optimization of macroscopic structures and lattice infill

Geoffroy-Donders, Perle; Allaire, Grégoire; Michailidis, Georgios; Pantz, Olivier

doi:10.1002/nme.6392

Cited by 18 publications

(8 citation statements)

References 45 publications

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“…where is the Lagrange multiplier associated with the volume constraint and f has been defined in (27). Simple ideas to determine the advection field could be used where θ is not only defined on the boundaries but also inside the shape as mentioned in [20]. While this allows less frequent remeshing compared to an advection field defined only on the boundaries, it results in the discontinuity of θ at the boundaries, which represents a major drawback.…”

Section: Methodsmentioning

confidence: 99%

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Damping optimization of viscoelastic cantilever beams and plates under free vibration

Joubert

Allaire

Amstutz

et al. 2022

Computers & Structures

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Section: Methodsmentioning

confidence: 99%

“…Before computing the shape derivative in the present context, the evolution of the thickness during the shape optimization has to be specified. Following the framework of [20], the thickness profile h will be transported by the same diffeomorphism while deforming the shape:…”

Section: Shape Optimizationmentioning

confidence: 99%

Damping optimization of viscoelastic cantilever beams and plates under free vibration

Joubert

Allaire

Amstutz

et al. 2022

Computers & Structures

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“…An alternative way to conquer this issue is to replace voxels with hexahedra to achieve well boundary conforming and adaptive cell size [11,12]. However, deformed microstructures filled in hexahedral cells exhibit a different mechanical behavior compared to that in voxel grid [13]. This means that we need to take shape parameters of deformed microstructures into account for the homogenization method.…”

Section: Introductionmentioning

confidence: 99%

DH-Net: Deformed Microstructure Homogenization via 3D Convolutional Neural Networks

Peng¹,

Liu²,

Huang³

et al. 2022

Preprint

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With the rapid development of additive manufacturing, microstructures are attracting both academic and industrial interests. As an efficient way of analyzing the mechanical behaviors of microstructures, the homogenization method has been well studied in the literature. However, the classic homogenization method still faces challenges. Its computational cost is high for topological optimization that requires highly repeated calculation. The computation is more expensive when the microstructure is deformed from a regular cubic, causing changes for the virtual homogeneous material properties. To conquer this problem, we introduce a fine-designed 3D convolutional neural network (CNN), named DH-Net, to predict the homogenized properties of deformed microstructures. The novelty of DH-Net is that it predicts the local displacement rather than the homogenized properties. The macroscopic strains are considered as a constant in the loss function based on minimum potential energy. Thus DH-Net is label-free and more computation efficient than existing deep learning methods with the mean square loss function. We apply the shape-material transformation that a deformed microstructure with isotropic material can be bi-transformed into a regular structure with a transformed base material, such that the input with a CNN-friendly form feeds in DH-Net. DH-Net predicts homogenized properties with hundreds of acceleration compared to the standard homogenization method and even supports online computing. Moreover, it does not require a labeled dataset

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“…In particular, conceptual links have been established between the multi-scale nature of topology optimization and the idea of tiling, and regularization to a method of incorporating manufacturing constraints. These have established a pathway to 3D print (almost) optimal structures (e.g., [24,32,19]).…”

Section: Introductionmentioning

confidence: 99%

Optimal design of responsive structures

Akerson

Bourdin

Bhattacharya

2022

Struct Multidisc Optim

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With recent advances in both responsive materials and fabrication techniques it is now possible to construct integrated functional structures, composed of both structural and active materials. We investigate the robust design of such structures through topology optimization. By applying a typical interpolation scheme and filtering technique, we prove existence of an optimal design to a class of objective functions which depend on the compliances of the stimulated and unstimulated states. In particular, we consider the actuation work and the blocking load as objectives, both of which may be written in terms of compliances. We study numerical results for the design of a 2D rectangular lifting actuator for both of these objectives, and discuss some intuition behind the features of the converged designs. We formulate the optimal design of these integrated responsive structures with the introduction of voids or holes in the domain, and show that our existence result holds in this setting. We again consider the design of the 2D lifting actuator now with voids. Finally, we investigate the optimal design of an integrated 3D torsional actuator for maximum blocking torque.

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Coupled optimization of macroscopic structures and lattice infill

Cited by 18 publications

References 45 publications

Damping optimization of viscoelastic cantilever beams and plates under free vibration

Damping optimization of viscoelastic cantilever beams and plates under free vibration

DH-Net: Deformed Microstructure Homogenization via 3D Convolutional Neural Networks

Optimal design of responsive structures

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