Optimization of Oriented and Parametric Cellular Structures by the Homogenization Method

Geoffroy-Donders, Perle; Allaire, Grégoire; Cortial, Julien; Pantz, Olivier

doi:10.1007/978-3-319-67988-4_58

Cited by 2 publications

(6 citation statements)

References 16 publications

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“…This difficulty is bypassed when the objective functional is the compliance functional because its minimum can be computed among a well-known subset of the full set of effective tensors, i.e., that of a sequential laminates: see [25] for details. To circumvent these challenges, we follow the same approach in [27,28], which is to limit the set of admissible composite designs to microstructures for which the Hooke's law can be numerically computed (e.g. : periodic composites with hexagonal cells).…”

Section: The Original Optimal Design Problem and Its Relaxed Formulationmentioning

confidence: 99%

“…Herein, we propose an homogenization method for topology optimization of a coupled fluid-structures built with periodic composite materials, characterized by the local density θ of the material and the associated homogenized Hooke's law A * , defined at each point x ∈ Ω of the working space. As in [28], we restrain our analysis to a simple class of composites in plan setting, i.e., our composite materials are periodically perforated by hexagonal cell in 2-d: a regular unit hexagon perforated by smooth hexagon hole, known as smooth honeycomb. This class of modulated periodic microstructures is known to be isotropic microstructures (or atleast very close to one); the assumption numerically displayed on Fig.…”

Section: Topology Optimization Problem Formulationmentioning

confidence: 99%

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Homogenization based topology optimization of fluid-pressure loaded structures using the Biot–Darcy Model

2023

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The ambition to develop simulation methods making it possible to predict the integrity or the properties of use (mechanical, diffusive, thermal, electromagnetic, vibratory, etc.) of structures (industrial or natural), materials or processes involved in the development of new advanced technologies is growing consistently. In a global context of permanent development of advanced technologies (notably in the field of energy) and a growing need for cost reduction, the development times for new concepts are increasingly reduced and therefore tend to exclude monolithic design of multiphysic structures. Here, we propose an homogenization based topology optimization method to design multi-scale and multiphysic structures experiencing fluid-pressure loads. Its effect is to allow for micro-perforated composite as admissible designs, where the design is characterized by the material density and its homogenized Hooke's law at each point of the working space, yielding composite designs made of fine mixture between the solid and void phases. The fluid-pressure loads is determined using Biot-Darcy's law and solved using the finite element method. This approach permits a computationally low cost of evaluation of of load sensitivities using the Lagrangian method. As no assumption is impose on the number of micro-perforation inside the solid domain, this method can be seen as a topology optimization algorithm. We seek minimizers of the elastic compliances, fluid-elastic compliances and of the weight of a solid structure under fluid-pressure loads.

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Section: The Original Optimal Design Problem and Its Relaxed Formulationmentioning

confidence: 99%

Section: Topology Optimization Problem Formulationmentioning

confidence: 99%

Homogenization based topology optimization of fluid-pressure loaded structures using the Biot–Darcy Model

2023

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“…In this direction, one possibility, investigated in [37,40], is to consider a regular, lattice-shaped infill pattern, parametrized by its local thickness and by the local orientation of bars. These parameters are then the optimization variables.…”

Section: Modeling and Optimization Of The Infill Designmentioning

confidence: 99%

“…16 Remark 6.1. A completely different and quite interesting method for creating non regular infills is the so-called deshomogenization method, introduced by O. Pantz and K. Trabelsi in [61,62], then used in [9,37,40]. A composite homogenized structure is projected onto a classical shape that resembles the original microstructure at a macroscopic (yet thin) scale.…”

Section: Modeling and Optimization Of The Infill Designmentioning

confidence: 99%

“…This echoes to the prior contributions [72,73], in which a local volume constraint is enforced so as to avoid large features and to obtain optimal non-regular infill structures. Let us mention another elegant and efficient way to get non-regular infill structures, introduced in [61,62], then used in [9,37,40], which is based on a post-treatment of optimized composite structures.…”

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confidence: 99%

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Shape and topology optimization considering anisotropic features induced by additive manufacturing processes

Dapogny

Estevez²,

Faure³

et al. 2019

Computer Methods in Applied Mechanics and Engineering

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This article considers the modelling of the effective properties of the constituent material of structures fabricated by additive manufacturing technologies; the influence of these properties on the design optimization process is analyzed, and the opportunities that they offer in this context are investigated. On the one hand, emphasizing on the case where the particular material extrusion techniques are used for the construction, we propose a model for the anisotropic material properties of shapes depending on the (user-defined) trajectory followed by the machine tool during the assembly of their 2d layers. On the other hand, we take advantage of the potential of additive manufacturing technologies for constructing very small features: we consider the optimization of the infill region of a shape with given external contour with the goal to improve at the same time its lightness and its robustness. The optimized and constraint functionals of the domain involved in the shape optimization problems in both contexts are rigorously analyzed, notably by relying on the notion of signed distance function. Eventually, several numerical experiments are conducted in two dimensions to illustrate the main points of the study.

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Optimization of Oriented and Parametric Cellular Structures by the Homogenization Method

Cited by 2 publications

References 16 publications

Homogenization based topology optimization of fluid-pressure loaded structures using the Biot–Darcy Model

Homogenization based topology optimization of fluid-pressure loaded structures using the Biot–Darcy Model

Shape and topology optimization considering anisotropic features induced by additive manufacturing processes

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