On the optimization of non periodic homogenized microstructures

Chenais, Denise; Mascarenhas, M. L.; Trabucho, L.

doi:10.1051/m2an/1997310505591

Cited by 8 publications

(10 citation statements)

References 11 publications

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“…This is consistent with the results obtained in [10,11,23,33]. However spatial changes in the periodicity are approximated by…”

Section: For (T X) ∈ (0 T ) × and Y ∈ X Where The Macroscopic Difsupporting

confidence: 92%

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Multiscale Modelling and Analysis of Signalling Processes in Tissues with Non-Periodic Distribution of Cells

Ptashnyk

2016

Vietnam J. Math.

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In this paper, a microscopic model for a signalling process in the left ventricular wall of the heart, comprising a non-periodic fibrous microstructure, is considered. To derive the macroscopic equations, the non-periodic microstructure is approximated by the corresponding locally periodic microstructure. Then, applying the methods of locally periodic homogenization (the locally periodic (l-p) unfolding operator, locally periodic two-scale (lt-s) convergence on oscillating surfaces and l-p boundary unfolding operator), we obtain the macroscopic model for a signalling process in the heart tissue.

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“…This is consistent with the results obtained in [10,11,23,33]. However spatial changes in the periodicity are approximated by…”

Section: For (T X) ∈ (0 T ) × and Y ∈ X Where The Macroscopic Difsupporting

confidence: 92%

“…Formal asymptotic expansion and two-scale convergence defined for periodic test functions, [27], were used to derive macroscopic equations for models posed in domains with locally periodic perforations, i.e., domains consisting of periodic cells with smoothly changing perforations [5,10,11,22,23,33].…”

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confidence: 99%

Multiscale Modelling and Analysis of Signalling Processes in Tissues with Non-Periodic Distribution of Cells

Ptashnyk

2016

Vietnam J. Math.

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“…The difficult part is to characterize dA eff . We make variations in formula (3.2) and, by classical arguments (see [12,13]) we obtain…”

Section: Shape Optimizationmentioning

confidence: 99%

Shape optimization of periodic structures

Barbarosie¹

2003

Computational Mechanics

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This paper describes a numerical approach to the optimization of effective properties of periodic perforations in an infinite body, in the frameworks of heat conduction and of linear elasticity. We implement a special finite element mesh in order to deal with the periodic nature of the problem. We compute the gradient of the functional to be minimized. We describe the process of mesh deformation and mesh regeneration. We give several numerical examples, some of them having practical relevance.

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“…the geometry of the cavities varies with space. Two scale convergence was applied in [14,30] to homogenize the warping, the torsion and the Neumann problems in two dimensional domains with smoothy changing holes and in [29] two scale convergence was generalized to a locally periodic and fibrous media. All these works deal with the case where the basic cell varies with space but the period in which the basic cell is spaced is constant and do not vary with space.…”

Section: Introductionmentioning

confidence: 99%

Unfolding Operator Method for Thin Domains with a Locally Periodic Highly Oscillatory Boundary

Arrieta¹,

Villanueva-Pesqueira²

2016

SIAM J. Math. Anal.

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: We analyze the behavior of solutions of the Poisson equation with homogeneous Neumann boundary conditions in a two-dimensional thin domain which presents locally periodic oscillations at the boundary. The oscillations are such that both the amplitude and period of the oscillations may vary in space. We obtain the homogenized limit problem and a corrector result by extending the unfolding operator method to the case of locally periodic media. We emphasize the fact that the techniques developed in this paper can be adapted to other locally periodic cases like reticulated or perforated domains where the period may be space-dependent.

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On the optimization of non periodic homogenized microstructures

Cited by 8 publications

References 11 publications

Multiscale Modelling and Analysis of Signalling Processes in Tissues with Non-Periodic Distribution of Cells

Multiscale Modelling and Analysis of Signalling Processes in Tissues with Non-Periodic Distribution of Cells

Shape optimization of periodic structures

Unfolding Operator Method for Thin Domains with a Locally Periodic Highly Oscillatory Boundary

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