کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4963872 | 1447415 | 2017 | 48 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On domain symmetry and its use in homogenization
ترجمه فارسی عنوان
در تقارن دامنه و استفاده از آن در همگن شدن
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کلمات کلیدی
دامنه متقارن، روش عنصر محدود همگن شدن معکوس،
موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
نرم افزارهای علوم کامپیوتر
چکیده انگلیسی
The present paper focuses on solving partial differential equations in domains exhibiting symmetries and periodic boundary conditions for the purpose of homogenization. We show in a systematic manner how the symmetry can be exploited to significantly reduce the complexity of the problem and the computational burden. This is especially relevant in inverse problems, when one needs to solve the partial differential equation (the primal problem) many times in an optimization algorithm. The main motivation of our study is inverse homogenization used to design architected composite materials with novel properties which are being fabricated at ever increasing rates thanks to recent advances in additive manufacturing. For example, one may optimize the morphology of a two-phase composite unit cell to achieve isotropic homogenized properties with maximal bulk modulus and minimal Poisson ratio. Typically, the isotropy is enforced by applying constraints to the optimization problem. However, in two dimensions, one can alternatively optimize the morphology of an equilateral triangle and then rotate and reflect the triangle to form a space filling D3 symmetric hexagonal unit cell that necessarily exhibits isotropic homogenized properties. One can further use this D3 symmetry to reduce the computational expense by performing the “unit strain” periodic boundary condition simulations on the single triangle symmetry sector rather than the six fold larger hexagon. In this paper we use group representation theory to derive the necessary periodic boundary conditions on the symmetry sectors of unit cells. The developments are done in a general setting, and specialized to the two-dimensional dihedral symmetries of the abelianD2, i.e. orthotropic, square unit cell and nonabelian D3, i.e. trigonal, hexagon unit cell. We then demonstrate how this theory can be applied by evaluating the homogenized properties of a two-phase planar composite over the triangle symmetry sector of a D3 symmetric hexagonal unit cell.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computer Methods in Applied Mechanics and Engineering - Volume 320, 15 June 2017, Pages 1-45
Journal: Computer Methods in Applied Mechanics and Engineering - Volume 320, 15 June 2017, Pages 1-45
نویسندگان
Cristian Barbarosie, Daniel A. Tortorelli, Seth Watts,