کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6876642 | 1442531 | 2018 | 26 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Auxetic deformations and elliptic curves
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
گرافیک کامپیوتری و طراحی به کمک کامپیوتر
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چکیده انگلیسی
In materials science and engineering, auxetic behavior refers to deformations of flexible structures where stretching in some direction involves lateral widening, rather than lateral shrinking. We address the problem of detecting auxetic behavior for flexible periodic bar-and-joint frameworks. Currently, the only known algorithmic solution is based on the rather heavy machinery of fixed-dimension semi-definite programming. In this paper we present a new, simpler algorithmic approach which is applicable to a natural family of three-dimensional periodic bar-and-joint frameworks with three degrees of freedom. This class includes most zeolite structures, which are important for applications in computational materials science. We show that the existence of auxetic deformations is related to properties of an associated elliptic curve. A fast algorithm for recognizing auxetic capabilities is obtained via the classical Aronhold invariants of the cubic form defining the curve. Related algorithmic alternatives are also considered.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computer Aided Geometric Design - Volume 61, March 2018, Pages 9-19
Journal: Computer Aided Geometric Design - Volume 61, March 2018, Pages 9-19
نویسندگان
Ciprian S. Borcea, Ileana Streinu,