کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
7155579 | 1462623 | 2015 | 31 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Non-standard extensions of gradient elasticity: Fractional non-locality, memory and fractality
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
سایر رشته های مهندسی
مهندسی مکانیک
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Derivatives and integrals of non-integer order may have a wide application in describing complex properties of materials including long-term memory, non-locality of power-law type and fractality. In this paper we consider extensions of elasticity theory that allow us to describe elasticity of materials with fractional non-locality, memory and fractality. The basis of our consideration is an extension of the usual variational principle for fractional non-locality and fractality. For materials with power-law non-locality described by Riesz derivatives of non-integer order, we suggest a fractional variational equation. Equations for fractal materials are derived by a generalization of the variational principle for fractal media. We demonstrate the suggested approaches to derive corresponding generalizations of the Euler-Bernoulli beam and the Timoshenko beam equations for the considered fractional non-local and fractal models. Various equations for materials with fractional non-locality, fractality and fractional acceleration are considered.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Communications in Nonlinear Science and Numerical Simulation - Volume 22, Issues 1â3, May 2015, Pages 197-227
Journal: Communications in Nonlinear Science and Numerical Simulation - Volume 22, Issues 1â3, May 2015, Pages 197-227
نویسندگان
Vasily E. Tarasov, Elias C. Aifantis,