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Three-dimensional lattice approach to fractional generalization of continuum gradient elasticityстатья
- Автор: Tarasov V.E.
- Журнал: Progress in Fractional Differentiation and Applications
- Том: 1
- Номер: 4
- Год издания: 2015
- Первая страница: 243
- Последняя страница: 258
- DOI: 10.12785/pfda/010402
- Аннотация: A relationship between discrete and continuous fractional-order nonlocal elasticity theory is discussed. As a discrete system we consider three-dimensional lattice with long-range interactions that are described by fractional-order lattice operators.We prove that the continuous limit of suggested three-dimensional lattice equations gives continuum differential equations with the Riesz derivatives of non-integer orders. The proposed lattice models give a new microstructural basis for elasticity of materials with power-law type of non-locality. Moreover these lattice models allow us to have a unified microscopic description for fractional and usual (non-fractional) gradient elasticity continuum.
- Добавил в систему: Тарасов Василий Евгеньевич
Прикрепленные файлы
| № | Имя | Описание | Имя файла | Размер | Добавлен |
|---|---|---|---|---|---|
| 1. | Полный текст | PFDA2015.pdf | 389,3 КБ | 1 октября 2015 [VasilyTarasov] |