基于空间弥散律的分数阶梯度弹性
Fractional Gradient Elasticity from Spatial Dispersion Law
摘要：
连续介质力学中的非局部弹性模型有两种不同的处理方法：梯度弹性模型（弱非局部性）和积分非局部模型（强非局部性）。这篇文章的重点是分数推广梯度弹性，使我们能够描述一个弱的非局部性的幂律型。本文提出了一种具有幂律型空间色散的格点模型作为分数梯度弹性连续体的微观模型。我们证明了连续极限将具有这种空间色散的格点方程映射成具有分数拉普拉斯算子的连续方程。从格点模型的分数阶弱空间色散出发，导出了非局部弹性理论中的幂律型弱非局部性。建议的连续方程，这是从晶格模型，描述了梯度弹性的分数推广。这些分数阶弹性方程的解适用于一些特殊情况：亚梯度弹性和超梯度弹性。
英文摘要：
Non-local elasticity models in continuum mechanics can be treated with two different approaches: the gradient elasticity models (weak non-locality) and the integral non-local models (strong non-locality). This article focuses on the fractional generalization of gradient elasticity that allows us to describe a weak non-locality of power-law type. We suggest a lattice model with spatial dispersion of power-law type as a microscopic model of fractional gradient elastic continuum. We prove that the continuous limit maps the equations for lattice with this spatial dispersion into the continuum equations with fractional Laplacians in the Riesz form. A weak non-locality of power-law type in the non-local elasticity theory is derived from the fractional weak spatial dispersion in the lattice model. The suggested continuum equations, which are obtained from the lattice model, describe a fractional generalization of the gradient elasticity. These equations of fractional elasticity are solved for some special cases: sub-gradient elasticity and super-gradient elasticity.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
