论文标题
多尺度非局部光束理论：分布式分数操作员的应用
Multiscale nonlocal beam theory: An application of distributed-order fractional operators
论文作者
论文摘要
这项研究提出了一个综合的理论框架，以模拟多尺度非局部弹性梁的响应。通过使用具有四阶张量作为强度功能的分布式（DO）分布式（DO）算子，该框架可以准确地捕获2D异质梁的各向异性行为，具有跨多个尺度的非局部效应。还介绍了一维（1D）多尺度非本地Timoshenko模型的基础，并基于DO操作员的多尺度特征。这种方法可实现重大的模型降低，而不会损害材料的异质非局部描述，从而导致有效，准确的多尺度非局部建模方法。使用1D和2D方法来模拟非局部束的机械响应。由DO或整数阶完全分辨模型（用作地面真实）产生的数值模拟的直接比较清楚地说明了DO公式捕获微结构对宏观响应的影响的能力。对计算成本的评估还表明了所提出的方法的效率。
This study presents a comprehensive theoretical framework to simulate the response of multiscale nonlocal elastic beams. By employing distributed-order (DO) fractional operators with a fourth-order tensor as the strength-function, the framework can accurately capture anisotropic behavior of 2D heterogeneous beams with nonlocal effects localized across multiple scales. Building upon this general continuum theory and on the multiscale character of DO operators, a one-dimensional (1D) multiscale nonlocal Timoshenko model is also presented. This approach enables a significant model-order reduction without compromising the heterogeneous nonlocal description of the material, hence leading to an efficient and accurate multiscale nonlocal modeling approach. Both 1D and 2D approaches are applied to simulate the mechanical responses of nonlocal beams. The direct comparison of numerical simulations produced by either the DO or an integer-order fully-resolved model (used as ground truth) clearly illustrates the ability of the DO formulation to capture the effect of the microstructure on the macroscopic response. The assessment of the computational cost also indicates the superior efficiency of the proposed approach.
