论文标题
分数壳理论：配方和应用非局部圆柱板的分析
Fractional-Order Shell Theory: Formulation and Application to the Analysis of Nonlocal Cylindrical Panels
论文作者
论文摘要
我们提出了一个基于分数计算的理论和计算框架，用于分析圆柱壳面板的非局部静态响应。分数衍生物的不同综合性质允许一种有效而准确的方法来说明弯曲结构中远程（非本地）相互作用的影响。更具体地说，使用框架不变的分数运动关系可以实现物理，数学和热力学一致的配方，以模拟非本地弹性相互作用。为了在涉及通用载荷和边界条件的实际场景下评估这些非局部壳的响应，扩展了分数 - 限制元素方法（F-FEM），以根据一阶剪切可构造的位移理论结合壳元素。最后，进行数值研究，以探索非本地圆柱壳板的线性和几何非线性静态响应。这项研究旨在为通过分数模型来研究弯曲结构的非局部行为的一般基础。
We present a theoretical and computational framework based on fractional calculus for the analysis of the nonlocal static response of cylindrical shell panels. The differ-integral nature of fractional derivatives allows an efficient and accurate methodology to account for the effect of long-range (nonlocal) interactions in curved structures. More specifically, the use of frame-invariant fractional-order kinematic relations enables a physically, mathematically, and thermodynamically consistent formulation to model the nonlocal elastic interactions. In order to evaluate the response of these nonlocal shells under practical scenarios involving generalized loads and boundary conditions, the fractional-Finite Element Method (f-FEM) is extended to incorporate shell elements based on the first-order shear-deformable displacement theory. Finally, numerical studies are performed exploring both the linear and the geometrically nonlinear static response of nonlocal cylindrical shell panels. This study is intended to provide a general foundation to investigate the nonlocal behavior of curved structures by means of fractional order models.
