Fractional-order structural stability: Formulation and application to the critical load of nonlocal slender structures
Fractional-order structural stability: Formulation and application to the critical load of nonlocal slender structures
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DOI：
10.1016/j.ijmecsci.2021.106443
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发表时间：
2021-07
影响因子：
7.3
通讯作者：
Sai Sidhardh;Sansit Patnaik;F. Semperlotti
中科院分区：
文献类型：
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作者：
Sai Sidhardh;Sansit Patnaik;F. Semperlotti
本研究提出一个框架，以进行稳定性分析的非局部固体的行为描述，根据分数阶连续介质理论。在这个配方中，空间分数阶算子被用来捕捉介质的非局部响应的非局部运动关系。我们使用几何非线性分数阶运动关系内的能量为基础的方法，建立非局部结构的拉格朗日-狄利克雷稳定性准则。这种基于能量的非局部结构稳定性的方法是可能的，由于一个正定的和一致的定义的变形能启用的分数阶运动学公式。在线性屈曲条件下，还导出了临界载荷的Rayleigh-Ritz系数。分数阶公式最后用于确定临界载荷的细长非局部梁和板的屈曲使用一个专用的分数阶有限元求解器。结果表明，与现有的研究相比，使用分数阶运动学方法时，在材料和几何刚度上观察到非局部相互作用的影响。这些意见支持定量通过解决方案的情况下研究，重点是分数阶非局部细长结构的临界屈曲响应，并直接比较分数阶的方法与经典的非局部方法。
This study presents a framework to perform stability analysis of nonlocal solids whose behavior is described according to the fractional-order continuum theory. In this formulation, space fractional-order operators are used to capture the nonlocal response of the medium by means of nonlocal kinematic relations. We use the geometrically nonlinear fractional-order kinematic relations within an energy based approach to establish the Lagrange-Dirichlet stability criteria for nonlocal structures. This energy based approach to nonlocal structural stability is possible due to a positive-definite and thermodynamically consistent definition of the deformation energy enabled by the fractional-order kinematic formulation. The Rayleigh-Ritz coefficient for critical load is also derived for linear buckling conditions. The fractional-order formulation is finally used to determine critical loads for buckling of the slender nonlocal beams and plates using a dedicated fractional-order finite element solver. Results establish that, in contrast to existing studies, the effect of nonlocal interactions is observed on both the material and the geometric stiffness, when using the fractional-order kinematics approach. These observations are supported quantitatively via the solution of case studies that focus on the critical buckling response of fractional-order nonlocal slender structures, and a direct comparison of the fractional-order approach with classical nonlocal approaches.