论文标题
弹性分数非局部模型的几何非线性响应
Geometrically Nonlinear Response of a Fractional-Order Nonlocal Model of Elasticity
论文作者
论文摘要
这项研究介绍了Euler-Bernoulli束的几何非线性和分数非定位模型的分析和有限元公式。 Euler-Bernoulli束中的有限非局部菌株是从框架不变和尺寸一致的分数（非局部）连续体配方中获得的。有限的分数应变理论提供了一个正定的确定配方，从而产生了数学良好的配方，该配方在载荷和边界条件上是一致的。使用变异原理获得了几何非线性和非局部Euler-Bernoulli束的管理方程和相应的边界条件。此外，开发了分数阶系统的非线性有限元模型，以实现全差异非线性统计方程的数值解决方案。经过基准问题进行彻底验证后，分数有限元模型（F-FEM）用于研究非局部光束的几何非线性响应，但受各种载荷和边界条件的约束。尽管在1D光束的上下文中呈现，但这种非线性F-FEM公式可以扩展到更高维的分数边界值问题。
This study presents the analytical and finite element formulation of a geometrically nonlinear and fractional-order nonlocal model of an Euler-Bernoulli beam. The finite nonlocal strains in the Euler-Bernoulli beam are obtained from a frame-invariant and dimensionally consistent fractional-order (nonlocal) continuum formulation. The finite fractional strain theory provides a positive definite formulation that results in a mathematically well-posed formulation which is consistent across loading and boundary conditions. The governing equations and the corresponding boundary conditions of the geometrically nonlinear and nonlocal Euler-Bernoulli beam are obtained using variational principles. Further, a nonlinear finite element model for the fractional-order system is developed in order to achieve the numerical solution of the integro-differential nonlinear governing equations. Following a thorough validation with benchmark problems, the fractional finite element model (f-FEM) is used to study the geometrically nonlinear response of a nonlocal beam subject to various loading and boundary conditions. Although presented in the context of a 1D beam, this nonlinear f-FEM formulation can be extended to higher dimensional fractional-order boundary value problems.
