论文标题
对Baldelli和Bourdin的一项批判性研究对Winkler型能量的渐近推导来自3D弹性的渐近推导
A Critical Study of Baldelli and Bourdin's On the Asymptotic Derivation of Winkler-Type Energies From 3D Elasticity
论文作者
论文摘要
在我们的分析中，我们表明Baldelli和Bourdin的作品仅在描述与弹性伪基因结合的胶片的行为时有效，在这种情况下，泊松的两个身体的比率在-1至1之间或0和0.5之间（Poisson的比率都足以在0和0.5）中，以及与呈现的条件不同的条件。我们还表明，对于所有泊松比，作者的相图是四维而不是二维的。同样，由于泊松的比率依赖性，作者出现的渐近量表不足以推导其提出的模型。此外，作者对位移场的缩放表明，除非正常位移为零，否则它们的方法不能适用于带有平面载荷的膜（或字符串）。最后，通过通过作者所暗示的方法来推导弹性伪基支持的板块基础类型解决方案，我们表明作者的方法不能应用于上覆的身体的结构（即板整合的限制）和基础（即平面自由的基础）识别范围的范围（即平面自由的状态），是识别平面的范围，这是识别范围的。尽管作者的工作有局限性，但我们通过表明与Winkler Foundation方程式的经典推导不同，Baldelli和Bourdin的方法不违反数量对话法律或违反数学弹性的管理方程。
In our analysis, we show that Baldelli and Bourdin's work is only valid when describing the behaviour of a film bonded to an elastic pseudo-foundation, where Poisson's ratios of both bodies are in between -1 and 0 or in between 0 and 0.5 (where both Poisson's ratios are sufficiently away from 0 and 0.5), and with an asymptotic condition that is different to what the authors present. We also show that, for all Poisson's ratios, the authors' phase diagram is four-dimensional and not two-dimensional. Also, due to the Poisson's ratio dependence, the asymptotic scalings that the authors present are insufficient to derive their proposed models. Furthermore, the authors' scaling of the displacement field implies that their method cannot be applicable to films (or strings) with planar loading, unless the normal displacement is zero. Finally, by deriving a Winkler foundation type solution for a plate supported by an elastic pseudo-foundation via the method implied by the authors, we show that the authors' method cannot be applied to plates due to the structure of the overlying body (i.e. the limits of integration of the plate) and the foundation (i.e. planar-stress free condition of the foundation), unless planar displacement field is identically zero. Despite the limitations of the authors' work, we highlight its strength by showing that unlike the classical derivation of the Winkler foundation equation, Baldelli and Bourdin's approach does not violate the volume conversation laws or violate the governing equations of mathematical elasticity.
