标题： 薄的非线性梯度弹性板的中面弹性模型 显示英文标题

标题： A midsurface elasticity model for a thin, nonlinear, gradient elastic plate

摘要： 本文推导了二维薄板中面的动力表面弹性模型，该薄板是三维、均匀、各向同性、非线性的梯度弹性板，厚度为$h$。 所得模型由板的五个可测量的物理特性参数化，并且在奇异极限情况下，存储的表面能量会退化为Koiter板的能量。 该模型修正了薄板中波传播中存在的理论问题，并且当与作者关于具有梯度弹性材料边界的Green弹性体的理论结合时，可以消除传统/经典模型中裂纹处存在的奇异性。 我们的方法不同于以往关于薄壳和板的研究，这些研究主要集中在从经典的三维Green弹性理论推导材料表面的弹性理论。 这项工作首次严格地基于母体非线性梯度弹性理论发展了表面弹性模型。 显示英文摘要

摘要： In this paper, we derive a dynamic surface elasticity model for the two-dimensional midsurface of a thin, three-dimensional, homogeneous, isotropic, nonlinear gradient elastic plate of thickness $h$. The resulting model is parameterized by five, conceivably measurable, physical properties of the plate, and the stored surface energy reduces to Koiter's plate energy in a singular limiting case. The model corrects a theoretical issue found in wave propagation in thin sheets and, when combined with the author's theory of Green elastic bodies possessing gradient elastic material boundary surfaces, removes the singularities present in fracture within traditional/classical models. Our approach diverges from previous research on thin shells and plates, which primarily concentrated on deriving elasticity theories for material surfaces from classical three-dimensional Green elasticity. This work is the first in rigorously developing a surface elasticity model based on a parent nonlinear gradient elasticity theory.