论文标题
Efrati等人的弹性理论的批判性研究是无约束的非欧盟板的弹性理论
A Critical Study of Efrati et al.'s Elastic Theory of Unconstrained non-Euclidean Plates
论文作者
论文摘要
在我们的分析中，我们表明Efrati等人的出版与板块理论的数学不一致。然而，它与壳理论的数学更一致，但与不正确的应变张量。因此，作者的数值结果表明，薄物体可以用很少的力大大拉伸，这在物理上是不现实的，并且在数学上是不可证实的。作者的所有理论工作，即曲线坐标中的非线性板方程，可以通过包含足够可区分的差异性和一组外部负载（例如外部应变场）来轻松纠正。
In our analysis, we show that Efrati et al.'s publication is inconsistent with the mathematics of plate theory. However it is more consistent with the mathematics of shell theory, but with an incorrect strain tensor. Thus, the authors' numerical results imply that a thin object can be stretched substantially with very little force, which is physically unrealistic and mathematically disprovable. All the theoretical work of the authors, i.e. nonlinear plate equations in curvilinear coordinates, can easily be rectified with the inclusion of both a sufficiently differentiable diffeomorphism and a set of external loadings, such as an external strain field.
