关于基尔霍夫-洛夫假说（修订和证明）
On the Kirchhoff-Love hypothesis (revised and vindicated)
摘要：
Kirchhoff-Love假设表达了一种运动学约束，当三维物体的一个尺寸比其他两个尺寸小得多时，这种约束被认为对三维物体的变形是有效的，就像板的情况一样。这一假设有着悠久的历史，随着生活的变迁而变化：甚至其归属也受到质疑，以及最近严格的降维工具（基于$Γ$ -收敛）已被证明与之不相容。我们发现，适当修改的Kirchhoff-Love假设版本是从三维非线性自由变分模型推导弹性板二维变分模型的有价值的手段。能量泛函因此，获得的弯曲能量的一些材料也显示包含拉伸板的中间表面的措施（旁边的预期措施的弯曲）。与$Γ$ -收敛的不相容性在与该方法和我们的方法接触的情况下似乎也被消除了。
英文摘要：
The Kirchhoff-Love hypothesis expresses a kinematic constraint that is assumed to be valid for the deformations of a three-dimensional body when one of its dimensions is much smaller than the other two, as is the case for plates. This hypothesis has a long history checkered with the vicissitudes of life: even its attribution has been questioned, and recent rigorous dimension-reduction tools (based on $Γ$-convergence) have proven to be incompatible with it. We find that an appropriately revised version of the Kirchhoff-Love hypothesis is a valuable means to derive a two-dimensional variational model for elastic plates from a three-dimensional nonlinear free-energy functional. The bending energies thus obtained for a number of materials also show to contain measures of stretching of the plate's mid surface (alongside the expected measures of bending). The incompatibility with $Γ$-convergence also appears to be removed in the cases where contact with that method and ours can be made.
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