论文标题
在Kirchhoff-Love假设上（修订和证明）
On the Kirchhoff-Love hypothesis (revised and vindicated)
论文作者
论文摘要
Kirchhoff-love假说表达了一种运动学约束，当它的一个尺寸之一远小于其他两个时，它被认为对三维体的变形有效，就像板的情况一样。该假设的历史悠久，涉及生命的历史：即使是它的归因也受到了质疑，并且最近证明，最近严格的减少维度的工具（基于$γ$ - 融合）也已被证明与之不相容。我们发现，Kirchhoff-Love假设的适当修订版是一种有价值的手段，可以从三维非线性非线性自由能函数中为弹性板的二维变异模型得出。因此，对于多种材料而获得的弯曲能也表明包含板中部表面拉伸的度量（与预期的弯曲度量旁边）。在可以与该方法接触的情况下，与$γ$ -Convergence的不兼容似乎也将被删除。
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.
