论文标题
板的线性化基尔乔夫理论，具有不相容的prestrain
The linearized Kirchhoff theory for plates with incompatible prestrain
论文作者
论文摘要
在本文中，我们从三维的非线性弹性能量中得出了一个线性化的基尔chhoff模型，因为其厚度$ h $倾向于零，其弹性能量尺度（例如$ h^β$），$ 2 <β<β<4。薄板。当中板$（ω，g = g_ {2 \ times2}）$始终是正面的，g = g_ {2 \ times2}）$时，通过使用各种方法来严格研究问题并确定非欧巴文版本的$γ-$极限。
In this paper, we derive a linearized Kirchhoff model from three dimensional nonlinear elastic energy of plates with incompatible prestrain as its thickness $h$ tends to zero and its elastic energy scales like $h^β$ with $2<β<4.$ The incompatible prestrain is given as a Riemannian metric $G(x')$ in the three dimensional thin plate which only depends on mid-plate of the thin plates. The problem is studied rigorously by using a variational approach and establishing the $Γ-$ limit of the non-Euclidean version of the nonlinear elasticity functional when the gauss curvature of the mid-plate $(Ω, g=G_{2\times2})$ is always positive, negative or zero.
