中文摘要：

本文建立了三维弹性壳体和其中性面上各点之间的某些微分几何关系表达式,它对形成二维线性、非线性弹性壳体模型非常重要。具体地,三维弹性体上各点的协变度量张量、逆变度量张量、度量张量矩阵的行列式以及Christoffel符号是由二维中性曲面上的微分几何表达式按壳体厚度方向的变量渐近展开来表示。

英文摘要：

The differential geometric relations between 3Delastic shell and the middle surface of shell are provided,which is of importance for forming 2Dlinear and nonlinear elastic shell models.Concretely,the metric tensor,the determinant of metric matrix field and the Christoffel symbols on the 3Delasticity are expressed by those on the 2D middle surface,which are featured by the asymptotic expressions with respect to the variable in the direction of thickness of the shell.