经历有限变形和有限转动薄壳结构的非线性理论

本文基于计及横向剪切变形的修正Ｋｉｒｃｈｈｏｆｆ－Ｌｏｖｅ假定，采用与反映壳体中面法向偏转的正交张量对应转角矢量来描述薄壳结构的有限转动，建立了经历有限变形和有限转动薄壳结构的非线性理论。其间，导出了其壳体黎曼空间中的Ｇｒｅｅｎ－Ｌａｇｒａｎｇｅ应变张量和第二类Ｐｉｏｌａ－Ｋｉｒｃｈｈｏｆｆ应力张量的表达形式，并通过虚功原理，建立了薄壳结构的非线性平衡关系。

A Non-Linear Theory for Analysis of Thin-Shell Structures Undergoing Finite Deformation and Finite Rotation

Based on the modified Kirchhoff-Love hypothesis with the inclusion of transverse shear deformation,a non-linear thin-shell theory for the analysis of shell structures is presented.In describing the finite rotation in thin-shell structures,rotation vectors are adopted in the present work,which correspond to the orthogonal tensor that indicates normal rotations of the shell mid-surface.Also derived in the paper are the Green-Lagrange strain tensor and the second Piola-Kirchhoff stress tensor in the Riemann space of the shell.Finally,on the basis of the virtual work,the non-linear equilibrium equations of thin-shell structures are developed.