Shells without drilling rotations: A representation theorem in the framework of the geometrically nonlinear 6-parameter resultant shell theory

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• 作者：Mircea Bî ; rsan^a ; ^b ; ^{mircea.birsan@uni-due.de" class="auth_mail} ; Patrizio Neff^c ; ¹ ; ^{patrizio.neff@uni-due.de" class="auth_mail}
• 关键词：6-parameter shell theory ; Drilling rotations ; Nonlinear elasticity
• 刊名：International Journal of Engineering Science
• 出版年：July 2014
• 年：2014
• 卷：80
• 期：Complete
• 页码：32-42
• 全文大小：471 K

文摘

In the framework of the geometrically nonlinear 6–parameter resultant shell theory we give a characterization of the shells without drilling rotations. These are shells for which the strain energy function W   is invariant under the superposition of drilling rotations, i.e. W   is insensible to the arbitrary local rotations about the third director d₃${\mathit{d}}_3$. For this type of shells we show that the strain energy density W   can be represented as a function of certain combinations of the shell deformation gradient F$\mathit{F}$ and the surface gradient of d₃${\mathit{d}}_3$, namely $W({\mathit{F}}^T\mathit{F}\text{,}{\mathit{F}}^T{\mathit{d}}_3\text{,}{\mathit{F}}^T{\text{Grad}}_s{\mathit{d}}_3)$. For the case of isotropic shells we present explicit forms of the strain energy function W having this property.