Abstract
The governing equations for incompressible plates exhibiting a direction of inextensibility are developed in this paper. The motivation for the analysis of such materials is the rise in popularity of fiber-reinforced thermoplastic composites, though the conclusions reached apply equally well to incompressible materials exhibiting very large degrees of anisotropy. In the course of the development, the importance of transverse shear response is demonstrated, indicating that lower order plate theories cannot be used to realistically model incompressible/inextensible materials. As is the case with other plate theories, the in-plane and transverse responses uncouple. A sample analysis, involving only the transverse response, is performed and the results are compared to a simplified solution that is likewise derived herein.
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