Alternate Exact Equations for the Inextensional Deformation of Arbitrary, Quadrilateral, and Triangular Plates

Abstract

Previously, a set of 9 exact differential equations was derived for the inextensional deformation of a plate bounded by two straight edges and two arbitrary curves. One straight edge is built-in. The other moves rigidly and is subject to a force and couple. The curved edges are stress-free. If the plate twists as it deforms, then, as shown herein, the 9 equations may be replaced by 7. The equations are written in a dimensionless form allowing a ready comparison with Mansfield’s theory that assumes small but finite angles of rotation. If the end load is a couple only, then an independent set of 5 equations emerges. These reduce to 4 for a quadrilateral plate. A numerical example compares the prediction of the exact equations against those of Mansfield. For triangular plates under tip forces only, an alternate, better conditioned, set of 9 differential equations is derived, and the behavior of the solutions near the tip is analyzed.