A novel dimensional reduction for the equilibrium study of inextensional material surfaces

A general framework is developed for finding the equations describing equilibrium of an inextensional material surface with arbitrary flat reference shape that deformed by applying tractions or moments to its edge. This facilitated using a representation all isometric deformations convert bending energy line integral over edge surface. Euler–Lagrange are derived, leading complete and definitive set equations, which system ordinary differential spatial directrix. Jump conditions apply at points where tangent and/or curvature may be discontinuous also derived. As simple but illustrative example, deformation rectangular strip subject various studied.