New Representations for the Curvature Tensor of a Surface with Application to Theories of Elastic Shells

Abstract Consider two points $P$ P and $Q$ Q on a surface. Modulo rotations about the normal vector to surface at , rotation can be defined that maps unit corresponding . With help of Weingarten’s formulae, new representations are established for components curvature tensor associated mean Gaussian curvatures in terms pair vectors with rotation. The formulae shown helpful demonstrating how different strain measures Kirchhoff-Love shell theory equivalent.