Physical Bending Strains in Linear Shell Theory

Expressions for the physical bending strains of linear shell theory in non-orthogonal coordinates are presented which are new in form, are completely analogous to the tangential strains in their vectorial definitions as well as their form, and are in complete agreement with the components of the curvature change tensor expressed in terms of physical components. The expressions obtained were made possible, in part, by the introduction of the tangential curvatures and radii of torsion in their general form and by the re-definition of the vector of rotation. A new vector of rotation is defined and its components are related to the three independent components of the skew-symmetric rotation tensor. It is shown that the tangent rotations and the rotation around the surface normal, customarily used in shell theory, are related to the independent components of the rotation tensor through the same general forulas.