Lagrange multipliers at the boundary in the inextensional bending theory of thin elastic shells

Abstract

The theory of inextensional deformations of shells is extended by introducing Lagrange multipliers at the boundary to supplement those operating in the interior. These are associated with a constraint on the metric on the closure of the shell midsurface. The additional multipliers allow for a richer set of external actions than those admitted by the conventional theory. In particular, they balance concentrated forces in the tangent plane of the surface applied at corners of the boundary.