A general, geometrically linear theory of inelastic thin shells

Abstract

A general theory of inelastic shells is developed under the assumption of geometrical linearity. It is assumed that the total strain rate tensor can be decomposed additively into a purely elastic and an inelastic part. First a complete description of the kinematics of shells is given where transverse shear strains are considered. All kinematic quantities are referred to the shell midsurface base vectors. Then, a new variational principle containing only kinematic quantities as dependent variables is introduced. To avoid many of the consistency problems faced with in shell theories, the functional is given in a mixed tensor representation. The new functional is first projected on the shell space and then reduced to the shell midsurface. This reduced form is obtained in a matrix representation where the lines of principal curvature of the shell midsurface are used as coordinate lines and physical components are introduced. This matrix representation can serve as a basis for a finite element approximation.