Thin-shell stress-strain state invariants

Abstract

Strain theory is considered for a three-dimensional body, which is represented as a one-parameter family of equidistant surfaces. The invariants have been determined for the finite strain tensor for an arbitrary surface by expanding the square of an area element. In an isotropic linearly elastic body that follows the Kirchhoff-Love hypotheses, all the invariants of the state of stress and strain are expressed in terms of those for the strain tensor for the surface equidistant from the basic one. The defining relationships are derived in the technical theory of shells for small strains and arbitrary displacements.