Duality in nonlinear theory of shells

Abstract

The computational problem of shell structures in large displacements and large rotations has prompted numerous theories and approximations. The introduction of the finite rotation was successfully realized in 1972 by Fraeijs de Veubeke in three-dimension, and led to the creation of a dual nonlinear variational principle where the stresses as new unknowns were statically admissible. Following this line, its extension to shells, though not so easy, allows to provide statically admissible surface stresses. Now stability problems are directly governed by accurate stresses, and particularly in case of shells. After a recall of the dual variational principle for shells with large displacements, finite rotations and transverse shear deformations, a dual theory of stability is developed, namely the stability criterion and the post-buckling in the dual theory.