Theory of elastic shells in the reference state

Geometrically nonlinear static FE-simulation of multilayered magneto-electro-elastic composite structures

“…The present finite rotation (FRT) shell element, assumes small strains and fully nonlinear finite rotation strain-displacement relations of Habip [30] is based on the Reissner-Mindlin first-order transverse shear deformation (FOSD) theory and the implementation of the finite element formulation of Wagner and Gruttmann [28]. The local a α and the orthonormal material t i coordinate systems of a four node shell element are shown in …”

Refined geometrically nonlinear theories of anisotropic laminated shells

“…Preliminaries concerning the derivation of the field equations. A modified version of the Hellinger-Reissner variational principle (see [24,25]) (referred to as the Hu-Washizu variational theorem) will be used in order to derive the basic field equation of the geometrically nonlinear theory of laminated shells. In its terms, the stationary condition applied to the functional jv,)…”

“…By invoking the arbitrary character of the variations SVt, SetJ, 8s'J (throughout 0r and on 0fiK and 0S25), the coefficients in the five integrands appearing in &Ji (i -1,5) must vanish independently, thus yielding the basic field equations of the nonlinear elasticity theory in terms of a reference state. The full nonlinear form of (8) and its linearized counterpart have been used in the substantiation of refined shell theories in [5,25] and [23], respectively. In the next developments, the geometrically nonlinear theory of anisotropic laminated shells will be substantiated by using the variational principle (8).…”

“…The basic field equations derived in Sections 6.1-6.5 may easily be specialized for this case. Some results pertaining to this theory are reported in [25,5,32,[40][41][42][43]. Moreover, a large diversity of high-order theories may result through various selection of ^in (14).…”

“…Employment in (11) of the partially nonlinear strain-displacement relationship 2<u -ru * vn + Vm <66> considered in conjunction with (65) and the further suppression in the ensuing developments of all nonlinear terms depending on Va, all these yield the field equations appropriate to a refined theory of multilayered shells of a von-Karman type. Several results belonging to such a theory (appropriate to single and multilayered shells and plates) are reported in [25,5,44,45] and [4,5,20,46], respectively.…”