A refined equivalent single-layer model of geometrically non-linear doublycurved layered shells using mixed variational approach

An extension of Reissner's mixed variational formula is presented based on Maupertuis' principle for geometrically non-linear elastic composite lamina ted structures. Legendre's transformation is used to introduce in the varia tional statement the complementary energy density as a function of stresses only. A refined equivalent single-layer model of doubly curved shells is e stablished using the resulting mixed variational formula. The present singl e-layer shell model accounts for the basic displacement assumptions of the first-order shear deformation theory, and stresses that are continuous thro ugh the shell thickness and consistent with the surface conditions. Therefo re, the present first-order shell model does not require any of the shear c orrection factors used in other first-order theories, and it recovers the i nterlaminar stresses without losing its simplicity. The present model can b e easily specialized to flat plates, cylindrical and spherical shells. (C) 2000 Elsevier Science Ltd. All rights reserved.