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

Abstract An extension of Reissner's mixed variational formula is presented based on Maupertuis’ principle for geometrically non-linear elastic composite laminated structures. Legendre's transformation is used to introduce in the variational statement the complementary energy density as a function of stresses only. A refined equivalent single-layer model of doubly curved shells is established using the resulting mixed variational formula. The present single-layer shell model accounts for the basic displacement assumptions of the first-order shear deformation theory, and stresses that are continuous through the shell thickness and consistent with the surface conditions. Therefore, the present first-order shell model does not require any of the shear correction factors used in other first-order theories, and it recovers the interlaminar stresses without losing its simplicity. The present model can be easily specialized to flat plates, cylindrical and spherical shells.

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