Abstract
This paper, which deals with geometrically nonlinear analysis of multilayered shell structures, presents an evaluation of the approximations made when simplified models are introduced. To this purpose, a transverse shear deformable shell finite element formulation including finite rotations and large displacements is employed and von Karman, as well as moderate and small rotation theories, are obtained as particular cases. Classical shear deformation type-results have been improved in moderately thick shell analysis by using modified multilayered shear stiffnesses. These stiffnesses have been calculated through a variational technique which accounts for parabolic interlaminar continuous transverse shear stress fields and zig-zag form of the in-plane displacements along the shell thickness. Stability problems of several flat and cylindrical thin and thick geometries, different multilayered lay-outs (cross-ply, angle-ply symmetrically and unsymmetrically laminated, including sandwich) and loading conditions are considered in the numerical investigations. It has been concluded that geometrical nonlinear effects are problem dependent, furthermore such effects become more significant in thick shell analysis with respect to thin structures.
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