A new third-order shear deformation theory with non-linearities in shear for static and dynamic analysis of laminated doubly curved shells

A geometrically nonlinear theory is developed for shells of generic shape allowing for third-order shear deformation and rotary inertia by using five parameters: in-plane and transverse displacements and the two rotations of the normal; geometric imperfections are also taken into account. The novelty is that geometrically nonlinear strain-displacement relationships are derived retaining full nonlinear terms in all the five parameters. These relationships are presented in curvilinear coordinates, ready to be implemented in computer codes. Higher order terms in the transverse coordinate are retained in the derivation so that the theory is suitable also for thick laminated shells. The theory is applied to laminated composite circular cylindrical shells complete around the circumference and simply supported at both ends. Initially static finite deformation and buckling due to lateral pressure is studied. Finally, large-amplitude forced vibrations under radial harmonic excitation are investigated by using the new theory and results are compared to another third-order shear deformation theory that neglects nonlinear terms in rotations of the normal.