Large Displacement and Rotational Formulation for Laminated Cylindrical Shells Including Parabolic Transverse Shear

摘要

A two dimensional geometrically nonlinear shell theory applicable to arbitrary geometries that can be described by orthogonal curvilinear coordinates and encompassing large displacements and rotations for small strain situations has been developed. Additionally, the theory includes a parabolic transverse shear stress distribution through the thickness. Flat plate and cylindrical shell solutions do not shear lock based upon exact elemental integrations. Transverse shear deformation was found to be significant for linear thick pinched cylinders and clamped pressure vessels. Orthotropic pressure vessels where the longitudinal stiffness is greater than the circumferential experience much more transverse shear deformation than do those where the circumferential stiffness is greater than the longitudinal. Middle surface inextensibility is often assumed in the closed form solutions used for comparison with the present approach. The consequences of this assumption is examined for both linear and nonlinear problems. The present formulation is applied to axially compressed quasi-isotropic cylindrical panels.