Governing equations of a stiffened laminated inhomogeneous conical shell

This study presents the dynamic equations of a stiffened composite laminated conical thin shell under the influence of initial stresses. The governing equations of a truncated conical shell are based on the Donnell-Mushtari theory of thin shells including the transverse shear deformation and rotary inertia. The extension-bending coupling is considered in the derivation. The composite laminated conical shell is also reinforced at uniform intervals by elastic rings and/or stringers. The stiffening elements are relatively closely spaced, and therefore the stiffeners are smeared out along the conical shell. The inhomogeneity of material properties because of temperature, moisture, or manufacturing processes is taken into account in the constitutive equations. A generalized variational theorem is derived so as to describe the complete set of the fundamental equations of the conical shell. Next, the uniqueness is examined in solutions of the dynamic equations of the conical shell, and the boundary and initial conditions are shown to be sufficient for the uniqueness in solutions. The equations of the laminated composite conical shell are solved by the use of the finite difference method as an illustrative example. The accuracy of results is tested by certain earlier results, and a good agreement is found.