Finite element analysis of bending-stiff composite conical shells with multiple delamination

Abstract

This paper presents a finite element method to investigate the effects of multiple delaminations on the free-vibration characteristics of graphite-epoxy bending-stiff composite pretwisted shallow conical shells. (We call bending-stiff a laminate configuration having maximum stiffness for the spanwise first bending mode.) The generalized dynamic equilibrium equation is derived from Lagrange's equation of motion neglecting the Coriolis effect for moderate rotational speeds. An eight-noded isoparametric plate bending element is employed in the finite element formulation incorporating rotary inertia and the effects of transverse shear deformation based on Mindlin theory. A multipoint constraint algorithm is utilized to ensure the compatibility of deformation and equilibrium of resultant forces and moments at the delamination crack front. The standard eigenvalue problem is solved by applying the QR iteration algorithm. Finite element codes are developed to obtain numerical results concerning the effects of twist angle and rotational speed on the natural frequencies of multiple delaminated bending-stiff composite conical shells. The mode shapes are also depicted for a typical laminate configuration. The numerical results obtained for comparison of single and multiple delaminated bending-stiff composite laminates are the first known nondimensional natural frequencies under the combined effect of rotation and twist for the type of analyses carried out here.

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