Finite Element Transient Dynamic Analysis of Delaminated Composite Conical Shells Subject to Low Velocity Impact

Abstract

This paper investigates on the transient dynamic response of delaminated composite pretwisted shallow conical shells subjected to low velocity normal impact. Turbomachinery blades with low aspect ratio could be idealized as twisted rotating cantilever composite conical shells. To derive the dynamic equilibrium equation, Lagrange’s equation of motion is used for moderate rotational speeds neglecting the Coriolis effect. An eight noded isoparametric plate bending element is employed in the finite element formulation incorporating rotary inertia and effects of transverse shear deformation based on Mindlin’s theory. To satisfy the compatibility of deformation and equilibrium of resultant forces and moments at the delamination crack front a multipoint constraint algorithm is incorporated which leads to unsymmetric stiffness matrices. The modified Hertzian contact law which accounts for permanent indentation is utilized to compute the contact force, and the time dependent equations are solved by Newmark’s time integration algorithm. Parametric studies are conducted in respect of triggering parameters like location of delamination, angle of twist and velocity of impactor for the centrally impacted graphite-epoxy torsion stiff composite conical shells.