Time dependent response of impact induced functionally graded conical shell considering porosity

Time dependent low-velocity single and multiple impact response of functionally graded (FG) untwisted and pretwisted conical shells are analysed considering porosity factor. A modified Hertzian contact law which accounts for permanent indentation is considered for the low velocity impact problem. An eight-noded isoparametric shell element is used for the finite element formulation while Newmark's time integration algorithm is used to solve the time dependent equations. The effects of porosity considering even and uneven porosity factor, initial velocity of impactor (VOI), mass of the impactor and twist angle of FG conical shell on the transient impact response of the conical shell are examined and analyzed. The contact force and indentation increase with increase of VOI and mass of the impactor while the contact duration decreases for both the occasions. Twist angle has a significant effect on contact force but has marginal effect on contact duration. Contact force for perfect (porosity free) FG conical shells is higher than that of porous FG conical shells. Lower contact force is observed for higher porosity factor. Even porous FG conical shell predicts lower contact force and higher shell displacement than that of an uneven porous FG conical for a given porosity factor.