Transient Dynamic Analysis of Pretwisted Functionally Graded Conical Shells Subject to Low Velocity Impact: A Finite Element Approach

This paper investigates on the problem of functionally graded (FG) shallow conical shells subjected to low-velocity impact by a solid spherical mass at the centre. Turbomachinery blades with low aspect ratio could be idealized as twisted rotating cantilever FG shallow conical shells. An analytic solution method is developed to solve and predict the impact response in terms of contact force, impactor displacement, initial velocity of impactor, target displacement and indentation of the FG conical shells with different sigmoidal power law exponent. A modified Hertzian contact law considering permanent indentation is used to calculate the contact force along with other impact response parameters. Using the Newmark’s time integration scheme the time dependent equations are solved. An eight noded isoparametric shell element is considered for the present finite element model. Parametric studies are performed to study the effects of triggering parameters like initial velocity of impactor (VOI), mass of the impactor (M₀) and twist angle (Ψ) considering different sigmoidal power law exponent (N) for Ni (Nickel)-ZrO₂ (Zirconia) and Ti (Titanium alloy-Ti–6Al–4V)-ZrO₂ (Zirconia) functionally graded conical shell subjected to low velocity impact.