A closed form solution for the impact analysis of elastic ellipsoidal thin shells

In this paper the impact of a hollow elastic ellipsoidal thin shell with an elastic flat half space is analyzed. Due to the nonlinearity and complexity of the impact equation, classical numerical solutions cannot be employed. A closed-form solution for this problem is accomplished, using Hertzian theory [6] and the Vella’s analysis [17] in conjunction with the Newtonian method and a linearization scheme. The closed-form solution facilitates a parametric study of this problem. In next step, the closed-form analytical solution is validated by other research studies and explicit finite element method. Good agreement between the closed-form solution and other numerical results is observed. Based on the closed-form solution the maximum total deformation of the shell, the maximum transmitted force and the time duration of the contact were determined. The variations of the total deflection and the transmitted force as a function of the shell thickness and the different geometry of the shell were also determined. Finally it is concluded that the closed form equations are trustworthy and appropriate to investigate the impact of elastic ellipsoidal shells.