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Research Papers

The Impact of Arbitrary Oriented Ellipsoidal Shell With a Barrier: Analytical Study

[+] Author and Article Information
Shahab Mansoor-Baghaei

Department of Mechanical Engineering,
The City College of the City University of New York,
New York, NY 10031
e-mail: sbaghaei@ccny.cuny.edu

Ali M. Sadegh

Department of Mechanical Engineering,
The City College of the City University of New York,
New York, NY 10031
e-mail: sadegh@ccny.cuny.edu

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received December 10, 2014; final manuscript received February 7, 2015; published online February 26, 2015. Assoc. Editor: Weinong Chen.

J. Appl. Mech 82(4), 041005 (Apr 01, 2015) (8 pages) Paper No: JAM-14-1574; doi: 10.1115/1.4029780 History: Received December 10, 2014; Revised February 07, 2015; Online February 26, 2015

In this paper, a closed form solution of an arbitrary oriented hollow elastic ellipsoidal shell impacting with an elastic flat barrier is presented. It is assumed that the shell is thin under the low speed impact. Due to the arbitrary orientation of the shell, while the pre-impact having a linear speed, the postimpact involves rotational and translational speed. Analytical solution for this problem is based on Hertzian theory (Johnson, W., 1972, Impact Strength of Materials, University of Manchester Institute of Science and Technology, Edward Arnold Publication, London) and the Vella’s analysis (Vella et al., 2012, “Indentation of Ellipsoidal and Cylindrical Elastic Shells,” Phys. Rev. Lett., 109, p. 144302) in conjunction with Newtonian method. Due to the nonlinearity and complexity of the impact equation, classical numerical solutions cannot be employed. Therefore, a linearization method is proposed and a closed form solution for this problem is accomplished. The closed form solution facilitates a parametric study of this type of problems. The closed form solution was validated by an explicit finite element method (FEM). Good agreement between the closed form solution and the FE results is observed. Based on the analytical method the maximum total deformation of the shell, the maximum transmitted force, the duration of the contact, and the rotation of the shell after the impact were determined. Finally, it was concluded that the closed form solutions were trustworthy and appropriate to investigate the impact of inclined elastic ellipsoidal shells with an elastic barrier.

FIGURES IN THIS ARTICLE
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Copyright © 2015 by ASME
Topics: Shells , Deformation
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Figures

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Fig. 1

Inclined ellipsoidal shell moving toward the stationary flat barrier

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Fig. 2

The ellipsoidal shell during contact

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Fig. 3

Total deflection of the shell during the impact for different initial velocities

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Fig. 4

Impact force of the ellipsoidal shell during the impact for different initial velocities

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Fig. 5

Angular velocity of the shell after the impact (rebound) with respect to time for different initial velocities

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Fig. 6

Rotations of the shell after the impact (rebound) for different initial velocities

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Fig. 7

FE model of the inclined impact problem

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Fig. 8

Total deflection of the shell for V0 = 1 m/s, β = 30

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Fig. 9

Velocity of the center of mass of the shell for V0 = 1 m/s, β = 30

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Fig. 10

Angular velocity of the shell during impact for V0 = 1 m/s, β = 30

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