Drew Mitchell

Publication Date


Document Type


First Advisor

Gau, Jenn-Terng

Degree Name

M.S. (Master of Science)

Legacy Department

Department of Mechanical Engineering


Mechanical engineering; Mechanics


This paper presents an exact analytical solution in tensor notation for solving the elastic wave propagation for any 3-dimensional shape objects with a hole (from infinitesimal to finite). For validating the proposed model, a case study of an axisymmetric thick walled cylindrical metallic tube with finite length under a dynamic impact, was modeled and computed. The case study was also computed and validated by using an explicit time integration finite element method, LS-Dyna, for comparison purpose. The LS-Dyna simulation results were used to calculate the boundary conditions for the proposed model for obtaining the analytical solution because in the real world applications these boundary conditions can be obtained through the measurement data or the signals of sensors. Based on the virtual boundary conditions obtained from simulation, the proposed model can compute the displacement field (transient response) of the object under the dynamic impact. Once the displacement field is available, all transient stress, strain, rotation etc. can be computed as needed. The obtained analytical displacement fields as a function of time and coordinates were compared with the simulation results from LS-Dyna. It has been proven in this paper that the efficiency, accuracy and robustness of the proposed model meet the needs of any potential applications.


Advisors: Jenn-Terng Gau.||Committee members: Brianno Coller; Iman Salehinia.||Includes illustrations.||Includes bibliographical references.


26 pages




Northern Illinois University

Rights Statement

In Copyright

Rights Statement 2

NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.

Media Type