Date of Award

Spring 2-2016

Document Type

Thesis

Degree Name

Master of Science in Mechanical Engineering (MSME)

Department

Mathematics

First Advisor

Simon Jones

Second Advisor

Lorraine Olson

Third Advisor

Allen Holder

Abstract

Elastodynamics is an academic field that is involved in solving problems related to the field of wave propagation in continuous solid medium. Finite element methods have long been an accepted way of solving elastodynamics problems in the spatial dimension. Considerable thought has been given to ways of implementing finite element discretization in the temporal dimension as well. A particular method of finite element solving called space-time finite element formulation is explored in this thesis, which is a relatively recent technique for discretization in spatial and temporal dimensions. The present thesis explores the implementation of the Space-Time finite element formulation in solving classical elastodynamics examples, such as the mass-on-spring for a single degree of freedom and for an axially vibrating bar with multiple degrees of freedom. The space-time formulation is compared with existing finite difference techniques, such as the central difference method, for computational expenditure and accuracy. In the mass-on-spring case, the central difference method and linear time finite elements yield relatively similar results, whereas quadratic time finite elements are more accurate but take more time computationally. In the axially vibrating bar case, central difference is computationally more efficient than the Space- Time finite element method. The final section concludes our findings and critiques the numerical effectiveness of the space-time finite element formulation.

Comments

To my Parents for wholeheartedly supporting my decision to pursue higher education in the U.S. and for their omnipresent hand of guidance and encouragement And to Prof Jones, for his teaching and mentoring. If not for him I would not have attempted Finite Element for my thesis topic. I find immense inspiration in his ideals of “perseverance” and “guilt”.

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