Type of Document Master's Thesis Author Kim, Kyusang Author's Email Address email@example.com URN etd-08302006-210744 Title The Atomic-scale Finite Element Method for Analyzing Mechanical Behavior of Carbon Nanotube and Quartz Degree Master of Science Department Civil Engineering Advisory Committee
Advisor Name Title Gutierrez, Marte S. Committee Chair Batra, Romesh C. Committee Member Dove, Joseph E. Committee Member Keywords
- finite element method
- computational mechanics
- mechanical behavior
- molecular dynamics
- atomic scale
- carbon nanotube
Date of Defense 2006-08-22 Availability unrestricted Abstract
The mechanical behavior of discrete atoms has been studied with molecular dynamics whose computational time is proportional to the square of the number of atoms, O(N2). Recently, a faster algorithm, Atomic-scale Finite Element Method (AFEM) with computational time proportional to the number of atoms, O(N), had been developed. The main idea of AFEM, compared with conventional finite element method is to replace nodes with atoms and elements with electric forces between atoms. When interpreting a non-linear system, it is necessary to use an iteration scheme.
A simulation of molecular dynamics based on the Verlet's method was conducted in order to validate AFEM in one dimension. The speed of AFEM was investigated in one and two dimensional atomic systems. The results showed that the computational time of AFEM is approximately proportional to the number of atoms, and the absolute computation time appears to be small. The frameworks of AFEM not only for multi-body potential but also pair potential are presented. Finally, AFEM was applied to analyze and interpret the mechanical behavior of a carbon nanotube and a quartz. The buckling behavior of carbon nanotube showed a good agreement with the results illustrated in the original literature.
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