The Atomic-scale Finite Element Method for Analyzing Mechanical Behavior of Carbon Nanotube and Quartz
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.
|dc.rights||I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to Virginia Tech or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report.||en_US|
|dc.subject||finite element method||en_US|
|dc.title||The Atomic-scale Finite Element Method for Analyzing Mechanical Behavior of Carbon Nanotube and Quartz||en_US|
|thesis.degree.name||Master of Science||en_US|
|thesis.degree.grantor||Virginia Polytechnic Institute and State University||en_US|
|dc.contributor.committeechair||Gutierrez, Marte S.||en_US|
|dc.contributor.committeemember||Dove, Joseph E.||en_US|
|dc.contributor.committeemember||Batra, Romesh C.||en_US|
Files in this item
This item appears in the following Collection(s)
Masters Theses