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dc.contributor.authorKim, Kyusangen_US

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.publisherVirginia Techen_US
dc.rightsI 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.subjectfinite element methoden_US
dc.subjectcomputational mechanicsen_US
dc.subjectmechanical behavioren_US
dc.subjectmolecular dynamicsen_US
dc.subjectatomic scaleen_US
dc.subjectcarbon nanotubeen_US
dc.titleThe Atomic-scale Finite Element Method for Analyzing Mechanical Behavior of Carbon Nanotube and Quartzen_US
dc.contributor.departmentCivil Engineeringen_US
dc.description.degreeMaster of Scienceen_US of Scienceen_US Polytechnic Institute and State Universityen_US Engineeringen_US
dc.contributor.committeechairGutierrez, Marte S.en_US
dc.contributor.committeememberDove, Joseph E.en_US
dc.contributor.committeememberBatra, Romesh C.en_US

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