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AN OPTIMIZATION METHOD FOR FINDING THE BENDING STIFFNESS OF A GRAPHENE SHEET

Roberts, Mark William
http://rave.ohiolink.edu/etdc/view?acc_num=akron1176223963

Abstract Details

2007, Master of Science, University of Akron, Applied Mathematics.
Consider the case where one set of parallel edges of a graphene sheet is fixed a small distance from a fixed, flat graphene sheet. The sheet with the fixed edges can be modeled as a continuous, uniform beam. The bending of the beam is modeled by a non-homogeneous non-linear fourth-order differential equation. The external forces on the beam are derived by assuming a Lennard-Jones potential form for the molecular interaction between the two sheets. To find the bending stiffness of the beam, numerical solutions to the differential equation are compared to Molecular Dynamics (MD) simulations of the bending of the graphene sheet. An optimization procedure is used to find the value of the bending stiffness which results in the closest match between the numerical solutions and the MD simulations. The results of the optimization indicate that the bending stiffness of the graphene sheet is dependent on the length of the sheet and the distance between the two sheets.
Curtis Clemons (Advisor)
Mathematics
Graphene; Carbon Nanotubes; Optimization

Recommended Citations

Citations

  • Roberts, M. W. (2007). AN OPTIMIZATION METHOD FOR FINDING THE BENDING STIFFNESS OF A GRAPHENE SHEET [Master's thesis, University of Akron]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=akron1176223963

    APA Style (7th edition)

  • Roberts, Mark. AN OPTIMIZATION METHOD FOR FINDING THE BENDING STIFFNESS OF A GRAPHENE SHEET. 2007. University of Akron, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=akron1176223963.

    MLA Style (8th edition)

  • Roberts, Mark. "AN OPTIMIZATION METHOD FOR FINDING THE BENDING STIFFNESS OF A GRAPHENE SHEET." Master's thesis, University of Akron, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=akron1176223963

    Chicago Manual of Style (17th edition)

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© 2007, all rights reserved.
This open access ETD is published by University of Akron and OhioLINK.