College
Buchtel College of Arts and Sciences
Date of Last Revision
2023-05-04 20:21:13
Major
Applied Mathematics
Honors Course
3450:498
Number of Credits
2
Degree Name
Bachelor of Science
Date of Expected Graduation
Summer 2021
Abstract
The goal of this project is to formulate a model that can predict the buckling of a graphene layer between two rigid substrates. The model will predict the buckling of the graphene layer when it is parallel to the substrates and an edge load is applied to the ends of the layer. Our main focus is to use the model to predict buckling loads given different assumptions for interaction forces between the graphene layer and the substrates. For this project continuum modeling will be used to create a model for the graphene buckling problem. This modeling leads to a total continuum energy whose minimizers correspond to equilibrium solutions of the buckling problem. Two terms in this total energy describe the interaction between the graphene layer and the substrates. From this total energy, standard techniques from Calculus of Variations are applied to derive the governing equations. These equations are a system of four nonlinear ordinary differential equations with boundary conditions. Techniques from Differential Equations and Linear Algebra will be used to analyze this 2-point boundary problem and predict buckling loads for the model as a function of what is assumed about the interaction terms.
Research Sponsor
Dr. J. Pat Wilber
First Reader
Dr. Curtis B. Clemons
Second Reader
Dr. Andreas Aristotelous
Honors Faculty Advisor
Dr. Curtis B. Clemons
Recommended Citation
Beckwith, Bradley, "Buckling Loads of a Graphene Layer Interacting with Rigid Substrates" (2021). Williams Honors College, Honors Research Projects. 1464.
https://ideaexchange.uakron.edu/honors_research_projects/1464
Completed signature page
Included in
Numerical Analysis and Computation Commons, Ordinary Differential Equations and Applied Dynamics Commons, Other Applied Mathematics Commons