College

Buchtel College of Arts and Sciences

Date of Last Revision

2021-12-13 05:13:14

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

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