Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
Full-Text Articles in Physical Sciences and Mathematics
Supercritical And Subcritical Pitchfork Bifurcations In A Buckling Problem For A Graphene Sheet Between Two Rigid Substrates, Jake Grdadolnik
Supercritical And Subcritical Pitchfork Bifurcations In A Buckling Problem For A Graphene Sheet Between Two Rigid Substrates, Jake Grdadolnik
Williams Honors College, Honors Research Projects
In this paper we study a model of the buckling of a sheet of graphene between two rigid substrates. We seek to understand the buckling of the sheet as the substrate separation is varied with a fixed load on each end of the sheet. We write down the expression for total energy of the system and from it derive a 2-point nonlinear boundary-value problem whose solutions are equilibrium configurations of the sheet. We cannot get an explicit solution. Instead, we perform a bifurcation analysis by using asymptotics to approximate solutions on the bifurcating branches near the bifurcation points. The bifurcating …