Abstract
In this paper, we consider the buckling of an Euler-Bernoulli graphene beam due to an axial compressive load. We formulate the problem as a non-linear (eigenvalue) two-point boundary value problem, prove some properties of the eigenpairs and introduce a suitable numerical shooting method scheme for approximating them. We present the perturbation and the numerical approximations of the first and second buckling loads and the corresponding shapes.
Highlights
It is well-known from materials science, physics, and chemistry perspective, that intense interest in graphene material is developing at an accelerating pace and has recently generated numerous publications and research
We considered the buckling of an Euler-Bernoulli beam made of graphene
We presented the numerical results for the first two eigenpairs and compared them
Summary
It is well-known from materials science, physics, and chemistry perspective, that intense interest in graphene material is developing at an accelerating pace and has recently generated numerous publications and research. Applications and the potential for graphene made structures are abundant. Numerous engineering nanoscale devices that use graphene as basic components, like nanoscale resonators, switches, and valves, are being developed by many industries. Understanding the response of individual graphene structure elements to applied loads is crucially important (see [1]-[9] and the reference there in for a comprehensive list of applications). The Euler buckling load of supported straight elastics beam subject to an end axial compressive load. How to cite this paper: Elgindi, M.B.M., et al (2014) On the Buckling of Euler Graphene Beams Subject to Axial Compressive Load.
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