Buckling of constrained hyper-elastic beams

Abstract: The deformation of elastic beams in confined spaces has a wide range of applications in, inter alia, health care and the petroleum industry. Historically, the literature has mainly focussed on one-dimensional beams models. This paper, however, follows a different approach, as we focus on two dimensional hyper-elastic beams confined by a set of parallel plates. Due to non-linearity of the governing equations, a finite element approach, implemented in FEniCS, is used to find numerical solutions to the model equations.