Bending and Buckling in Elastic Patterned Sheets

In this bachelor thesis we study models for the elastic deformations of patterned quasi 2D sheets. The main ingredients for these models are elastic beams and we focus on four different models for elastic beams in this study. We start from the theory of elasticity and derive four beam models for both inextensible and extensible beams, by using the Euler Lagrangian equations. One of these models is the classic Euler-Bernoulli beam model, which is valid for elastic beams that are not compressible and have only small, weakly non-linear deflections. The other models are extensions of this model and are valid for strong nonlinear behaviour and/or compressible beams. With these models we analyze the compression and buckling of beams with various boundary conditions such as a pinned-pinned beam and a beam attached to two circular, freely rotary nodes. Finally we also present some simulations for both a single beam between two circular, freely rotary nodes and the elastic patterned sheets.

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Bending and Buckling in Elastic Patterned Sheets