Theoretical and numerical investigation of the equilibrium shape of curved strips and tapered rods

Abstract

The bending of elastic strips and rods is a field of research that continues to offer new possibilities for exploration. This dissertation focuses on two distinct problems within this context. These are the search for the equilibrium shape of thin inextensible elastic strips, such as a Möbius strip made out of paper, and the optimal shape of tapered columns that are stable against buckling. A theoretical approach based on the principle of virtual work is used to investigate both problems. This produces novel governing non-linear differential equations that describe both equilibrium and form.In order to discover the equilibrium shapes, numerical algorithms are developed that are based on Dynamic Relaxation. There are two ways in which they are used, one as an explicit form-finding tool, and the other as a way of solving differential equations.Results are provided that extend current theoretical models. The numerical schemes produce three-dimensional shapes for strips, going beyond the canonical Möbius strip, and solution shapes for tapered columns made from non-linear elastic materials.With the aid of analytical and numerical tools, finding the form of the Möbius strip and the tallest possible column are interesting challenges in the search for new shapes that are driven by physical and material rules. These have applicability in structural engineering, architecture, nano-technology and even artisticendeavour.

Date of Award	24 Aug 2016
Original language	English
Awarding Institution	University of Bath
Supervisor	Christopher Williams (Supervisor), Richard Harris (Supervisor) & Paul Shepherd (Supervisor)