A finite-difference formulation of elastic rod for the design of actively bent structures

Abstract

A discrete formulation of elastic rod has been tailored for the particular design task of geometric modelling, form finding and analysis of actively bent structural systems. The rod element is fully described by using vector based quantities, hence making it easy to implement and be suitable for explicit resolution methods such as the Dynamic Relaxation (DR). From this point of view, the model under consideration aims to provide a natural enhancement, of existing DR schemes of elastic rods, primarily formulated for analysis/design of stressed spline structures with isotropic cross-section, whilst, the proposed formulation allows for the general case of initially straight rods with anisotropic cross-section and torsional stiffness effects, to be taken into consideration. In order to avoid numerical conditioning problems, the method adopts a reduced Degrees of Freedom approach, however, the design limitations usually involved with such an approach, are ‘removed’ by adopting the Bishop theory of framed curves, hence making it possible to reduce to only three (translations) the Degrees of Freedom to be explicitly computed by numerical integration of the corresponding acceleration terms.