Modelling of structures made of filiform beams: Development of a curved finite element for wires

Abstract

This paper presents a finite element formulation of curved thin beams, useful for modelling structures made of filiform elements. The proposed element is intended to model structures formed by several wires, subjected to very large bending displacements so that their final shapes can be completely different from the original ones. The model is based on the description of the planar wire geometry through the integration of the radius of curvature, which is approximated by means of a cubic polynomial. The solution of an overdetermined system is necessary to compute the coefficients of the polynomial. This approach allows determining the stiffness matrix of the curved wire in closed form, through the application of Castigliano's Theorem. A technique for automatic remeshing during large deformations, based on the curvature change, is also discussed in the paper. To validate the model refined finite element analyses and an experimental test have been carried out. The solution is performed analytically, and it allows to identify the actual stiffness matrix of a curved wire, considering only the degrees of freedom at the ends.