Non-material finite element rod model for out-of-plane bending of an elastic strip with natural curvature

Abstract

A novel finite element formulation for elastic unshearable rods in three-dimensional space is presented. Looking forward to future implementations of axially moving belts, we use a mixed Eulerian-Lagrangian kinematic formulation, which has the advantage that the element nodes are fixed in one spatial coordinate and the material points are flowing through the mesh, hence it is possible to discretize the elements in the free spans coarser than the ones in contact with the pulleys. Here, we present the solution of hanging rods with a flat cross-section including a natural curvature, which causes an out-of-plane bending as well as torsion of the rod. For validation purposes we limit ourselves to equilibrium solutions (for which purely Lagrangian elements would be also applicable) with clamped boundary conditions. The results are compared with a shell model of the hanging strip. Preliminary results concerning the frictionless contact problem for a steel belt hanging on two pulleys are discussed.