A Simple Absolute Nodal Coordinate Formulation for Thin Beams With Large Deformations and Large Rotations

Abstract

A simple but effective formulation of beams with large deformation and large rotation is derived from the principles of continuum mechanics. Proper assumptions are imposed, and the beam strain tensors are formulated from the Green strain tensors. The mass matrix is constant, and the elastic forces and the stiffness matrix entries are polynomials of the generalized coordinates, so numerical quadratures are not required in each time step of simulation, which makes the current approach much more superior in numerical efficiency than other formulations. The shape of the cross sections can be arbitrary, either uniform or nonuniform, and the beam can be either straight or curved. The generalized free of traction assumption ensures the strains in the cross section and the beam strains are independent, which resolves the Possion's locking issue and renders this approach can be accurately applied to general composite material beams. The elastic line approach (ELA) in the absolute nodal coordinate formulation (ANCF) can be derived from the current formulation.