A LOCKING-FREE APPROXIMATION OF CURVED RODS BY STRAIGHT BEAM ELEMENTS

We consider an elastic model for a curved rod with arbitrary three-dim ensional geometry, incorporating shear and membrane as well as bending and torsion effects. We define an approximation procedure based on a discretization by linear Timoshenko beam elements. Introducing an equi valent mixed problem, we establish optimal error estimates independent of the thickness, thereby proving that shear and membrane locking is avoided. The approximation scheme is tested on specific examples and t he numerical results confirm the estimates obtained by theory.