https://hal.inria.fr/hal-00839737Chapelle, DominiqueDominiqueChapelleLCPC - Laboratoire Central des Ponts et ChaussÃ©esA locking-free approximation of curved rods by straight beam elementsHAL CCSD1997[MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA]Chapelle, Dominique2013-06-29 17:42:452022-09-30 04:10:192013-06-29 17:42:45enJournal articles10.1007/s0021100502881We consider an elastic model for a curved rod with arbitrary three-dimensional 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 equivalent 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 the numerical results confirm the estimates obtained by theory.