Elimination of self-straining in isogeometric formulations of curved Timoshenko beams in curvilinear coordinates

Isogeometric formulations of curved Timoshenko beams in curvilinear coordinates often result in self-straining of membrane and shear strains, due to the discretization of the local displacement field. Self-straining means a failure in exact representation of rigid body motions, which consequently deteriorates response quality. To overcome the difficulty of self-straining, we propose an invariant formulation that discretizes the global displacement field. It turns out that the approximated membrane, shear, and bending strain measures are invariant regardless of initial geometry in the proposed formulation. For effective applications to any arbitrarily curved structures and locking-free formulations to alleviate membrane and shear locking, the proposed invariant formulation is combined with selective reduced integration (SRI) and B̄ projection method. Numerical examples demonstrate the effectiveness and applicability of the proposed invariant formulation, which gives much more accurate results together with both SRI and B̄ projection method, in comparison to the existing isogeometric formulations.