A locking-free meshfree curved beam formulation with the stabilized conforming nodal integration

A locking-free meshfree curved beam formulation based on the stabilized conforming nodal integration is presented. Motivated by the pure bending solutions of thin curved beam, a meshfree approximation is constructed to represent pure bending mode without producing parasitic shear and membrane deformations. Furthermore, to obtain the exact pure bending solution (bending exactness condition), the integration constraints corresponding to the Galerkin weak form are derived. A nodal integration with curvature smoothing stabilization that satisfies the integration constraints is proposed under the Galerkin weak form for shear deformable curved beam. Numerical examples demonstrate that the resulting meshfree formulation can exactly reproduce pure bending mode with arbitrary dicretizations, and the method is stable and free of shear and membrane locking. Computational efficiency and accuracy are achieved simultaneously in the proposed formulation.