Removing membrane locking in quadratic NURBS-based discretizations of linear plane Kirchhoff rods: CAS elements

NURBS-based discretizations suffer from membrane locking when applied to primal formulations of curved thin-walled structures. We consider linear plane Kirchhoff rods as a model problem study how remove discretizations. In this work, we propose continuous-assumed-strain (CAS) elements, an assumed strain treatment that removes quadratic NURBS for ample range slenderness ratios. CAS elements take advantage the C1 inter-element continuity displacement vector given by interpolate using Lagrange polynomials while preserving C0 strain. are first element type able broad ratios combines following characteristics: (1) No additional degrees freedom added, (2) systems algebraic equations need be solved, and (3) The nonzero pattern stiffness matrix is preserved. Since only computations required proposed evaluate derivatives basis functions unit tangent at knots, scheme barely increases computational cost with respect locking-prone discretization formulation. benchmark problems show convergence independent ratio local Bbar ANS depends heavily on ratio. numerical examples also spurious oscillations in stress resultants caused large-amplitude resultants.