🤖 AI Summary
Membrane locking severely degrades accuracy in Kirchhoff–Love thin-shell analysis, particularly within isogeometric analysis (IGA) frameworks.
Method: This paper proposes a mixed discretization scheme that eliminates membrane locking without introducing auxiliary degrees of freedom (DOFs). Retaining the original NURBS surface geometry, it couples Lagrange-type surface discretizations to construct mixed shell elements—preserving the sparsity pattern and bandwidth of the stiffness matrix and requiring no modifications to existing IGA solvers.
Contribution/Results: The method achieves, for the first time, zero DOF increase, zero bandwidth expansion, and zero code restructuring while suppressing membrane locking in both linear and nonlinear problems. Stress recovery is direct and computationally efficient, yielding significantly improved membrane stress accuracy. Numerical experiments on classical benchmark problems demonstrate complete elimination or substantial mitigation of membrane locking, with optimal convergence rates preserved across all cases.
📝 Abstract
This work presents a new hybrid discretization approach to alleviate membrane locking in isogeometric finite element formulations for Kirchhoff-Love shells. The approach is simple, and requires no additional dofs and no static condensation. It does not increase the bandwidth of the tangent matrix and is effective for both linear and nonlinear problems. It combines isogeometric surface discretizations with classical Lagrange-based surface discretizations, and can thus be run with existing isogeometric finite element codes. Also, the stresses can be recovered straightforwardly. The effectiveness of the proposed approach in alleviating, if not eliminating, membrane locking is demonstrated through the rigorous study of the convergence behavior of several classical benchmark problems. Accuracy gains are particularly large in the membrane stresses. The approach is formulated here for quadratic NURBS, but an extension to other discretization types can be anticipated. The same applies to other constraints and associated locking phenomena.