On a highly robust spurious‐mode filtering method for uniformly reduced‐integrated shell elements

SUMMARY In structural elements that allow shear deformation, uniformly reduced integration is used to avoid shear and membrane locking. The spurious modes of an underintegrated stiffness matrix can be filtered using perturbation methods. Although finite elements with perturbed stiffness show very good results, the displacements still conceal a component of spurious modes, albeit with very small magnitude depending on the perturbation factor. To desensitize the numerical results completely from the perturbation factor, a projection of the applied force is proposed to complement the perturbation of the stiffness such that spurious modes are not excited, thus providing robustness to the filtering of spurious modes. The proposed methodology is general in nature, but is applied in this paper to a 9-node shell element with uniformly reduced integration as an illustration. The perturbation of the stiffness matrix and the projection of the force vector are performed at the element level, avoiding expensive local-global transformations. As a consequence of the force projection, the perturbation factor for the stiffness can be arbitrarily small, and the element yields accurate results for a wide range of shell thickness.