Neue Publikation in Computer Methods in Applied Mechanics and Engineering

Locking is a common effect in finite element and isogeometric analysis. In the case of plates, transverse shear locking is most prominent, for shells several other types of locking exist. A common cure are mixed methods that introduce additional fields of unknowns into the variational formulation. These fields reduce constraints and thus alleviate locking significantly. As a drawback, the discretized additional fields increase computational costs considerably. These fields are often eliminated by static condensation, which requires the inverse of a part of the stiffness matrix. In Lagrange-based finite elements, this inverse is computed on the element-level, due to a discontinuous interpolation of additional fields. Since isogeometric analysis features higher continuity, static condensation must be performed on the patch-level, which requires a costly matrix inversion on the patch-level. In this contribution, the virtual shear parameters of a mixed isogeometric plate formulation are interpolated by enhanced approximate dual basis functions. This allows to conduct row-sum lumping of the relevant matrix part at a potentially minimized loss of accuracy, since this part becomes diagonally dominant. For a properly chosen integration space, this lumped matrix becomes the identity matrix. Thus, the proposed condensation procedure does not require an inversion anymore. The crucial and novel point is the proposed treatment of knot vectors with internal knots in the initial geometry representation. With the help of several single- and multi-patch examples, including different initial continuities, we show that the proposed procedure obtains optimal error convergence rates in all cases, while without these modifications, convergence rates are significantly deteriorated.

Link zur Publikation: https://doi.org/10.1016/j.cma.2026.119255