Investigations on adapted interpolation orders for a mixed isogeometric plate formulation

Abstract

AbstractIn order to overcome locking effects that especially occur for lower order finite element formulations, different methods can be employed. This can be conducted using mixed formulations or adapted approximation orders, for instance. Hence, in order to tackle shear locking that is caused by non‐matching interpolation degrees in the shear strain equation, an irreducible and a mixed Reissner‐Mindlin plate formulation with accordingly adapted conforming discretizations are derived within the scope of this contribution. In addition, non‐uniform rational B‐splines (NURBS) are employed therefore, in order to benefit from the properties and refinement strategies offered by isogeometric analysis (IGA) and to achieve more accurate results. The effect of various combinations of interpolation orders on the convergence behavior and the ability to alleviate locking is investigated for both the irreducible and the mixed isogeometric plate formulation and examined for a benchmark example. This is also supplemented by investigations on the stability of the considered variants, tested by the existence of the correct number of zero‐energy modes.