A shear deformable, rotation-free isogeometric shell formulation

Abstract

A finite element formulation for a geometrically linear, shear deformable (Reissner–Mindlin type) shell theory is presented, which exclusively uses displacement degrees of freedom. The total displacement is subdivided into a part representing the membrane and bending deformation, enriched by two extra “shear displacements”, representing transverse shear deformation. This rotation-free approach is accomplished within the isogeometric concept, using C1-continuous, quadratic NURBS as shape functions. The particular displacement parametrization decouples transverse shear from bending and thus the formulation is free from transverse shear locking by construction, i.e. locking is avoided on the theory level, not by choice of a particular discretization. Compared to the hierarchic formulation proposed earlier within the group of the authors (Echter et al., 2013), the method presented herein avoids artificial oscillations of the transverse shear forces. Up to now, a similar, displacement based method to avoid membrane locking has not been found. Thus, in the present formulation the mixed method from Echter et al. (2013) is used to avoid membrane locking.