Treatment of Reissner–Mindlin shells with kinks without the need for drilling rotation stabilization in an isogeometric framework

Abstract

This work presents a framework for the computation of complex geometries containing intersections of multiple patches with Reissner-Mindlin shell elements. The main objective is to provide an isogeometric finite element implementation which neither requires drilling rotation stabilization, nor user interaction to quantify the number of rotational degrees of freedom for every node. For this purpose, the following set of methods is presented. Control points with corresponding physical location are assigned to one common node for the finite element solution. A nodal basis system in every control point is defined, which ensures an exact interpolation of the director vector throughout the whole domain. A distinction criterion for the automatic quantification of rotational degrees of freedom for every node is presented. An isogeometric Reissner-Mindlin shell formulation is enhanced to handle geometries with kinks and allowing for arbitrary intersections of patches. The parametrization of adjacent patches along the interface has to be conforming. The shell formulation is derived from the continuum theory and uses a rotational update scheme for the current director vector. The nonlinear kinematic allows the computation of large deformations and large rotations. Two concepts for the description of rotations are presented. The first one uses an interpolation which is commonly used in standard Lagrange-based shell element formulations. The second scheme uses a more elaborate concept proposed by the authors in prior work, which increases the accuracy for arbitrary curved geometries. Numerical examples show the high accuracy and robustness of both concepts. The applicability of the proposed framework is demonstrated.

Isogeometric Kirchhoff–Love shell formulations for general hyperelastic materials

“…While the initial motivation of IGA was to better integrate design and analysis by this common geometry description, it has also been found in various studies that IGA has superior convergence properties compared to classical finite elements on a per degree-of-freedom basis [24][25][26]. Over the last years, IGA has attracted enormous interest in nearly all fields of computational mechanics and it also gave new life to the development of shell formulations, including rotation-free shells [27][28][29], ReissnerMindlin shells [30][31][32][33], blended shells [34], hierarchic shells [35], and solid shells [36][37][38][39][40]. The high continuity naturally inherent in the isogeometric basis functions allows for a straightforward implementation of C 1 thin shell models.…”

Phase-field description of brittle fracture in plates and shells

“…In the past ten years, IGA has gained enormous interest in nearly all fields of computational mechanics and, in particular, it has led to many new developments in shell analysis. The smoothness of the basis functions allows for efficient implementations of rotation-free KirchhoffLove shell models [27][28][29][30][31][32][33], but there are also several developments in the context of ReissnerMindlin shells [34][35][36][37] and solid-shells [38][39][40][41][42], as well as novel approaches such as blended shells [43], hierarchic shells [44], and rotation-free shear deformable shells [45]. Furthermore, IGA was applied successfully to phase-field modeling of fracture.…”

Developments of the mixed grid isogeometric Reissner–Mindlin shell: Serendipity basis and modified reduced quadrature

“…However, it will bear the same drawback as the KL shell element, that is the basis functions cannot be used. Dornisch et al (2013) developed an exactly calculated fiber vectors IGA ReissnereMindlin shell element and its multiple patches version (Dornisch and Klinkel, 2014), they are formulated with the geometrically exact formulation. As for the IGA plates, one can read the literatures (Thai et al, 2013;Nguyen-Xuan et al, 2014;Thai et al, 2014).…”