Patch coupling with the isogeometric dual mortar approach

Abstract

The use of a common set of basis functions for design and analysis is the main paradigm of isogeometric analysis. The characteristics of the commonly used non-uniform rational B-splines (NURBS) surfaces require methods to handle non-conforming meshes to attain an efficient computational framework. The isogeometric mortar method uses constrained approximation spaces to enforce a coupling of deformations at the interface between patches in a weak manner. This method neither requires additional degrees of freedom nor the choice of empirical parameters. The main drawback of the standard isogeometric mortar approach is the non-local support of the mortar basis functions along the interface. This yields a large number of nodes per element for elements adjacent to the interface. Thus, the computational costs increase significantly for mesh refinement. This issue is remedied by the use of dual basis functions for the mortar method, which is referred to as dual mortar method. In this contribution several choices for the dual basis functions for B-splines are proposed and compared. A special focus is set on the support of the dual basis functions and on the support of the resulting mortar basis functions. Numerical examples show the influence of the choice for the dual basis functions on the accuracy of the global stress distribution, on the fulfillment of the interface conditions and on numerical efficiency. The use of approximate dual basis functions is shown to be competitive to computations of conforming meshes in terms of accuracy and efficiency.

Separate control meshes for displacements and rotations for a shear locking free isogeometric Reissner‐Mindlin plate

“…In this way, the compatibility requirement for pure bending is fulfilled and shear locking is avoided. The method is tested for an isogeometric Reissner-Mindlin plate formulation, which is based on a degenerated shell formulation [2]. Basic examples are chosen and the results are compared to the unaltered isogeometric Reissner-Mindlin plate and the finite element Method using MITC elements.…”

“…The used plate element is derived from continuum theory and is only described by its midsurface. The thickness direction is defined by the director vector [2]. Since the considered examples are only linear elastic problems, the update of the director vector is given as d = D + b, where b T = β 1 β 2 0 .…”