Patch coupling in isogeometric analysis of solids in boundary representation using a mortar approach

Abstract

SummaryThis contribution is concerned with a coupling approach for nonconforming NURBS patches in the framework of an isogeometric formulation for solids in boundary representation. The boundary representation modeling technique in CAD is the starting point of this approach. We parameterize the solid according to the scaled boundary finite element method and employ NURBS basis functions for the approximation of the solution. Therefore, solid surfaces consist of several sections, which can be regarded as patches and discretized independently. The main objective of this study is to derive an approach for the connection of independent sections in order to allow for local refinement and thus an accurate and efficient discretization of the computational domain. Nonconforming sections are coupled with a mortar approach within a master‐slave framework. The coupling of adjacent sections ensures the equality of mutual deformations along the interface in a weak sense and is enforced by constraining the NURBS basis functions on the interface. We apply this approach to nonlinear problems in two dimensions and compare the results with conforming discretizations.