@misc{ChasapiDornischKlinkel, author = {Chasapi, Margarita and Dornisch, Wolfgang and Klinkel, Sven}, title = {Patch coupling in isogeometric analysis of solids inboundary representation using a mortar approach}, series = {International Journal for Numerical Methods in Engineering}, volume = {121}, journal = {International Journal for Numerical Methods in Engineering}, number = {14}, issn = {1097-0207}, doi = {10.1002/nme.6354}, pages = {3206 -- 3226}, abstract = {This contribution is concerned with a coupling approach for nonconforming NURBS patches in the framework of an isogeometric formulation for solids inboundary representation. The boundary representation modeling technique inCAD 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. Non-conforming 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 non-linear problems in two dimensions and compare the results with conforming discretizations.}, language = {en} } @misc{ChasapiDornischKlinkel, author = {Chasapi, Margarita and Dornisch, Wolfgang and Klinkel, Sven}, title = {Coupling of patches for isogeometric analysis of solids in boundary representation}, series = {VII International Conference on Isogeometric Analysis}, journal = {VII International Conference on Isogeometric Analysis}, publisher = {CIMNE}, address = {Barcelona}, pages = {1}, abstract = {In this contribution we present a coupling approach for non-conforming NURBS patches in the framework of an isogeometric formulation in boundary representation [1]. In order to fit the boundary representation modeling technique in CAD, we follow the idea of the scaled boundary finite element method [2] for the parameterization of the solid. Thus, two-dimensional solid surfaces are partitioned into sections in relation to a central point, the scaling center. Each section is parameterized with a circumferential parameter along the boundary and a radial scaling parameter in the interior of the domain. We employ NURBS basis functions for the approximation of the solution in both parametric directions. The approximation in scaling direction is flexible and allows for local refinement within the computational domain. For the coupling of non-conforming sections we employ a mortar approach as presented in [3]. We establish a master-slave relation for the interface control points between adjacent sections based on the equality of mutual deformations along the interface. The coupling is realized in a weak manner by constraining the basis functions, which means that the NURBS basis functions of the slave side are related to those of the master side so that the solution of both sections along the interface is equal in a weak sense. This approach is derived numerically and its application to nonlinear problems is straightforward. We study several numerical examples of linear and nonlinear problems in solid mechanics and compare the results with conforming computations.}, language = {en} }