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

Abstract

This 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. K E Y W O R D Sboundary representation, mortar methods, multi-patch coupling, nonconforming NURBS patches, nonlinear isogeometric analysis, solids

Isogeometric analysis of 3D solids in boundary representation for problems in nonlinear solid mechanics and structural dynamics

“…Also, an efficient discretization of the domain might necessitate local refinement with nonmatching B‐spline approximations in scaling direction. The presented approach is, in principle, flexible and can be used for nonconforming discretizations by adopting an appropriate coupling method 44,45 …”

“…The presented approach is, in principle, flexible and can be used for nonconforming discretizations by adopting an appropriate coupling method. 44,45…”

Scaled boundary isogeometric analysis with C1 coupling for Kirchhoff‐Love theory

“…bad approximation results, if we want strong global C r -smoothness with r ≥ 1; see [4]. Consequently, in literature one can find the concept of weak patch-coupling to define proper multipatch IGA spaces; see [5][6][7]. But in 2D, if one restricts oneself to a special class of parametrizations, the so-called analysis-suitable G 1 parametrizations, the strong C 1 coupling of patches is possible; cf.…”

Smooth multi-patch scaled boundary isogeometric analysis for Kirchhoff–Love shells

“…As complex shell structures often consist of multi-patch geometries, C 1 continuity needs to be enforced at patch boundaries. Common approaches to ensure higher continuity on multiple patches are Nitsche methods [7,8], mortar methods [9,10], and penalty methods [11][12][13][14], among others [15,16]. However, all of these methods are coupling techniques in a weak sense that can only represent the isogeometric discretization space approximately C 1 smooth.…”