Kirchhoff–Love shell representation and analysis using triangle configuration B-splines

Abstract

This paper presents the application of triangle configuration B-splines (TCB-splines) for representing and analyzing the Kirchhoff–Love shell in the context of isogeometric analysis (IGA). TCB-splines offer flexibility in modeling complex geometries with C1 continuity, making them naturally fit into the Kirchhoff–Love shell formulation with complex geometries. We first propose a linear least-squares-based framework to reparametrize the mid-surface of a thin shell, which consists of multiple (trimmed) NURBS patches and is topologically equivalent to an open disk with a finite number of holes, into a single TCB-surface defined over a carefully computed parametric domain. We then utilize TCB-splines for geometric representation and solution approximation in shell analysis. We verify the accuracy and robustness of our method by applying it to linear and nonlinear benchmark shell problems. The applicability of the proposed approach to shell analysis is further exemplified by performing geometrically nonlinear Kirchhoff–Love shell simulations of a pipe junction and a front bumper represented by a single patch of TCB-splines.