Nonconforming isogeometric analysis for trimmed CAD geometries using finite-element tearing and interconnecting algorithm

Abstract

Inspired by the nonconforming finite-element method, and with the intention of resolving difficulties in constructing analysis-suitable geometry in isogeometric analysis, an isogeometric method based on multipoint constraints and a finite-element tearing and interconnecting algorithm, called nonconforming isogeometric analysis, is proposed. The major purpose of the algorithm is to enable the application of isogeometric analysis directly to trimmed CAD geometries. The basic idea is to build a constraint equation system about the control points belonging to different trimmed spline patches and the normal derivatives of the geometric functions at properly selected interface points, and then to enforce the control variables and the normal derivatives of the displacement functions to obey the constraint equation system using the isoparametric concept. A spline version of the finite-element tearing and interconnecting method is then employed to obtain numerical solutions. Examples provided in this paper demonstrate the accuracy and efficiency of the new method.