A study on the analysis of shell structures using adaptive t-spline finite element method

Abstract

In the present work, the adaptive T-spline-based finite element method is presented. T-splines have been proposed by Sederberg $\It{et al}$. A T-spline surface is a NURBS surface with T-junctions and is defined by a control grid called a T-mesh. The T-junctions enable T-spline surfaces to be refined locally whereas local refinement is inefficient for NURBS. With this property, even patches with unmatched boundaries can be combined seamlessly. T-spline-based analysis framework is presented. In this analysis framework, T-splines are employed both for description of geometries and for approximation of field variables. CAD geometric models are directly used for analysis, and thus additional modeling and discretization for CAE is not necessary. Geometric exactness is preserved in the whole analysis procedure. In addition, the interaction with CAD is quite efficient. Some numerical examples for 2-D problems and their analysis results are demonstrated for the verification of the method. T-spline finite element method is applied to the analysis of shell structures. Shell formulation based on NURBS or T-splines has fundamental limitations in that rotational DOFs, which are necessary in the shell formulation, cannot be directly given to control points. In the present work, shell formulation for T-spline finite element method, which is based on the Reissner-Mindlin shell theory, is proposed. The idea for assigning rotational DOFs to physical points of elements is proposed. In this formulation, normal vectors and their rotations are interpolated using T-spline shape functions. The analysis framework for shell structures is verified through some benchmarking problems. Although local refinement can be implemented efficiently using T-splines, where to refine is another task to be resolved. For the efficient computation, systematic refinement process is indispensable. In the current study, explicit $\It{a posteriori}$error estimation is applied for T-spline finite eleme...