Goal-Adaptive Meshing of Isogeometric Kirchhoff-Love Shells

TL;DR

This paper introduces an adaptive meshing workflow for isogeometric Kirchhoff-Love shell analysis using THB-splines and the DWR method, enabling efficient and goal-oriented refinement for complex structural problems.

Contribution

It develops a novel adaptive meshing framework incorporating THB-splines, mesh admissibility, and DWR-based error estimation for improved shell analysis accuracy.

Findings

High accuracy of the DWR estimator demonstrated

Efficient degree of freedom allocation in benchmark problems

Effective goal-oriented mesh refinement for complex analyses

Abstract

Mesh adaptivity is a technique to provide detail in numerical solutions without the need to refine the mesh over the whole domain. Mesh adaptivity in isogeometric analysis can be driven by Truncated Hierarchical B-splines (THB-splines) which add degrees of freedom locally based on finer B-spline bases. Labeling of elements for refinement is typically done using residual-based error estimators. In this paper, an adaptive meshing workflow for isogeometric Kirchhoff-Love shell analysis is developed. This framework includes THB-splines, mesh admissibility for combined refinement and coarsening and the Dual-Weighted Residual (DWR) method for computing element-wise error contributions. The DWR can be used in several structural analysis problems, allowing the user to specify a goal quantity of interest which is used to mark elements and refine the mesh. This goal functional can involve, for example, displacements, stresses, eigenfrequencies etc. The proposed framework is evaluated through a set of different benchmark problems, including modal analysis, buckling analysis and non-linear snap-through and bifurcation problems, showing high accuracy of the DWR estimator and efficient allocation of degrees of freedom for advanced shell computations.