Kirchhoff–Love shell formulation based on triangular isogeometric analysis

Abstract

This article presents application of rational triangular Bézier splines (rTBS) for developing Kirchhoff–Love shell elements in the context of isogeometric analysis. Kirchhoff–Love shell formulation requires high continuity between elements because of higher order PDEs in the description of the problem. Non-uniform rational B-spline (NURBS)-based IGA has been extensively used for developing Kirchhoff–Love shell elements, as NURBS-based IGA can provide high continuity between and within elements. However, NURBS-based IGA has some limitations; such as, analysis of a complex geometry might need multiple NURBS patches and imposing higher continuity constraints over interfaces of patches is a challenging issue. Addressing these limitations, isogeometric analysis based on rTBS can provide C1 continuity over the mesh including element interfaces, a necessary condition in finite elements formulation of Kirchhoff–Love shell theory. Based on this technology, we use Cr smooth rational triangular Bézier spline as the basis functions for representing both geometry and solution field. In addition to providing higher continuity for Kirchhoff–Love formulation, using rTBS elements we can achieve three significant challenging goals: optimal convergence rate, efficient local mesh refinement and analysis of geometric models of complex topology. The proposed method is applied on several examples; first, this technique is verified against multiple plate and shell benchmark problems; investigating the convergence rate on the benchmark problems demonstrates that the optimal convergence rate can be obtained by the proposed technique. We also apply our method on geometric models of complex topology or geometric models in which efficient local refinement is required. Moreover, a car hood is modeled with rTBS and structurally analyzed by using the proposed framework.