2020/12/22 by Daniel Schöllhammer, Schöllhammer, Daniel, Benjamin Marussig +3
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Computational Engineering #FOS: Computer and information sciences #Finance #Polynomial and algebraic computation #and Science (cs.CE)
paper · pdf · doi:10.48550/arxiv.2012.11975
openalex publication_date 2020/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Shell analysis is a well-established field, but achieving optimal higher-order convergence rates for such simulations is a difficult challenge. We present an isogeometric Kirchhoff-Love shell framework that treats every numerical aspect in a consistent higher-order accurate way. In particular, a single trimmed B-spline surface provides a sufficiently smooth geometry, and the non-symmetric Nitsche method enforces the boundary conditions. A higher-order accurate reparametrization of cut knot spans in the parameter space provides a robust, higher-order accurate quadrature for (multiple) trimming curves, and the extended B-spline concept controls the conditioning of the resulting system of equations. Besides these components ensuring all requirements for higher-order accuracy, the presented shell formulation is based on tangential differential calculus, and level-set functions define the trimming curves. Numerical experiments confirm that the approach yields higher-order convergence rates, given that the solution is sufficiently smooth.