Quadrature rules for isogeometric shell formulations: study using a real-world application about metal forming

This paper studies quadrature rules for simulating large deformations of shells using isogeometric analysis. Several recently proposed rules and their effects on a real-world application known as incremental sheet forming are investigated. It is observed that, when tackling real-world applications, unexpected problems arise and, therefore, theoretical studies only with manufactured solutions are not enough for a complete verification of a method. The chosen application reveals problems with certain quadratures and that some simple stabilization strategies cannot completely suppress hourglass modes. Additionally, the effects of quadrature rules on the total computational costs are demonstrated and the influence of the maximum stable time step is assessed using a highly demanding simulation