We present a comprehensive study on the approximation power of NURBS and the significance of exact geometry in stability analyses of shells. Pre-buckling analyses are carried out to estimate the critical load levels and the initial buckling patterns. Various finite element solutions obtained with the commercial code ANSYS are compared with solutions from the isogeometric version of the finite element method, using our in-house code NumPro. In some problem setups, the isogeometric shell elements provide superior accuracy compared to standard (as opposed to isogeometric) shell finite elements, requiring only a fractional amount of degrees of freedom for the same level of accuracy. The present study systematically investigates the sources of this superior accuracy of the isogeometric approach. In particular, hypotheses are tested concerning the influence of exact geometry and smoothness of splines.

我们对 NURBS 的逼近能力和精确几何在壳稳定性分析中的重要性进行了全面研究。进行预屈曲分析以估计临界载荷水平和初始屈曲模式。使用我们的内部代码 NumPro，将使用商业代码 ANSYS 获得的各种有限元解决方案与有限元方法的等几何版本的解决方案进行比较。在某些问题设置中，等几何壳单元提供了比标准（与等几何相反）壳有限元更高的精度，相同精度水平只需要一小部分自由度。本研究系统地研究了等几何方法的这种卓越准确性的来源。尤其是，