The effect of higher order continuity in the solution field by using NURBS basis function in isogeometric analysis (IGA) is investigated for an efficient mixed finite element formulation for elastostatic beams. It is based on the Hu-Washizu variational principle considering geometrical and material nonlinearities. Here we present a reduced degree of basis functions for the additional fields of the stress resultants and strains of the beam, which are allowed to be discontinuous across elements. This approach turns out to significantly improve the computational efficiency and the accuracy of the results. We consider a beam formulation with extensible directors, where cross-sectional strains are enriched to avoid Poisson locking by an enhanced assumed strain method. In numerical examples, we show the superior per degree-of-freedom accuracy of IGA over conventional finite element analysis, due to the higher order continuity in the displacement field. We further verify the efficient rotational coupling between beams, as well as the path-independence of the results.

翻译：本文研究了在等几何分析（IGA）中使用NURBS基函数时，高阶连续性解场对弹性静力梁的高效混合有限元公式的影响。该方法基于考虑几何和材料非线性的Hu-Washizu变分原理。我们为梁的应力合力和应变附加场提出了降阶的基函数，这些场允许在单元间不连续。这种方法显著提高了计算效率和结果精度。我们采用具有可伸长方向矢的梁公式，通过增强假定应变法丰富横截面应变以避免泊松锁定。在数值算例中，我们展示了由于位移场的高阶连续性，IGA在每自由度精度上优于传统有限元分析。我们进一步验证了梁单元间的高效旋转耦合以及结果的路径无关性。