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）中采用NURBS基函数时，解场高阶连续性对弹性静力学梁高效混合有限元列式的影响。该列式基于考虑几何与材料非线性的胡-鹫津变分原理。我们针对梁的应力合力与应变附加场，提出了一种允许跨单元间断的降阶基函数方法。这一方法显著提升了计算效率与结果精度。我们采用带可伸缩方向矢量的梁列式，并通过增强假设应变法对横截面应变进行扩充以避免泊松锁定。数值算例表明，由于位移场的高阶连续性，IGA相较于传统有限元分析在每自由度精度上具有优越性。我们进一步验证了梁间高效转动耦合效果以及结果的路径无关性。