A new director-based finite element formulation for geometrically exact beams is proposed by weak enforcement of the orthonormality constraints of the directors. In addition to an improved numerical performance, this formulation enables the development of two more beam theories by adding further constraints. Thus, the paper presents a complete intrinsic spatial nonlinear theory of three kinematically different beams which can undergo large displacements and which can have precurved reference configurations. Moreover, the hyperelastic constitutive laws allow for elastic finite strain material behavior of the beams. Furthermore, the numerical discretization using concepts of isogeometric analysis is highlighted in all clarity. Finally, all presented models are numerically validated using exclusive analytical solutions, existing finite element formulations, and a complex dynamical real-world example.

提出了一种新的基于导向器的几何精确梁有限元公式，这是通过对导向器的正交约束的弱执行而提出的。除了改进的数值性能外，该公式还通过添加更多约束来支持两个以上的梁理论的开发。因此，本文提出了三个运动学不同的梁的完整的固有空间非线性理论，该梁可以经历大的位移并且可以具有预先弯曲的参考构型。而且，超弹性本构定律允许梁的弹性有限应变材料性能。此外，使用等几何分析的概念进行的数字离散化在所有情况下都得到了突出显示。最后，所有展示的模型均使用独家分析解决方案进行了数值验证，