This work addresses simultaneous use of geometrically exact shear-rigid rod and shell finite elements and describes both models within the same framework. Parameterization of the rotation field is performed by Rodrigues rotation vector, which makes the incremental updating of the rotational variables remarkably simple. For the rod element, cubic Hermitian interpolation for the displacements together with quadratic Lagrange interpolation for the incremental torsion angle were employed, while, for the triangular shell element, a complete quadratic Lagrange interpolation was used. The internal incremental torsion angle resulting from the displacement field within the shell element is then made compatible with the boundary incremental torsion angle of the shell element by an internal Lagrange multiplier. The compatibility between contiguous shell elements as well rod elements is mastered in the standard way by simply connecting nodes. This technique is an important contribution of the work, whose performance is illustrated by several numerical examples.

这项工作解决了同时使用几何精确的刚性刚度杆和壳有限元的问题，并在同一框架内描述了这两种模型。旋转场的参数化由Rodrigues旋转矢量执行，这使得旋转变量的增量更新非常简单。对于杆单元，采用位移的三次Hermitian插值，对于增量扭转角采用二次Lagrange插值，而对于三角形壳单元，则采用完整的二次Lagrange插值。然后通过内部拉格朗日乘数使由壳单元内的位移场产生的内部增量扭转角与壳单元的边界增量扭转角兼容。通过简单地连接节点，以标准方式掌握了连续壳单元和杆单元之间的兼容性。该技术是这项工作的重要贡献，其性能通过几个数值示例得以说明。