Fully intrinsic equations and boundary conditions involve only force, moment,
velocity, and angular velocity variables, but no displacement or rotation variables.
This paper presents variable-order finite elements for the geometrically exact,
nonlinear, fully intrinsic equations for both nonrotating and rotating beams. The
finite element technique allows for
hp-adaptivity. Results show that these finite
elements lead to very accurate solutions for the static equilibrium state as well as for
modes and frequencies for infinitesimal motions about that state. For the same
number of variables, the accuracy of the finite elements increases with the order of
the finite element. The results based on the Galerkin approximation (which is a
special case of the present approach) are the most accurate but require evaluation of
complex integrals. Cubic elements are shown to provide a near optimal combination
of accuracy and complexity.
