Variable-Order Finite Elements for Nonlinear, Intrinsic, Mixed Beam Equations

The paper presents variable-order finite elements for nonlinear, mixed, fully intrinsic equations for both non-rotating and rotating blades. 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. The results based on the Galerkin approximation (which is a special case of the present approach) are more accurate as compared to finite elements with the same number of variables. Furthermore, the accuracy of the finite elements increases with the order of the finite element. Cubic elements seem to be the optimal combination of accuracy and complexity.