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In this article, a superelement formulation and a quadratic beam element based on the absolute nodal coordinate formulation are applied to the simulation of high-speed rotating structures. To this end, these formulations are briefly reviewed by highlighting their distinctive features. The performance of the studied formulations is examined using two numerical examples. The first test is a spinning beam example in which the transient response is examined. An unbalanced rotating shaft is studied in the second example, in which both transient and modal analyses are performed. The results produced using both formulations are compared against those produced in the commercial finite element software ANSYS and those available in literature. The article tests in a rotating machine dynamics context two element types which have not been formulated primarily with rotating applications in mind. This is useful in investigating the versatility of these elements.

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This study introduces higher-order three-dimensional plate elements based on the absolute nodal coordinate formulation (ANCF) for large deformation multibody applications. The introduced elements employ four to eight nodes and the St. Venant-Kirchhoff material law. A newly proposed eight-node element is carefully verified using various numerical experiments intended to discover possible locking phenomena. In the introduced plate elements, the usage of polynomial approximations of second order in all three directions is found to be advantageous in terms of numerical performance. A comparison of the proposed eight-node element to the introduced four-node higher-order plate elements reveals that the usage of in-plane slopes as nodal degrees of freedom has a negative effect on numerical convergence properties in thin-plate use-cases.

This paper introduces a new planar gradient deficient beam element based on the absolute nodal coordinate formulation. In the proposed formulation, the centerline position is interpolated using cubic polynomials while shear deformation is taken into account via independently interpolated linear terms. The orientation of the cross section, which is defined by the axial slope of the element's centerline position combined with the independent shear terms, is coupled with the displacement field. A structural mechanics based formulation is used to describe the strain energy via generalized strains derived using a local element coordinate frame. The accuracy and the convergence properties of the proposed formulation are verified using numerical tests in both static and dynamics cases. The numerical results show good agreement with reference formulations in terms of accuracy and convergence.