A review of the current state of the absolute nodal coordinate formulation (ANCF) is proposed for large-displacement and large-deformation problems in flexible multibody dynamics. The review covers most of the known implementations of different kinds of finite elements including thin and thick planar and spatial beams and plates, their geometrical description inherited from FEM, and formulations of the most important elements of equations of motion. Much attention is also paid to simulation examples that show reasonableness and accuracy of the formulations applied to real physical problems and that are compared with experiments having significant geometrical nonlinearity. Current and further development directions of the ANCF are also briefly outlined.

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