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A formal procedure and invariants of a transition from conventional finite elements to the absolute nodal coordinate formulation. (English) Zbl 1272.70003

Summary: In this paper, finite elements based on the absolute nodal coordinate formulation (ANCF) are studied. The formulation has been developed by various authors for the dynamical simulation of large-displacement and large-rotation problems in flexible multibody dynamics. This study introduces a procedure to track the general geometrical properties of ANCF elements back to their prototypes in the conventional finite-element method (FEM), which deals with small-displacement problems. In this study, it is shown that each known ANCF element can be derived from a conventional FEM using a universal transform. Moreover, some important static and dynamic properties of the elements in small-displacement problems are automatically preserved. In the past, the authors of each newly proposed ANCF element have made unnecessary efforts to show the consistency of the above mentioned properties.

MSC:

70-08 Computational methods for problems pertaining to mechanics of particles and systems
70E55 Dynamics of multibody systems

Software:

BEAM189
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References:

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