Finite elements using absolute nodal coordinates for large-deformation flexible multibody dynamics

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A family of structural finite elements using a modern absolute nodal coordinate formulation (ANCF) is discussed in the paper with many applications. This approach has been initiated in 1996 by A. Shabana. It introduces large displacements of 2D/3D finite elements relative to the global reference frame without using any local frame. The elements employ finite slopes as nodal variables and can be considered as generalizations of ordinary finite elements that use infinitesimal slopes. In contrast to other large deformation formulations, the equations of motion contain constant mass matrices and generalized gravity forces as well as zero centrifugal and Coriolis inertia forces. The only nonlinear term is a vector of elastic forces. This approach allows applying known abstractions of real elastic bodies: Euler–Bernoulli beams, Timoshenko beams and more general models as well as Kirchhoff and Mindlin plate theories. Shabana et al. proposed a sub-family of thick beam and plate finite elements with large deformations and employ the 3D theory of continuum mechanics. Despite the universality of such approach it has to use extra degrees of freedom when simulating thin beams and plates, which case is most important. In our research, we propose another sub-family of thin beams as well as rectangular and triangle plates. We use Kirchhoff plate theory with nonlinear strain–displacement relationships to obtain elastic forces. A number of static and dynamic simulation examples of problems with 2D/3D very elastic beams and plate underwent large displacements and/or deformations will be shown in the presentation.