Abstract
A two-node spatial beam element with the Euler-Bernoulli assumption is developed for the nonlinear dynamic analysis of slender beams undergoing arbitrary rigid motions and large deformations. During the analysis, the global displacement and rotation vectors with six degrees of freedom are selected as the nodal coordinates. In addition, the “shear locking” problem is avoided successfully since the beam cross-sections are always perpendicular to the current neutral axes by employing a special coupled interpolation of the centroid position and the cross-section orientation. Then a scheme is presented where the original transient strains representing the nodal forces are replaced by proposed average strains over a small time interval. Thus all the high frequencies can be filtered out and a corresponding equivalent internal damping will be produced in this new formulation, which can improve the computation performance of the proposed element for solving the stiff problem and evaluate the governing equations even by using the nonstiff ordinary differential equation solver. Finally, several numerical examples are carried out to verify the validation and efficiency of this proposed formulation by comparison with the analytical solutions and other research works.
Highlights
Lots of slender structures in engineering are composed by beams, such as framed structures, robot arms, large deployable space structures, and turbine propellers
The geometrically exact beam theory [4, 5, 11] allows formulating problems involving arbitrarily large displacements, rotations, and strains, which has provided the basis of many recent finite element formulations
The centroid position and the cross-section orientation are coupled interpolated by a special approach, which guarantees the perpendicularity between the crosssection and the deformed neutral axes
Summary
Lots of slender structures in engineering are composed by beams, such as framed structures, robot arms, large deployable space structures, and turbine propellers. Euler-Bernoulli hypothesis makes the construction of the interpolation function of the beam element more difficult, it provides an idea to interpolate the finite rotation field without direct discretization, which will benefit from shear-locking-free and objectivity of rotational strains. Based on this idea, a spatial Euler-Bernoulli element is developed in this paper for the rigid-flexible coupling dynamic analysis. A spatial Euler-Bernoulli element is developed in this paper for the rigid-flexible coupling dynamic analysis In this element, each node has six generalized nodal coordinates, including the global displacement vector and the rotation vector.
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