An overview of the ANCF approach, justifications for its use, implementation issues, and future research directions

When a beam moves through a curved tube, there exists a large number of contacts between the beam and the inner wall of the tube. Usually, it is necessary to use fine Lagrangian meshes to discretize the beam for possible contact area in order to obtain sufficiently accurate results, even if the contact is only once for a very short time. Accordingly, the computation process is very time-consuming due to the large number of degrees of freedom (DOF) of the discretized system. To solve this problem, an Arbitrary Lagrangian–Eulerian (ALE) formulation of a Timoshenko beam based on geometrically exact beam theory, which considers the rotation around the axis of the beam, is presented in this paper. In this formulation, the mesh nodes of the beam are not associated with the material points, which provides the flexibility to mesh the beam freely. For this reason, the ALE mesh nodes can be arranged along the tube and constrained to move just within the corresponding tube cross section. The axial movement of the beam can be described by the material points flowing through the axially constrained mesh nodes. In so doing, only the beam in the high-curvature section of the tube needs to be finely meshed, resulting in a significant reduction of the DOF of the whole system. Several examples are presented and discussed to demonstrate the correctness and efficiency of the proposed method.

An Arbitrary Lagrangian–Eulerian formulation of a geometrically exact Timoshenko beam running through a tube

An efficient multibody dynamic model of arresting cable systems based on ALE formulation

\n Dynamic analysis of power transmission lines with ice-shedding is conducted in this work. The power transmission line is first simplified as a uniform slender round beam. While the beam can have large displacements, rotations, and deformations, its strains are assumed to be small. The bending stiffness of the transmission line is considered here, but its shear and torsion effects are neglected. An efficient absolute nodal coordinate beam formulation is developed based on the above assumptions, and the number of generalized coordinates of each element of the beam is reduced to the least. The mass matrix is constant and the generalized elastic force is evaluated by constant stiffness tensors and generalized coordinates; hence, the current formulation is very efficient. Dynamic responses of power transmission lines with ice-shedding are then calculated. A benchmark planar two-span line is first considered, and the results are validated by the commercial finite element software abaqus. By examining strain states of the transmission line, it is found that its bending stiffness cannot be neglected in this dynamic analysis. Dynamic analysis of a three-dimensional three-span line is then conducted, where towers are not in a straight line and elevation differences between adjacent towers are considered. Several cases with common ice detachment mechanisms are considered, and dynamic responses of the cable and reaction forces of insulators due to ice-shedding are analyzed.

Dynamic Analysis of Power Transmission Lines With Ice-Shedding Using an Efficient Absolute Nodal Coordinate Beam Formulation

Prediction models for dynamic response parameters of transmission lines after ice-shedding based on machine learning method

An Accurate and Robust Geometrically Exact Curved Beam Formulation for Multibody Dynamic Analysis

\n A novel approach is developed to approximate the full mass matrix in the rotational-coordinate-based beam formulation, which can improve the efficiency of calculating its inverse in dynamic analyses. While the rotational-coordinate-based beam formulation can reduce numbers of elements and generalized coordinates, its mass matrix is a full matrix, such that corresponding Jacobian matrix is also full, and it is time-consuming to calculate its inverse. To increase efficiency of calculating its inverse, the full mass matrix is approximated in this work. Two approximations are adopted: (1) a double integral is approximated by a single integral; and (2) a full matrix is approximated by a sum of several rank-one matrices. Through this way, the approximate mass matrix can be decomposed as a band-diagonal sparse matrix and multiplication of low-rank matrices, and its inverse can be efficiently calculated using Sherman–Woodbury formula. Through this way, the approximate mass matrix can be efficiently calculated. Several numerical examples are presented to demonstrate the performance of the current approach, and its accuracy and efficiency are analyzed.

On the Approximation of the Full Mass Matrix in the Rotational-Coordinate-Based Beam Formulation

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Papers

An Accurate and Robust Geometrically Exact Curved Beam Formulation for Multibody Dynamic Analysis

Dynamic Analysis of Power Transmission Lines With Ice-Shedding Using an Efficient Absolute Nodal Coordinate Beam Formulation

On the Approximation of the Full Mass Matrix in the Rotational-Coordinate-Based Beam Formulation