A new cable element using the absolute coordinate formulation

In this paper, based on the previous studies on the finite elements of gradient deficient absolute nodal coordinate formulation (ANCF), a new spatial transverse isotropic cable element is proposed to numerically study under the frame of multibody dynamics. Cable element is popular nowadays because the numerically stiff behavior resulting from shear terms in existing ANCF beam elements that employ the continuum mechanics approach to formulate the elastic forces and the resulting locking phenomenon make these elements less attractive for cable structures. Also in practical engineering, cable has a high tension strength and a low bending resistance, which means ignoring the bending strain is acceptable and feasible. And assuming that cable material is transverse isotropic can greatly improve the computational efficiency. Based on above asumption, a new gradient transverse isotropic cable element of ANCF is proposed. The elastic force of the finite elements and their Jacobian J can be further derived Once the formulation of the element strain energy is deduced based on ANCF. Both generalized-alpha method and scaling technique are utilized to develop calculating program aimed to solve dynamics equations precisely and efficiently. Finally, numerical example of capturing mechanism is given to demonstrate the applicability and effectiveness of the proposed element of ANCF for flexible multibody system dynamics.