Dynamic simulation of frictional multi-zone contacts of thin beams

In the framework of multibody system dynamics, a computational approach is proposed in this study to simulate the frictional contact dynamics of thin beams with multiple contact zones and subject to both large motions and large deformations. The initially straight and gradient deficient beam elements of the absolute nodal coordinate formulation (ANCF) degenerated from a curved beam element of ANCF are used to mesh the contacting thin beams. A detection strategy for multi-zone contacts is proposed based on the previous work of authors. The mutual penetration of two thin beams is a multi-peak function of the local coordinates of the beam predicted to have a larger contact zone. By checking all the local minima of the function, the contact zones of two thin beams can be efficiently located. With help of the master-slave approach, the contact zones can be accurately determined. The normal contact force is computed by using the penalty method, while the tangential friction force is efficiently computed via the piecewise analytic expression of the LuGre friction model derived within a fine integration step. In addition, the generalized forms and Jacobians of the normal and tangential contact forces can be derived via the principle of virtual work. To compute the contact forces accurately, the Gauss integration is used to integrate the contact force formulations. The generalized-alpha method is used to solve the final dynamic equations for constrained flexible multibody systems of thin beams with multi-zone contacts. A numerical example is presented to validate the piecewise analytic expression of the LuGre friction model first, and then, the other three numerical examples are given to demonstrate the effectiveness of the proposed approach for multi-zone contacts of thin beams.