Dynamic computation of 2D segment-to-segment frictionless contact for a flexible multibody system subject to large deformation

A new formulation of segment-to-segment frictionless contact dynamics is proposed for the planar multibody systems subject to large deformations, based on the absolute nodal coordinate formulation, which is not only able to describe both large deformations and overall motions, but also to offer the C¹-continuous surface representation for contact problems. The mortar method is used to discretize the contact constraints, established in an integral form on the nonconforming contact surfaces. A rescale and reconstruction strategy is proposed to recover the gap function as following. The gap function is revised via a scale factor first, and then the slope of the gap function is reconstructed via weighted average method. To satisfy the frictionless contact condition, the magnitude of the normal contact force is discretized via the third-order Hermite interpolation, while the direction of the force is along the normal vector of the contact surface. The penalty method is used to enforce the contact constraints. The generalized forms and Jacobians of the contact forces are derived. The generalized-alpha method is adapted to solve the dynamic equations. Finally, four numerical examples are given to verify the accuracy, convergence, and robustness of the proposed algorithm.