A frictionless contact formulation for planar multibody systems

A novel contact formulation for 2D flexible bodies is presented here, utilizing the penalty method. The algorithm focuses on the intersection area between the master and slave perimeters. After performing a geometric collision test, the contact force module is evaluated as a linear function of this overlapping region. The direction of the contact force is determined by computing a weighted average of the outward normal unit vectors at the boundary nodes of the contact region, where the weights account for both tributary areas and nodal indentation distances. This formulation can be applied to both rigid and flexible bodies. In the latter case, the global contact force is decomposed into the nodal forces following specific assumptions. The methodology is first compared with the Hertzian theory benchmark of two contacting cylinders. Subsequently, the method is benchmarked against the well-established segment-to-segment (STS) penalty formulation using a pin bouncing inside a journal bearing as a case study. Finally, three numerical simulations, including a standard patch test, a Geneva mechanism, and an ordinary gearbox, are studied to demonstrate the efficiency of the proposed method.