Simulating mechanical systems with frictional contact using a nonsmooth generalized‐alpha method

Abstract

AbstractIn this paper, we introduce a nonsmooth generalized‐alpha method for the simulation of mechanical systems with frictional contact. In many engineering applications, such systems are composed of rigid and flexible bodies, which are interconnected by joints and can come into contact with each other or their surroundings. Prominent examples are automotive, wind turbine, and robotic systems. It is known from structural mechanics applications, that generalized‐alpha schemes perform well for flexible multibody systems without contacts. This motivated the development of nonsmooth generalized‐alpha methods for the simulation of mechanical systems with frictional contacts [2, 3, 5]. Typically, the Gear‐Gupta‐Leimkuhler approach is used to stabilize the unilateral constraint, such that numerical penetration of the contact bodies can be avoided ‐ a big issue of the most popular time‐stepping schemes such as Moreau's scheme. The nonsmooth generalized‐alpha method presented in this paper is derived in [2] and in contrast to [3,5] accounts for set‐valued Coulomb‐type friction on both velocity and acceleration level. Finally, we validate the method using a guided flexible hopper as a benchmark mechanical system.