High fidelity simulation of contact-rich multibody systems

Zusammenfassung

In 1983, Andersen proposed the RATTLE algorithm as an extension of the SHAKE algorithm. The RATTLE algorithm is a well-established method for simulating mechanical systems with perfect bilateral constraints. This paper further extends RATTLE for simulating nonsmooth mechanical systems with frictional unilateral constraints (i.e. frictional contact). With that, it satisfies the need for higher-order integration methods within the framework of nonsmooth contact dynamics in phases where the contact status does not change (i.e. no collisions/constant sliding states). In particular, the proposed method can simulate impact-free motions, such as persistent frictional contact, with second-order accurate positions and velocities and prohibits penetration by unilateral constraints on position level.

Zusammenfassung

This paper introduces a family of Lobatto IIIA-IIIB methods for simulating mechanical systems with frictional contact. These methods extend the existing schemes by addressing both bilateral and unilateral constraints, as well as set-valued Coulomb friction. The Lobatto IIIA-IIIB methods presented in this paper make a substantial contribution to the ongoing endeavor of developing event-capturing versions of high-order schemes. By stating a generalized version of the principle of virtual action for nonsmooth mechanical systems, the integrators are derived from an appropriate discretization of it. The discrete contact laws are found by discretizing the impenetrabilty condition as well as the Newton-type frictional impact laws in an event-capturing way. The presented discrete contact laws exhibit no contact penetration and satisfy the involved unilateral constraints both on position and on velocity level. This behavior is showcased using benchmark examples.

Zusammenfassung

In 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.

Zusammenfassung

In this article, the existing nonsmooth generalized-alpha method for the simulation of mechanical systems with frictionless contacts, modeled as unilateral constraints, is extended to systems with frictional contacts. On that account, we complement the unilateral constraints with set-valued Coulomb-type friction laws. Moreover, we devise a set of benchmark systems, which can be used to validate numerical schemes for mechanical systems with frictional contacts. Finally, this set of benchmarks is used to numerically assert the properties striven for during the derivation of the presented scheme. Specifically, we show that the presented scheme can reproduce the dynamics of the frictional contact adequately and no numerical penetration of the contacting bodies arises—a big issue for most popular time-stepping schemes such as the one of Moreau. Moreover, we demonstrate that the presented scheme performs well for multibody systems containing flexible parts and that it allows general parametrizations such as the use of unit quaternions for the rotation of rigid bodies.