A Fast Algorithm for Contact Dynamics of Multibody Systems Using the Box Friction Model

Abstract

One of the major challenges in dynamics of multibody systems is to handle redundant constraints appropriately. The box friction model is one of the existing approaches to formulate the contact and friction phenomenon as a mixed linear complementarity problem (MLCP). In this setting, the contact redundancy can be handled by relaxing the constraints, but such a technique might suffer from certain drawbacks, specially in the case of large number of redundant constraints. Most of the common pivoting algorithms used to solve the resulting mixed complementarity problem might not converge when the relaxation terms are chosen as small as they should be. To overcome the aforementioned shortcoming, we propose a novel approach which takes advantage of the sparse structure of the formulated MLCP. This novel approach reduces the sensitivity of the solution of the problem to the relaxation terms and decreases the number of required pivots to obtain the solution, leading to shorter computational times. Furthermore, as a result of the proposed approach, much smaller relaxation terms can be used while the solution algorithms converge.

Monolithic Friction and Contact Handling for Rigid Bodies and Fluids Using SPH

“…Nevertheless, LCPs became a popular model to formulate rigid contact problems [Bar89, Bar93a, Bar94, Bar95, Ste00, GZO10, AO11, BET14, AE21], and a number of methods to solve LCPs have been developed [Bar94, KSJP08, CA09, Ebe10, CM11, Erl13]. The box friction model [OTSG09, TBV12, GNKT16, PAK*19, ANEK21] can be used to reduce the number of variables by ignoring the coupling between friction directions. As a consequence, friction forces might violate the Coulomb constraint and there are no guarantees concerning the principle of maximum dissipation [Erl17].…”

Dynamic analysis and wear calculation of space deployable mechanism considering spherical joints with clearance and coating

“…[8][9][10][11] The dynamics researches of the space mechanism considering spherical joint with clearance mainly includes two aspects: (i) The contact problems, especially the dynamics problem of mechanisms considering joint with clearance, are often highly nonlinear and difficult to solve. In order to solve dynamics problem more quickly and effectively, researchers have proposed many optimized or simplified numerical calculation methods, [12][13][14] but these numerical dynamics calculation methods for the mechanism considering spherical joint with clearance will not be discussed in this paper. (ii) At present, most researches in this field focus on determining the contact collision process of the mechanism system considering spherical joint with clearance, and trying to modify and improve the contact force model.…”