Multi-rigid-body dynamics problems with unilateral constraints, like frictionless and frictional contacts, are characterized by nonsmooth dynamics. The issue of nonsmoothness can be addressed with methods that apply a mathematical regularization, called continuous contact methods; alternatively, hard constraints with complementarity approaches can be proficiently used.
This work presents an attempt at integrating consistently modeled unilateral constraints in a general purpose multibody formulation and implementation originally designed to address intrinsically smooth problems. The focus is on the analysis of generally smooth problems, characterized by significant multidisciplinarity, with the need to selectively include nonsmooth events localized in time and in specific components of the model. A co-simulation approach between the smooth Differential-Algebraic Equations solver and the classic Moreau-Jean timestepping approach is devised as an alternative to entirely redesigning a monolithic nonsmooth solver, in order to provide elements subject to frictionless and frictional contact in the general-purpose, free multibody solver MBDyn. The implementation uses components from the INRIA’s Siconos library for the solution of Complementarity Problems. The proposed approach is applied to several problems of increasing complexity to empirically evaluate its properties and versatility.
The applicability of the family of second-order accurate, A/L stable multistep integration algorithms used by MBDyn to nonsmooth dynamics is also discussed and assessed.