Co-simulation techniques enable the coupling of physically diverse subsystems in an efficient and modular way. Communication between subsystems takes place at discrete-time instants and is limited to a given set of coupling variables, while the internals of each subsystem remain undisclosed and are generally not accessible to the rest of the simulation environment. In noniterative co-simulation schemes, commonly used in real-time applications, this may lead to the instability of the numerical integration. The stability of the integration in these cases can be enhanced using interface models, i.e., reduced representations of one or more subsystems that provide physically meaningful input values to the other subsystems between communication points. This work describes such an interface model that can be used to represent nonsmooth mechanical systems subjected to unilateral contact and friction. The dynamics of the system is initially formulated as a mixed linear complementarity problem (MLCP), from which the effective mass and force terms of the interface model are derived. These terms account for contact detachment and stick–slip transitions, and can also include constraint regularization in case of redundancy in the system. The performance of the proposed model is shown in several challenging examples of noniterative multirate co-simulation schemes of a mechanical system with hydraulic components, which feature faster dynamics than the multibody subsystem. Using an interface model improves simulation stability and allows for larger integration step-sizes, thus resulting in a more efficient simulation.
Simulation of large-scale multibody systems with unilateral contacts requires formulations with which good computational performance can be achieved. The availability of many solver algorithms for Linear Complementarity Problems (LCP) makes the LCP-based formulations a good candidate for this. However, considering friction in contacts asks for new friction models compatible with this kind of formulations. Here, a new, regularized friction model is presented to approximate the Coulomb model, which allows to formulate the multibody system dynamics as a LCP with bounds. Moreover, a bristle approach is used to approximate the stiction force, so that it improves the numerical behaviour of the system and makes it able to handle redundancy coming from the friction interfaces. Several examples using a 3D wheel model has been carried out, and the proposed friction model shows a better approximation of the Coulomb model compared to other LCP-based formulations.
Substructuring permits parallelization of physics simulation on multi-core CPUs. We present a new substructuring approach for solving stiff multibody systems containing both bilateral and unilateral constraints. Our approach is based on non-overlapping domain decomposition with the Schur complement method, which we extend to systems involving contact formulated as a mixed bounds linear complementarity problem. At each time step, we alternate between solving the subsystem and interface constraint impulses, which leads to the identification of the active constraints. By using the active constraints to compute the effective mass of subsystems within the interface solve, we obtain an exact solution. We demonstrate that our simulations have preferable behavior compared to standard iterative solvers and substructuring techniques based on the exchange of forces at interface bodies. We observe considerable speedups for structured simulations where a user-defined partitioning can be applied, and moderate speedups for unstructured simulations, such as piles of bodies. In the latter case, we propose an automatic partitioning strategy based on the degree of bodies in the constraint graph. Because our method makes use of direct solvers, we are able to achieve interactive and real-time frame rates for a number of challenging scenarios involving large mass ratios, redundant constraints, and ill-conditioned systems.
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