Metodo Interior Point per la Dinamica Non-Smooth di Sistemi Multicorpo

Simulations of non-smooth dynamic of rigid and flexible body systems, such those involving contacts, require the solution of complementarity problems that can be effectively addressed only with specific solving techniques. A wide variety of issues can arise from this kind of problems, such as ill-posed/redundant matrices, odd mass ratios of bodies in contact, and the concurrent presence of flexible and rigid bodies. The development of this thesis is motivated by the need of an improved scheme that is able to deal with all the aforementioned issues at once. One of the most promising solution strategies for large scale complementarity problems, namely the Interior-Point method, is proposed and implemented in its most performing variant, the primal-dual path-following scheme, according to a custom Mehrotra predictor-corrector scheme. The sparsity of the system is leveraged in order to improve performance, and a whole set of tools, from matrix classes to linear solver interfaces, has been developed in C++ language. The algorithm has been implemented into an open-source dynamic simulation library. Thanks to the novel solver, both unilateral and bilateral constraints, involving flexible and rigid bodies can be fit into the same time-stepping scheme.