Non-smooth Dynamics Research Of Multi-body Systems Based On The Linear Complementary Problem

Non-smooth problems exist widely in many engineering fields, e.g., aeronautics, astronautics, machinery and vehicles. The nonsmooth factors, such as collision, friction, etc, will cause the non-smooth or discontinuous dynamics responses and often bring difficults for numerical computations. The study on the non-smooth multibody dynamics has been a hot topic in the field of multibody system dynamics, and using the Linear Complementarity Problem(LCP) based algorithms to slove the non-smooth problems has attracted many researchers’ attention. In this thesis, based on the LCP, the non-smooth contact-impact dynamics of multibody systems are studied, the main research contents are as follows:1. The basic concepts, algorithms and two set-valued mappings related to the LCP are introduced. Various friction models are introduced, the constraint conditions are translated into linear complementary conditions, and the set-valued mappings in mechanics model are established.2. The governing equations of the non-smooth multibody system are drived based on the LCP, and the non-smooth generalized-alpha algorithm is used to slove the non-smooth dynamics governing equations.3. Several classic numerical examples are simulated to validate the non-smooth generalized-alpha algorithm. Comparative studies are performed to explore the effects of the friction models on the non-smooth dynamic reponses. The non-smooth dynamic characteristics of a rigid slider-crank system with translational clearance joint are also studied. The non-smooth Stribeck effect caused by the frictional forces is observed.4. Finally, the tire-soil non-smooth interaction dynamics is studied. The tire is modelled by using the plate elements of Absolute Nodal Coordinate Formulation(ANCF), the rigid rim is modelled by using the Absolute Nodal Coordinate Formulation Reference Nodes(ANCF-RN), and the soil is described by using the Discrete Element Method(DEM). The Vetlet method is used to solve the dynamics equations for the soil DEM particles.