Modeling and simulation of complex mechanical systems
How can the real world with all its complexity and dynamics on very different time and length scales fit in a computer program? Well, it can't. Something have to go. The question is what properties of the real world need to be captured in order to make a virtual replica realistic. And then there is the how.
The answers depends on the domain of interest. We focus on the dynamics of the macroscopic world and on realizing simulations that capture maximum complexity using minimal computational time. One class of applications are realtime visual interactive simulators for training, education, research & development, design & prototyping and computer games. Another application is off-line simulation of large-scale mechanical systems as a tool for understanding complex dynamics in industry processes and to find new approaches for optimization and control.
Image curtsey of Oryx Simulations.
Complex mechanical systems
By complexity we mean systems of many bodies; described by a multitude of different models, e.g., particles, rigid bodies, fluids and solids; interactions of complex nature, e.g., frictional and viscoplastic contacts; and with dynamics on several different time and length scales.
The art of discretization
For computational reasons the virtual system consists of a finitie number of elements with a finite number of properties. The level of granularity is directly linked to the information content in the simulation and how computational intense it becomes. The elements evolves in discrete time as well. In geometric discrete mechanics one starts with a discrete lagrangian and action principle. This way the fundamental symmetries of nature (like conservation of momentum and energy) can be built in to the discrete model and thus avoiding the risk of breaking these laws by numerical approximations. In study of complex dynamics this property is often more important than computing the indivdual trajectories to high accuracy.
Having discrete time means that the actual dynamics on time-scales shorter than that of the simulation time-step cannot be simulated directly. Instead, the effect must be modelled indirectly. One efficient way is to use kinematic constraints. This limits the degrees of freedomand forces the system to move on a hypersurface of the original phase-space. This can be used for modeling frictional contacts, mechanical joints as well as fluid incompressibility, shear resistance and the inextensibility of a cable. It is also possible to relax the constraints and give them a well-defined viscoelastic properties.
Each simulation time-step typycally involves solving a mixed linear complementarity problem (MLCP), i.e., a linear system of equations with complementarity conditions. The standard techniques are often dreadfully slow and sometimes very unstable. Fast and stable numerical solution techniques can, however, be tailored by recogninizing the inherent topology of the physical systems or even adapting the models to the best computational techniques. This become particulary important when searching to apply parallel computing technices and iterative solvers to strongly coupled dynamical systems.
The research in Umeå is focused on: ways to adaptively change the model resolution models while maximally perserving the physical invariants, information content and numerical robustness; hybrids of discrete rigid element models and meshless fluid models for simulation of granular matter flows; modeling of complex force networks and viscoelastic interactions with manybody constraints; impulse proagation in complex mechanical systems; adapting physical models for parallel computing - using multicore and GPGPU - and direct and iterative hybrid solver techniques. The research is located to UMIT Research Lab and run in collaboration with a number of research groups and industry partners, including Algoryx Simulation, Oryx Simulation, LKAB, Komatsu Forest and Volvo Construction Equipment.