Body Wise Time Integration of Multi Body Dynamic Systems

Abstract

Several papers have been published in the past on the issue of decomposing a nonlinear system into subsystems for more efficient time integration. In this paper each body of a multi body system is considered as one subsystem. The subsystems (the bodies) are interacting via connection forces. The sources of such connection forces are constraints or directly applied forces. This contribution is restricted to constraint forces only. During a step which is named “body iteration”, those forces are considered as constant and the state of the system is computed for each body separately. This can be massively parallelized which can be an efficiency advantage in case of computational costly problems like the ones occurring in parameter estimation. During an “constraint update step” the constraints are evaluated based on the body’s current state. If the error is not small enough the interface forces are updated and the inner loop is executed once again until the error of the constraints is negligible. It turns out, that the constraints can be updated separately as well, which can be used again for parallel computing. In the paper, the theory will be outlined and implemented using an N body pendulum. Finally, the advantages and disadvantages of this approach are critically discussed.