A general co-simulation framework for the generation of coupling condition schemes based on a novel weak formulation at the interface

Abstract

Abstract Co-simulation techniques are widely used to enable global simulation of a coupled mechanical system via composition of simulators. Within this work, the focus is initially placed on a new scheme for the numerical integration of each subsystem since the corresponding accuracy affects directly the correct solution of a decomposed model. Following that, the new co-simulation methods are introduced. Specifically, a novel coupling strategy for satisfying the coupling conditions in their integral (weak) form, in the time domain, is proposed. This formulation constitutes a general framework for the generation of coupling condition schemes with varying accuracy and stability properties, based on the choice of basis and order of polynomials for the involved quantities, thus creating a whole new perspective on the field of co-simulation. In addition, the point-collocation method, which is mainly employed in the literature, is easily recognized as a degenerate case of this general weak formulation. The essential ideas of the new techniques are initially introduced by utilizing a simple linear model of two masses, constrained with a fixed joint. Subsequently, nonlinear models of a single and a double planar pendulum are investigated for the new numerical integration and co-simulation techniques, respectively. The models examined are relatively simple, but the developed methods have general validity and can be applied for coupling arbitrary multibody or structural solvers.